mim wmm mmmmiimm Sg.J=J Ug i Ji(itii i U!ilti.it).UK t wi 3 .1 J j ) 'l J > J PREFACE. The product of the latest tlioiight in number teaching is fairly represented in the writings of Commissioner W. T. Harris, in the reports of the Committee of Ten and the Committee of Fifteen, and in McLellan and Dewey's "Psychology of Number." The attempt to make a book in which the theory of these educa- tors shall be wrought into a practical scheme of instruction may well call forth the greatest skill and most serious efforts of any author. To this task the writers of this book have set their hands, and the teaching public must say how well they have succeeded. The arrangement of the number work for the ORDER OF elementary grades should be determined by the DEVELOPMENT. Order of the child's mental development rather than by the logic of the subject itself. This requires a progressive arrangement of all material, thereby secur- ing a proper sequence of processes, and a careful grading of exer- cises. The young child is more susceptible to likenesses than to differences. His judgments and classifications are therefore hasty and inexact. Before he can make sharp distinctions, he must first have the means at hand to observe, and guidance in forming approximate judgments of length, width, and size of objects con- trasted and comj^ared. Froebel lays great stress upon this phase of early training. He says: "Every external object comes to man with the invitation to determine its nature and relationships, and everything comes to be known only as it is connected with the opposite of its kind. The first law of all phenomena is the law of opposites or contrast." The use of color in the lines and squares in the early part of this book is for assistance in this work of comparison and V ' lyi '\ '..:•::; PREFACE. ; c0iitta§t./ 'Pages.? to 11 provide for this early indefinite compari- ison, and also suggest other varieties of the same kind of work. The idea of number and of numerical opera- MATERiAL. tious should be acquired from the concrete. Dr. Harris in the introduction to the "Psychology of Number" says, "The first lessons in arithmetic should be based on the practice of measuring in its varied applications." The Committee of Ten says, "The fundamental operations of arith- metic should not only be j)erformed symbolically by numbers, but practically by joining lines together, dividing them, etc." This appeal to the concrete involves the use of certain materials, and any successful book based on this method of instruction must provide these in the book itself. This the Rational Arith- metic does in great variety: e. g., colored lines and squares; the various schemes for graphic illustration and for number com- binations, — such as the multiplication tables on pages 64, 107, etc.; the construction of figures for linear and square measure on pages 101, 120, etc.; the visual presentation of fractions on pages 178, 250, etc. By means of these the child is also trained to make use of other material which will aid him in grasping the principles involved. In this book the early presentation of number THE UNIT. is made by the use of the quantitative, and therefore definite, unit, as against the qualita- tive unit, or individual. That is, the use of lines, of inch, cent, pint, pound, is not like the use of toothpicks, a mere assembling of individual things, but a measuring of quantities; and number is essentially a development of quantity. For example, by joining lines together the child learns that four is equal to four ones, three and one or one and three, and two and two or two twos. Moreover, the child learns that one is one-fourth of four, and that two are one-half of four, thus learning his fractions along with his integers. The child learns these facts by joining lines together; that is, he not only learns the facts from the book, but he knows them as a result of actual experiment. At first all the lines or surfaces used should be actual measurements, so that the PREFACE. vii child will learn by observation to apply at sight the information which he first acquires. This measuring of lines bears the same relation to the kind of work usually given that the laboratory experiment bears to the lecture. The boy, not the teacher, joins the lines together for the same reason that the student performs his experiment in physics for himself. He is next led to apply his facts to other concrete problems, such as : If John has one marble and Henry has three, how many have both? which are not constructive, but which oblige him to use his judgment. Finally the number combinations thus learned and applied are fixed by a series of drills. An essential feature of these drill tables is that they make the subject less formidable to the child. For example, the tables on page 43 show that if the child adds three, say, to a series of numbers ending in six, all the sums will end in nine. As soon as the child masters the develop- ment of a number, he is taught to associate it with certain facts of his daily life; as, for example, in connection with the number eight, is given the table of dry measure, and with the number twelve, the foot, the months, and the mysteries of the clock face. In this way the child is sure to be interested, and his powers both of memory and of judgment are developed. Throughout the book much use is made of graphic illustrations and concrete problems, such as drawing to scale. The problems from beginning to end deal PROBLEMS. with realities, and aj^peal so far as possible to the child's environment or experience. This gives to the work an interest which cannot otherwise be secured, and cul- tivates the power of observation and the application of numbers to every-day objects and experiences. The order of treatment in every new subject, so far as possible, has been, first, to give the concrete form which will present the principle; second, to give the abstract principle or law which has been illustrated; and lastly, to make various applications of this principle in a series of problems that will fix the knowledge of number relations definitely in the child's mind. viii PREFACE. The authors desire to make special acknowledgment of their indebtedness to the many superintendents, principals, and teach- ers who have assisted in the perfection of the book by suggestions and corrections both in the manuscript and proofs. The Authors raTEODUCTION FOR TEACHEES Since most children will know many of the PREFATORY, number facts found in this book up to page 49, the teacher must adapt the uses of these pages to the needs of his pupils. If they have but little knowledge of the simplest combinations up to 12, then they should study the first part of the book very slowly and carefully until these number facts are thoroughly fixed in mind. If, on the other hand, they are familiar with most or all of the combinations of these 49 pages, they need only review them rapidly, laying stress upon the construction and the acquiring of facility in the number combinations, such as those on pages 15, 23, 35, 41, 43, etc. The work from pages 7 to 11 supplies ma- coMPARisoN. terial for a great variety of indefinite compari- sons, designating the objects by color. From these exercises will come the power to apply readily and intelli- gently the terms longer, shorter; larger, smaller; higher and loicer. Through the definite comparisons, beginning with page 12, the child learns to answer the questions Jioio tniichf hoio manyf and by means of these answers develops the idea of number and numerical operations. Interest, judgment, acts of construction, all join in giving the child knowledge of number and power to use it. Throughout the book are introduced various CONSTRUCTION, forms of constructive work such as the drawing of lines and rectangles in the earlier part of the book, and the construction problems on pages 101, 103, 105, 122, 128, 188, 196, etc. These not only add variety, but lead to increased power and facility, and will suggest to the teacher other forms of constructive work for the pupil. If pupils are not supplied with rulers, the teacher may show them how to ix X INTRODUCTION FOR TEACHERS. make their own. Take a strip of heavy paper or cardboard and cut it the length of the green line on page 18; then measure from one end of this ruler and mark on it the length of each line. This will give a six-inch ruler marked in inches. By means of the first figure on page 178, -^ and ^ inches may also be marked. The child's natural tendency to separate COUNTING. wholes into parts and to unite the parts into wholes again, is indicated by his effort in count- ing by ones. This natural tendency should be encouraged, as it is a means of gaining facility in number. The counting table on page 42 should be worked out according to the sugges- tions at the foot of the page. At various points through the book pupils should be trained to form similar counting tables by 2's, 3's, 4's, 5's, etc. This not only interests the child, but is a great aid in securing skill in number combinations. Great effort should be made to render purely FUNDAMENTAL automatic the fundamental combinations. The COMBINATIONS, first scrics of these will be found at the foot of page 43. Drills on the others are frequent and thorough, beginning with the material on page 108. The remainder of the 45 fundamental combinations are: 456567677889 987987989899 From page 68 to 87 the number knowledge DENOMINATE acquired is applied to the simplest form of de- NUMBEES. nominate numbers. This work leads the child to apply the numbers already learned to his every- day experience, by becoming familiar with a few simple facts of liquid and dry measures, weights, money and time. Children should be urged to construct simple problems which .will apply these facts of denominate numbers. Great care should be taken not to exceed FUNDAMENTAL the work planned in the fundamental opera- OPERATioNS. tions, pages 88 to 100. At this stage the child will get his first knowledge of the formal use of these operations, and only the simplest forms of these processes INTRODUCTION FOR TEACHERS. xi should be taught. In the second part, pages 164 to 177, another step is taken in the study of these operations and the same caution still applies. The final treatment is found on pages 230 to 235_ and there the child should be required to master these truly fundamental processes of the science of arithmetic. The plan of the book requires constant re- REViEWS. views of the work that has previously been done. While the character of the drills and problems is such that necessarily this preceding work must have been thor- oughly done, still the teacher should not fail to turn frequently to certain pages in the book and review them with special care. At various points suggestive reviews are indicated, as on pages 70, 130, 131, 146, 155, etc. Too much attention can hardly be given to the ORAL AVORK. Oral work throughout the entire book. Many of the drill tables provide abstract number work of this sort and the teacher should see that such work is done orally. On certain images, as on 130, 131, 160, 161, etc., a division of the page points out those which are distinctly oral problems. On many other pages there are problems which may be solved orally and the teacher should see that this is done, determining by the advancement of the j^^ipils, which should be oral and which written. In both oral and written work care should FORMS OF be taken that the statements of problems are STATEMENT, clcar and concise. The following examples will serve as illustrations: examples: (a) A man spends $2.40 for coffee, 80 cents for tea, $2.50 for flour, $1.75 for butter, and $1 for bacon. What is the amount of his purchase? Statement: The amount of his purchase is the sum of 82.40, 80c, $2.50, $1.75, and $1, which is $8.45. (&) What change should he receive from $10? Statement: He should receive the difference between $10 and $8.45, which is $1,55. (c) At $85 a head, what will 96 horses cost? Statement: 96 horses will cost 96 times $85, or $8,160. (cV) In an orchard of 156 trees there are 12 rows. How many trees in a row? xli INTRODUCTION FOR TEACHERS. Statement: There are as many trees as there are 12's in 156, or 13. (d-) Divide 96 marbles equally among 8 boys. Statement: Each boy will receive }^ of 96 marbles, or 12 marbles. Brief written statements should also be made from time to time, from the beginning of the 4th year, of problems in multiplication and division; e. g.: 1. $85=: cost of one horse. 96=rnumber to be bought. 2. 156=number of trees. 510 12= " rows. 765 156.-4-12=13, " in each row. $8160=cost of 96 horses. 3. 96=whole number of marbles. 8=number of boys to receive equal number. % of 96--- 12, number of marbles each boy receives. kSakah C. Brooks. CONTENTS. PAGE. Preface, ..-.-----v Introduction for Teachers, ------ ix PART FIRST. Indefinite Comparison: With Lines, - - - 7 With Surfaces, ..--.-' 9 With Solids, - - - 10 With General Objects, ------ 11 Definite Comparison with Lines: Linear Measure (Numbers from 4 to 12), - 12 Counting Table (jNotation and Numeration),.- - . - - 42 Fundamental Combinations, - - - - - - 43 DoHnite Comparison with Surfaces: Square Measure (Numbers from 1 to 24), -------- 44 Multiplication by 5. - - - - - - - 65 Drill Tables on Numbers from 2 to 60, - - - - 66 Definite Comparison with Solids: Cubic Measure, - - - 68 Liquid Measure, -...--. 74 Dry Measure, ...-----76 Weights, -.----.-- 78 United States Money, ....-.- 80 Time, - - - - 82 Fundamental Operations: Addition, 88 Subtraction, - - . . - . - 93 Multiplication, -------- 95 Division (Short), 97 PART SECOND. Linear Measure, .---.-.- 101 Multiplication by 6, - - - - - - - 106 xiii XIV CONTENTS. PAGE. Square Measure, -------- HI Multiplication by 7, - - - - - - - 116 Areas of Triangles, .--.-.- 120 Multiplication by 8, - - - - - - - 124 Cubic Measure, - - - - - - - - 128 Multiplication by 9, - - - - - - .134 Weights, - - - 140 Multiplication by 10, - - - - - - - 142 United States Money, - - - - - - - 146 Multiplication by 11, - - - ^ - - - 148 Multiplication by 12, 152 Time, --------- 156 Writing and Reading Numbers (Notation and Numeration), - - 162 Fundamental Operations: Addition, - _ 164 Subtraction, ------- 168 Multiplication, - - - - - - - - 172 Division (Short), ------- 176 Fractions (Common), ------- 178 PART THIRD. Linear Measure, -------- 185 Combinations of 123^^, - 190 Division (Long), -------- 197 Square Measure, .--._-- 200 Combinations of 13, - - - - - - - 204 Combinations of 14, - - - - - - - 207 Areas of Triangles, -------- 209 Cubic Measure, - - - - - - . - 214 Combinations of 15, - - - - - - - 218 Liquid Measure, 220 Combinations of 16, - - - - - - - 222 Dry Measure, -------- 224 Combinations of 16^, ------- 226 Notation and Numeration: Arabic and Roman, - . - 228 CONTENTS. XV Fundamental Operations: Addition, Subtraction, Multiplication, Division (Long), Combinations of 20, Weights, Time, United States Money, Paper Measure, - Fractions (Common), Denominate Numbers, - Bills, - Fractions (Decimal), Percentage, - PAGE. 230 - 231 232 - 234 237 - 238 240 - 244 245 . 250 254 • 258 262 . 264 J 1 5 » > 3 3 » , J > .> ' , J J 5 , ' -. ' > ' ■> ' PART FIRST. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10, 11. 12. 13. 14. 15. 16. 17. 18. The red line is longer than which line ? The orange line is shorter than which line ? The yellow line is shorter than which line? The green line is longer than which line ? The purple line is shorter than which line ? The blue line is longer than which line ? Which line is longer than the red line ? Which lines are shorter than the red line ? Which lines are longer than the orange line? Which lines are shorter than the orange line ? Which lines are longer than the yellow line? Which lines are longer than the green line ? Which lines are shorter than the green line ? Which lines are longer than the ]3urple line ? Which lines are shorter than the purple line? Which lines are shorter than the blue line ? Is any one of these lines longer than the blue line? Is any one shorter than the yellow line ? 7 ->^'' THE RATIONAL ARITHMETIC. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. ! ; i 15. 16. 17. 18. "Whicli line is longest? Whicli line is next longest? • Which line is shortest? What line is next shortest ? The red line is longer than which line? The red line is shorter than which lines ? The green line is longer than which lines ? The green line is shorter than which lines ? The blue line is longer than which lines ? The blue line is shorter than which lines ? The orange line is longer than which lines ? The orange line is shorter than which line ? Two lines are equal, which are they ? How many of these lines are longer than the yellow line? How many of these lines are longer than the red line ? How many of these lines are longer than the green line? How many of these lines are shorter than the orange line? How many of these lines are shorter than the purple line? PART FIRST. 9 / liijjjiiiijfi,, . ■^ tiy 1. WMcli two squares are tlie largest? 2. WMcli two squares are tlie smallest? 3. The blue square is larger than wliicli squares? 4. The orange square is smaller than which square ? 5. The orange square is larger than which squares? 6. The green square is larger than which squares? 7. The green square is smaller than which squares? 8. The purple square is smaller than which squares? 9. The yellow square is larger than which square? 10. The yellow square is smaller than which squares? 1 1 . The red square is larger than which squares ? 12. How many squares are larger than the red square? How many are smaller ? 18. How many squares are smaller than the green square ? How many are larger ? 14. How many squares are larger than the pur^^le square ? How many are smaller ? f^. How many squares are larger than the yellow square ? 10 THE RATIONAL ARITHMETIC. "^lue rectangle ? 5. How many rows of 5 square inches are there in the rectangle ? One row is what part of its area ? 0. How many square inches are there in its surface? 7. How many rows of 2 square inches are there in the surface ? 8. What part of its area is one row? Two rows? Three rows ? Four rows ? 9. What part of its area is 1 square inch? 2 square inches? 3 square inches? 4 square inches? 10. The area of the red rectangle equals what part of the area of the blue rectangle ? 11. How many two -inch squares can be made from the red rectangle ? From the blue rectangle ? 12. How many rectangles 3 inches long and 1 inch wide can be made from the red rectangle ? From the blue rectangle? 13. How many square inches are there in a two -inch square ? 14. What are the dimensions of a rectangle having the same area as a two -inch square? 15. What is the length of the perimeter of a one -inch square? Of a two -inch square? Of the red rect- angle ? 16. Draw rectangles containing 6 square inches. 48 THE RATIONAL ARITHMETIC. 1. How long and how wide is tlie orange rectangle ? 2. What is its area? 3. How many rows of 6 square inches are there in the rect- angle ? 4. One row is what j)art of the rectangle ? 5. How many rows of 2 square inches are there ? 6. What part of the area is one row? Two rows ? Three rows ? Four rows? Five rows ? 7. How many two -inch squares can be made from the rectangle ? 8. How many rectangles 3 inches long ahd 2 inches wide caii l)e made ? How nkany rectangles 3 inches long and 1 Inch wide ? 9. Draw other rectan- gles containing 12 square inches. PART FIRST. 49 1. In tlie preceding figures, find the one tliat shows two ones; the figure that shows two twos; two threes; two fours; two fives; tAVo sixes. 2. HoAV many 2^s in 2 ? How many 2's in 8 ? How many 2's in 4? How many 2's in 10? How many 2's in 6? How many 2's in 12? 3. One side of a square piece of glass is two inches long. How many square inches does it contain ? 4. How many square rods are there in a field that is three rods long and two rods wide ? 5. The top of a desk contains six square feet, and is three feet long. How ^vide is it ? 6. There are eight square feet in a window that is four feet high. How ^nde is it? 7. How many square yards of carpet are there in a piece one yard wide and four }'ards long ? In a piece two yards wide and four yards long ? 8. A sidewalk is two feet mde. How long will a part of it be that contains twelve square feet ? 9. How many square feet are there in one side of a board that is two feet long and one foot wide? How many square feet are there in both sides ? 10. A table is two feet wide and three times as long. What is its length ? How many square feet does it contain ? 11. A piece of land is three rods long and one rod wide. How many rods of fence will be required to inclose it? 12. A field is four rods long and two rods wide. What is the length of all of its sides? What is its area ? 50 THE RATIONAL ARITHMETIC. ) ^r ftfii- PART FIRST. 51 1. What do we call the yellow figure? What is its area ? 2. What part of its surface is one row? Two rows? 3. AVhat part of its surface is 1 square inch? 2 square inches? 4 square inches? 3 square inches? 4. How many two -inch squares can he cut from the yellow square ? How many can be made from it ? Draw a square and illustrate. 5. What are the dimensions of the green rectangle? 0. How many two-inch squares can be cut from it? How many can be made from it ? DraAV a square and illustrate. • ^ 7. How many three -inch squares can be made from it? 8. How many rectangles containing 2 square inches can be made from it? How many containing 3 square inches ? 4 square inches ? 6 square inches ? 9. Draw: A square containing 4 square inches. What are its dimensions? A rectangle containing 4 square inches. What are its dimensions? A square containing 9 square inches. What are its dimensions? A rectangle containing 9 square inches. What are its dimensions? A rectangle containing 8 square inches. What are its dimensions? A rectangle containing 10 square inches. What are its dimensions ? A rectangle containing 12 square inches. What are its dimensions? 6^ THE RATIONAL ARITHMETIC. 1. What are tlie dimensions of tlie blue rectangle? 2. What is its area? 3. What squares and rectangles can be cut or made from it ? PART FIRST. 53 1. What is the largest square tliat can be cut from tlie blue rectangle ? 2. How many rows of 3 square inches are there in the blue rectangle? 3. How many rows of 5 square inches are there? 4. What part of the area is 3 square inches? 6 square inches? 9 square inches? 12 square inches? 5. What part of the area is 5 square inches? 10 square inches? 6. What is the length of the perimeter of the blue rectangle ? 7. Draw another rectangle whose area is 15 square inches. 8. 6 and 6 are 9 and 3 are 8 and 4 are 10 and 2 are 7 and 5 are 9. 12 less 3 is 12 less 6 is 12 less 9 is 12 less 4 is 12 less 8 is 12 and 3 are fi anrl 9 are .5 anrl 10 are 8 and 7 are • 11 and 4 are 1.^ less .5 is . • 15 less 3 is 15 less 10 is • 15 less 9 is 15 less 12 is 10. What part of 12 is 3? AVhatpart of 12 is 4? What part of 12 is 9? What jiart of 12 is 6? What fjart of 12 is 8? 11. 3 is i of ? 3 is 1 of ? 3 is i of ? 3 is I of ? 4 is ^ of ? 4 is 4 of ? What part of 15 is 5 ? What part of 15 is 3? What part of 1 5 is 9 ? What part of 15 is 10? What part of 15 is 12 ? 5 is ^ of ? 5 is J of ? 6 is i of i 54 THE RATIONAL ARITHMETIC. PART FIRST. 55 1. Wliat are the dimensions of the red rectangle? 2. What is its area? 3. How many rows of 6 square inches are there in the rectangle ? 4. What part of the area is one row? What part is two rows ? 5. How many rows of 3 square inches are there in the rectangle ? 6. What part of the area is one row? What part is two rows ? Three rows ? Four rows ? Five rows ? 7. What part of the area is 1 square inch? What part is 2 square inches? 3 square inches? 9 square inches? 10 square inches? 8. How many two -inch squares can be cut from the rectangle ? How many can be made fi^om it ? 9. How many three -inch squares can be cut from the rectangle ? 10. How many rectangles 2 inches long and 1 inch wide can be made fi'om the i*ed rectangle ? 11. How long is the perimeter of the red rectangle ; 12. 9 and 9 are 18 - 9 = 6 and 12 are 18 - 6 = 3 and 15 are 18 — 3 = 10 and 8 are 18 - 12 = 13. In 18 there are how many 6's ? What part of 18 is 6 ? In 18 there are how many 3's ? What part of 18 is 3 ? In 18 there are how many 9's ? What part of 18 is 9 ? In 18 there are how many 2's ? What part of 18 is 2 ? 14. How many 3's in 3? How many 3's in 12? How many 3's in 6 ? How many 3's in 15 ? How many 3's in 9? How many 3's in 18? 56 THE RATIONAL ARITHMETIC. 1. What is the length of one side of the orange square? 2. How many rows of square inches are there in its surface ? 3. One row is what part of the surface? Two rows are what part? Three rows are what part? Four rows are what part ? 4. How many square inches are there in each row ? 5. How many square inches are there in the entire area ? 6. 1 square inch is what part of a row ? 2 square inches are what part? 3 scpiare inches are what part? PART FIRST. 57 1. 1 square inch is what part of the entire area? 2 square inches are what part? 3 square inches are what part? 4 square inches? 8 square inches? 12 square inches? 2. How many two -inch squares can be made from the orange square? How many three -inch squares? 3. How many rectangles 2 inches long and 1 inch vnde can be made from the orange square ? 4. How many rectangles 3 inches long and 1 inch wide can be made from it ? How many rectangles 3 inches long and 2 inches wide ? 5. How many 4 square inches in a four-inch square? How many 8 square inches ? How many 2 square inches? 3 square inches? 5 square inches? 7 square inches ? 6 square inches ? (\. Draw a four -inch square. 7. Take away one row of square inches. How many square inches are left ? 8. Take away two rows. How many square inches* are left ? Take away three rows. How many square inches are left? 9. Draw rectangles containing 16 square inches. 10. 4 and 12 are 16 - 8 = 8 and 8 are 16 — 4 = 6 and 10 are 16 — 6 — 14 and 2 are 16 - 2 = 11. What part of 16 is 4? 12 is f of ? What part of 16 is 8 ? 6 is f of ? What part of 16 is 12 ? 4 is i of ? What part of 16 is 2 ? 2 is i of ? What part of 16 is 6 ? 8 is 4 of ? 58 THE RATIONAL ARITHMETIC. *i 1. What are the dimensions of the yellow rectangle? 2. How many rows of 5 square inches are there in the rectangle? What j^art of the area is one row? Two rows ? PART FIRST. 50 1 . How many rows of 4 square inclies are there in the yellow rectangle ? What part of the area is one row ? Two rows ? Three rows ? 2. 1 square inch is what part of a four-inch row? Of a five -inch row? Of the entire area? 5 square inches are what part? 10 square inches? 8 square inches? 3. How many two -inch squares can be cut from the yellow rectangle? How many can be made from it? 4. How many three -inch squares can be made from the rectangle ? How many four-inch squares ? 5. If one row of 5 square inches were taken aw^ay from the yellow rectangle, how many square inches would be left? If two rows were taken away, how many square inches would be left ? 6. If one row of 4 square inches were taken away from the yellow rectangle, how many square inches would be left? If two rows were taken away, hoAY many. square inches would be left? 7. Draw other rectangles containing 20 square inches. 8. 5 and 15 are 20 — 15 = 10 and 10 are 20 - S = 4 and 16 are 20 - 10 = 8 and 12 are 20 - 4 = 9. What part of 20 is 5 ? 4 is | of ? What part of 20 is 15 ? 12 is I of ? What part of 20 is 4 ? 5 is J of ? What part of 20 is 8 ? 8 is f of ? What part of 20 is 10? 10 is i of ? What part of 20 is 16 ? 15 is | of ? 60 THE RATIONAL ARITHMETIC. PART FIRST. Gl 1. What are tlie dimensions of the green rectangle? 2. What is its area? 3. How many rows of 6 square inches are there in its surface ? What part of its area is one row ? Two rows? Three rows? 4. How many rows of 4 square inches are there in the rectangle? What part of its area is one row? Two rows? Three rows? 5. What part of the area of the rectangle is 1 square inch ? What part is 2 square inches ? 3 square inches? 4 square inches? 6 square inches? 6. How many two -inch squares can be cut from the green rectangle? How many three-inch squares? How many four-inch squares? 7. What rectangles can be cut or made from the green rectano^le ? 8. 12 and 12 are 18 and 6 are _ 14 and 10 are 16 and 8 are _ 9. What part of 24 is 3? What part of 24 is 4 ? What part of 24 is 2 ? What part of 24 is 12? What part of 24 is 8 ? What part of 24 is 6 ? 10. How many 4's in 4? How many 4's in 8 ? How many 4's in 12 ? 11. How many 5's in 5? How many 5's in 10? 24 - 16 - 24 - 12 24 - 10 - 24-6 i of 24 = 1 of 24 = 4 of 24 I of 24 i of 24 - tV of 24 = How many 4's in 16? How many 4's in 20? How many 4's in 24 ? How many 5's in 15? How many 5's in 20? 62 THE RATIONAL ARITHMETIC. Draw figures to illustrate areas of rectangles that are 2 inclies by 2 inclies. 1x4. 4x5. 4x6. 2x6. 3 inclies by 3 inclies. 5X2. 3.x 6. 2 X 10. 1 x 5. 4 inches by 2 inches. 4x4. 5x4. 1x6. 3x8. 3 inches by 4 inches. 5X3. 3x1. 4X3. 3x2. What are the areas of rectangles that are 3 inches by 7 inches? 5x8? 4 x 10? 3X9? 4X9? 5X9? 3 X 10? 5 X 10? 3 X 11? 4 X 11? 5 X 11? 4 inches by 7 inches ? 5 inches by 7 inches ? 3 inches by 8 inches ? 4 inches by 8 inches ? What is the width of a rectangle that contain? 4 square inches, and is 2 inches long ? 6 square inches, and is 3 inches long ? 9 square inches, and is 3 inches long ? 12 square inches, and is 4 inches long? 8 square inches, and is 4 inches long ? 24 square inches, and is 8 inches long ? X 12? X 12? X 12? X 5? 5X6? 3 4 5 5 s 10 square inches 18 square inches 12 square inches 24 square inches 16 square inches 18 square inches 14 square inches 24 square inches 15 square inches 20 square inches 25 square inches 30 square inches 20 square inches and is 5 inches lono-? and is 6 inches long? and is 6 inches long ? and is 6 inches long ? and is 8 inches long ? and is 9 inches long ? and is 7 inches long ? and is 12 inches long? and is 5 inches long? and is 4 inches long ? and is 5 inches long ? and is 6 inches long ? and is 10 inches long? PART FIRST. 63 1. Draw: A line 1 iiicli long. A line tmce as long as the first line. A line three times as long as the first line. A line twice as long as the second line. A square mth each of its sides the length of the first line. A square w^ith each of its sides the length of the second line. A square mth each of its sides the length of the third line. A square with each of its sides the length of the fourth line. 2. ITow many square inches are there in each square? 8. The area of the one -inch square equals what jiart of the area of the other s([uares? 4. The area of the two-inch square is how many times that of the one -inch square? It equals what jiart of the area of the three-inch S(]^uare? Of the four -inch square? T). The area of the three -inch square is how many times that of the one-inch square? Of the two- inch square? It equals what jDart of the area of the four -inch square? (k Tiie area of the four-inch square is how many times that of the otlier squares? 7. How many two -inch squares can he made from the three-inch square? From the four-inch square? Note — By means of square measure, the tables may be taught ; ^. e., liow many square inches in a rectangle 2 by 2 inches, 2 by 3 inches, 2 by 4 inches? etc, or, how long is a rectangle that contains 4 square inches, and is 2 inches wide? That contains square inches and is 2 inches wide? 64 THE RATIONAL ARITHMETIC. j A P! /-» — n A ' D L» U F p- /^ H L. r u n ) 1 1 \{ 1 D U l\ L. 1 1 1. Compare each figure with eacQi of the other figures. 2. A is 5. How many 5\s in B ? How manv in C ? In D? E? F? G? H? I? J? K? 'l? 3. A equals 5, B equals 10. To what is C equal? D? E? F? G? H? I? 3i K? L? PART illlST. 65 1. A equals what part of B? What part of C? Of D? E? F? G? H? I? J? K? L? 2. 5 is what part of 10? What part of 15? Of 20? 25? 80? 85? 40? 45? 50? 55? 60? :\. B equals how many A's ? What part of C ? Of D ? E? F? G? H? I? J? K? L? 4. 10 is how many 5V? What part of 15? Of 20? 25? 80? 85? 40? 45? 50? 55? 60? 5. G equals how many A's? How many B's? What partofD? OfE*^? F? G? H? I? J? K? L? 6. 15 is how many 5's? How many lO's? What part of 20? Of 25? 30? 85? 40? 45? 50? 55? 60? 7. D equals how manyA's? How many B's? How many C\s? What part of E? Of F? G? H? I? J? K? L? 8. 20 is how many 5's? How many 10\s? How many 15's? What part of 25 ? Of 80? 85? 40? 45? 50? 55? 60? 9. E equals how many A's? How many B's? How many C's? How many D's? What part of F? OfG? H? I? J? K? L? 10. 25 is how many 5 's? How many lO's? How many 15's? How many 20\s? What part of 80? Of 85? 40? 45? 50? 55? 60? 11. F equals how manyA's? How many B's? How many C's? How many D's? How many E's? What part of G? OfH? I? J? K? L? 12. 80 is how many. 5's? How many lO's? How many 15's ? How many 20's ? How many 25\s ? What part of 85? Of 40? 45? 50? 55? 60? 18. G equals how many A's ? How many B's? Etc. G6 THE RATIONAL ARITHMETIC. DRILL TABLES. 2x1- 2 - - 2 — 1 2 of 4 3 X 2 ■- 2x8- 24 - - 2 1 2 of 8 - 3 X 12 2X5- 4 - . 2 1 2 of 1 2 - 3 X 4 - 2X7=- 22 - r- 2 1 2 of 16 3 X 10 2X9 6 - - 2 1 2 of 20 = 3 X 6 - 2 X 11 - 20 - - 2 — 1 2 of 24 - 3 X 8 : 2X2- 8 - - 2 1 2 of 2 3 X 1 : 2X4 = 18 - - 2 — 1 2 of 6 = 3 X 11 2X6 10 - - 2 1 2 of 10 3 X 3 ■- 2X8- 16 - ^ 2 — 1 2 of 14 - 3 X 9 : 2 X 10 12 - - 2 i of 18 3 X 5 : 2 X 12 - 14 - - 2 1 2 of 22 = 3 X 7 : 3 - - 3 1 3 of 6 - 2. 3 of 6 - 4 X 1 : 9 -^ - 3 — 1 3 of 12 - 2 3 of 12 4 X 3 : 15 - - 3 1 3 of 18 - 2 3" of 18 = 4 X 5 ■- 21 - - 3 i of 24 of 24 -: X 7 27 - - 3 1 3 of 30 - 2 3 of 30 - 4 X 9 : 33 - - 3 — i of 36 - 1 of 36 4 X 11 6 - r 3 — 1 3 of 3 = 2 of 3 4 X 2 : 12 - - 3 — 1 3 of V) = 2 of 9 ■:: X 4 = 18 - r 3 — 1 3 of 15 - 2 3 of 15 4 X 6 = 24 - :- 3 1 "3^ of 21 - 3 of 21 - 4 X 8 - 30 - 'r- 3 1 of 27 = 2 3 of 27 = 4 X 10 36 - ^- 3 — 1 "3: of 33 - 2 "3 of 33 4 X 12 PART FIRST. 67 DRILL TABLES. 8 - - 4 16 " i- 4 24 - - 4 32 - - 4 40 - - 4 48 H - 4 4 H - 4 12 -. - 4 20 - - 4 28 -^ - 4 36 - - -: 44 - - 4 i of 4 1 of 4 = 5 XI- 1 of 12 i of 12 = 5 X 4 1 of 8 i of 8 - 5 X 2 i of 16 = i of 16 5 X 5 1 of 24 - i of 24 5 X 3 - 1 of 32 f of 32 - 5 X 6 = 1 of 20 f of 20 5 X 9 - 1 of 28 - i of 28 5 X 7 = i of 36 = i of 36 - 5 X 8 I of 48 1 of 48 = 5 X 12 = iof 40 f of 40 - 5 X 10 -- i of 44 = i of 44 - 5 X 11 = 10 - - 5 25 -^ - 5 40 - - 5 - - 5 20 - - 5 55 -■ 15 -• - 5 30 - - 5 45 - ^ 5 35 - '- 60 - h 5 50 - h 5 -i-ofS- |of5- 4 of 5 : 4 of 20 =-- f of 20 = 4 of 20 4 of 10 - 1- of 10 = 4 of 10 4 of 25 -1 of 25 = 4 of 25 i of 15 - I of 15 = 4 of 15 4 of 30 = 1 of 30 - 4 of 30 I of 60 1 of 60 - 4 of 60 4- of 35 1 of 35 4 of 35 Iof 55 f of 55 = 4 of 55 4 of 40 - 1 of 40 4 of 40 I of 50 - *j 1 of 50 4 of 50 1 of 45 - 1 of 45 - 4 of 45 08 THE RATIONAL ARITHMETIC. /^S nilT iJiiiipliiPiP- JBt ■ml iiiiiilHB---^ JSU MSB ii J j if' ■i !l liilillliillillililiiili^ PART FIRST. 69 1. Place two one-incli cubes in a row. 2. Place another row of two one- inch cubes in front of the first row. 3. How many rows of one-inch culjes are there? 4. How many one-inch cubes, or cul)ic inches, are there in a row ? How many are there in both rows ? 5. Place four more one -inch cubes on top of these cubes. 6. How many layers of cubes are there? 7. How many cubic inches are there in a layer? How many are there in both layers? 8. Find a two -inch cube. 9. Build a two-inch culx' with the one-inch cubes. 10. How many layers of one -inch cubes are there in the two -inch cube? 11. How many rows are there in each layer ? 1'2. How many one -inch cubes are there in each row? VS. How many one -inch cubes are there in both rows? 14. How many one-inch cubes are there in both layers? 15. Take away one layer of cubes. 16. How many one -inch cubes are taken? What part of the two -inch cube is taken? 17. Take away one row from the remaining layer. 18. What part of the layer is taken? What part of the two-inch cube is taken ? 19. Take away a one -inch cube from the remaining row. 20. What part of the row is taken ? What part of the layer is taken? What part of the two -inch cube ? 21. A one-inch cube is what part of a two-inch cube? Two one -inch cubes are what part? Three one- inch cubes are w^hat part? Four are what part? Five ? 70 THE RATIONAL ARITHMETIC. {Refer to figures on page 68 and use solids.) 1. In a two-inch cube there are how many one -inch cubes ? 2. In one -half of a two -inch cube there are how many one -inch cubes? 3. In one -half of one -half of a two -inch cube, how many one -inch cubes are there? What part of the two-inch cube are these one-inch cubes? 4. One-fourth is what part of one-half? 5. Point out one-fourth of the two-inch cube. 6. Point out three -fourths of the two -inch cube. 7. Point out on^ -third of three -fourths of the two -inch cube. 8. What part of the two -inch cube is one -third of three- fourths of it? What part is two-thirds of three- fourths of it ? 9. What part of one-half of the two-inch cube is a one- inch cube? What j)art is two one-inch cubes? Three one -inch cubes? 10. What part of the two-inch cube is one-fourth of one-half of it? Two-fourths of one-half? Three- fourths of one-half? 11. One -eighth is what part of one -fourth? 12. One-eighth is what j)art of one-half? 13. One-eighth is what part of three -fourths? 14. Two -eighths are what part of three -fourths? 15. One-half equals how many fourths? 16. One-half equals how many eighths? 17. One -fourth equals how many eighths? 18. Three-fourths equal how many eighths? 19. One-third of three-fourths equals how many eighths ? PART FIRST. 71 1. Build with cubes a solid that is equal to two rows of 3 cubic inches. 2. What are its dimensions? 3. Build a solid tliat is equal to t\\ o layers of two rows of 3 cubic inches. 4. What are its dimensions? 5. Build the following solids, tell their dimensions, and the number of cubic inches in each: One layer of two rows of 3 cubic inches. Two layers of two rows of 3 cubic inches. One layer of two rows of 4 cubic inches. Two layers of two rows of 4 cubic inches. One layer of three rows of 5 cubic inches. Two layers of two rows of 5 cubic inches. Two layers of one row of 8 cubic inches. Two layers of one row of 7 cubic inches. Four layers of one row of 4 cubic inches. Two layers of one roAv of 6 cubic inches. Two layers of three rows of 3 cubic inches. Four layers of one row of 5 cubic inches. Three layers of two rows of 4 cubic inches. Four layers of three rows of 2 cubic inches. One layer of three rows of 8 cubic inches. Two layers of one row of 9 cubic inches. One layer of two rows of 12 cubic inches. 0. Give the dimensions of solids containing: 8 cubic inches. 12 cubic inches. 6 cubic inches. 10 cubic inches. 9 cubic inches. 16 cubic inches. Note. — Have the pupils handle various solids and estimate their length, breadth, and height. After estimating, measure. 72 THE RATIONAL ARITHMETIC. CUT . ; CUT OUT ; 1 our CUT ; 1 CUT OUT . 1 OUT 1. To make a box that will hold 4 cubic inches, draAv a figure like the illustration. Cut out the corners, fold on dotted lines, and paste the square pieces cut from the corners, over the joinings. 2. Make a box that will hold 6 cubic inches. 15 cubic inches. S cubic inches. 16 cubic inches. 10 cubic inches. 18 cubic inches. 12 cubic inches. 20 cubic inches. 14 cubic inches. 24 cubic inches. PART FIRST. 73 1. A box is three inclies long, two inclies wide, and two inclies liigh. How many cubic inches will it hold ? 2. How wide is a box that contains eight cubic inches, and is two inches high and two inches long ? 3. How long is a box that contains sixteen cubic inches, and is two inches wide and two inches hi2:h ? 4. How high is a box that contains twelve cubic inches, and is two inches long and two inches wide ? 5. A brick six inches long and two inches wide contains twentv-four cubic inches. How thick is it? 6. A bin is four feet long, two feet wide, and four feet high. How many cubic feet does it contain ? 7. In a block of marble there are sixteen cu1:>ic feet. It is four feet long and two feet wide. How high is it? 8. A ])ook is six inches long, four inches wide, and one inch thick. Hoav manv cubic inches are there in it ? 9. How many cubic feet will a glass case hold that is fiYQ feet high, two feet wide, and two feet long? 10. How many cul)ic yards are there in a room that is three yards long, two yards ^vdde, and three yards high ? 11. A ditch is four feet mde and three feet dee^D. How many cubic feet are there in a part two feet long? How many in a part three feet long? 12. How many cubic yards will a wagon box hold that is three yards long, two yards wide and one yard high? 18. How many cubic feet are there in a pile of wood four feet long, two feet wide, and two feet high ? 74 THE RATIONAL ARITHMETIC. Igill 4 gills 8 gills 32 gills 1 pint 2 pints 8 pints 1 quart 4 quarts 1 gallon 1. What is sold by tlie gill ? 2. Measure and find how many gills in a pint. 8. One pint equals how many gills? 4. One gill equals what part of a pint? Two gills equal what part? Three gills equal what part? 5. One and one -half pints equal how many gills? 6. If a pint of Avater weighs a pound, how much will a gill weigh ? How much will three gills weigh ? 7. What is sold by the pint and quart? 8. Measure and find how many pints in a quart. 9. One quart equals how many pints? 10. One pint equals what part of a quart? 11. IIow many gills are there in one-half of a quart? How many are there in a quart ? 12. One and one-half quarts equal how many joints? 18. If a })int of water weighs a pound, how much will a quart weigh ? 14. What is sold by the gallon? 15. Measure and find how many quarts in a gallon. PART FIRST. 75 1. One gallon equals how many quarts? 2. One quart equals wliat part of a gallon? Two quarts equal what part? Three quarts equal what part? 3. One and one-half gallons equal hoAV many quarts? 4. If a quart of water weighs two pounds, how much will a gallon weigh ? 5. How many quarts are there in one -half of a gallon? In one-fourth? 0, How many pints are there in one-fourth of a gallon? How many are there in a gallon? 7. How many gills are there in one-fourth of a gallon? 8. Tell how many gills equal two pints; one and one- half pints; two quarts. 9. Tell how many pints equal three quarts; two and one -half quarts; two gallons. 10. Tell how many quarts equal two gallons. 11. At 24 cents a quart, how much will a |)int of mo- lasses cost? 12. How much will a gallon of milk cost at 6 cents a quart ? 13. How much will a quart of cream cost at 4 cents a gill? 14. A can holds twelve quarts; how many gallons ^vill it hold ? 15. How many quarts does a three-gallon jug hold? 1<>. How many quarts of milk are there in sixteen pints? In twenty pints? In twenty -four pints? 17. A boy had two gallons of mineral water, and sold four pints of it. How many pints had he left? How many gallons? 76 THE RATIONAL ARlTHxMETIC. 1 pint 2 pints 1 quart 16 pints 8 quarts 1 peck 64 pints 32 quarts 4 pecks 1 bushel 1. What articles are sold by tlie bushel? 2. Find by measuring how many pecks there are in a bushel. 3. One peck equals what part of a bushel ? 4. One-half of a bushel equals how many pecks? One-fourth of a bushel equals how many pecks? Three-fourths equal how many pecks? 5. How many pecks are there in one and one-half bushels ? 6. Find by measuring how many quarts there are in one peck. 7. One quart equals what j)art of a peck? 8. Put four quarts into the peck measure. part of the measure is filled. 9. Two quarts equal what part of a peck? equal what part ? 10. How many quarts are there in one and one -half pecks ? 11. How many quarts fill a bushel measure? 12. One quart e([uals what part of a bushel? Tell what Six quarts PART FIRST. 77 1. How many pints are there in a quart? In eight quarts? In thirty-two quarts? 2. How many pints are there m a peck? In one-half of a peck? In one -fourth of a peck? 3. How many bushels do twelve pecks equal ? Sixteen pecks ? Twenty pecks ? 4. How many pecks do sixteen quarts equal ? Thirty - two quarts? 5. At 8 cents a quart, what mil six pints of cranber- ries cost? 6. If cherries cost 10 cents a quart, what will one -half of a peck cost ? 7. A boy picked one and one-half bushels of cherries. He sold them by the peck; how many pecks did he sell ? How many dollars did he receive for them at one-half dollar for a peck? 8. How many bags holding one bushel each will be required to hold twenty -four pecks of corn ? How many holding two bushels each will be required ? 9. At 4 cents a quart what will a peck of beans cost? What will three-fourths of a peck cost? 10. If there are ten bushels of wheat in a bin and twenty pecks are taken out, how many pecks are left? How many bushels are left ? 11. A man can dig five bushels of potatoes in one hour. How many pecks can he dig in two hours ? 12. If oats cost 30 cents a bushel, what will two pecks cost? 13. A can holds sixteen quarts of berries. Ten pints of berries are taken out; how many pints are left? How many quarts are left? 78 THE RATIONAL ARITHMETIC. 1 ounce 4 ounces 8 ounces 16 ounces 1 pound 2 pounds 3 pounds 4 pounds 1 . One pound equals how many ounces ? 2. The one- ounce weight equals what part of the pound weight ? 3. Two one -ounce weights together equal what part of the pound weight? 4. The four -ounce weight equals what part of the pound weight? 5. The eight- ounce weight equals what part of the pound weight? 6. The four-ounce weight and the eight-ounce weight together equal what part of the pound weight? 7. The four -ounce weight and two one -ounce weights together equal what part of the pound weight? 8. The eight -ounce weight and two one -ounce weights together equal what part of the pound weight? 9. What part of the two -pound weight does a one- ounce weight equal ? A four-ounce weight? An eight-ounce weight? 10. Four eight- ounce weights together equal which other weight? Note.— Have bean bags of different sizes holding exact weights, as, four pounds, three pounds, two pounds, one pound, eight ounces, four ounces; also, sixteen one-ounce weights. Have the pupils estimate the relation of the weights by handling. PART FIRST. 79 1. Wliicli three weights together equal one pound? Which six weights ? Which nine weights ? 2 Which three weights together equal two pounds? Which four weights ? Which six weights ? 8. Give three ways in which these weights may be combined to equal three pounds. Four pounds. 4. At 6 cents a pound, what will three and one -half pounds of sugar cost? 5. How many four -ounce jDackages can be made from three pounds of tea ? 6. How many jars, each holding twelve ounces, can be filled from one and one-half pounds of butter? 7. What is the weight in ounces of two packages of tea, one holding three -fourths of a pound, and the other one -half of a pound? 8. A man bought two pounds of salt and used twenty - four ounces of it. How many ounces had he left ? What part of a pound had he left ? 9. If cinnamon costs 10 cents an ounce, what will half a pound cost? 10. What will two ounces of sunflower seed cost at 40 cents a pound ? 11. If one pound of cofPee costs SG cents, what Avill eight ounces cost? 12. What will one pound and four ounces of canarv seed cost at 2 cents an ounce? 1?>. If one pound of ])iitter costs 24 cents, what anIII four ounces cost? Twelve ounces? 14. A man bought two pounds of rice, and sold it in eight-ounce pack^xges, at 8 cents a package. How much did he receive for the rice? 80 THE RxVnONAL ARITHMETIC. 5 nickels 5 cents 5 dimes 4 quarters 1 dollar 2 half-dollars 1. How many cents equal a nickel? 2. How many nickels equal a dime? How many cents equal a dime? 3. How many nickels equal a quarter? How many cents equal a quarter? 4. How many quarters equal a half-dollar ? Hoav many dimes equal a half-dollar? How many nickels equal a half-dollar? 5. How many half -dollars equal a dollar? How many quarters equal a dollar ? How many dimes ? 6. Which two pieces of money equal a dime? 7. Which three pieces of money equal a quarter? 8. Which two pieces of money equal seventy-five cents? Which three pieces? 9. Which two pieces of money equal a dollar? Which three pieces ? Which four pieces ? 10. To how many quarters are two dollars equal ? Four dollars? Five and one -half dollars? 11, To liow many half-dollars are six quarters equal ? PART FIRST. 81 1. A boy bought a top for 25 cents, and paid for it in nickels. How many nickels did lie spend for it? 2. A book wortk 30 cents is bought with a half-dollar. How many dimes are needed to make the correct change ? 3. A package of flower seed costs 10 cents. How many quarters Avill pay for five packages ? How many dimes ? 4. How many 5 -cent car fares can be paid with a quarter? With 15 cents? 5. Harry has 5 dimes in his bank; John has 1 quarter and 2 dimes in his. Which has the more money ? 6. At 10 cents each, how many balls can be bought for a quarter, a dime and a nickel together? 7. A pound of candy costs 50 cents. How much can be bought for 1 dollar? For 25 cents? For 75 cents? For 5 cents? 8. How many 50 cents will pay for a chair that costs 5 dollars? 9. A sled costs 1^ dollars. How many 25 cents will be required to pay for it ? 10. Joe bought a book for 30 cents, paper for 25 cents, and two pencils at 10 cents each. What did he pay for all ? What two pieces of money would pay for them ? What three pieces ? 11. If a gill of cream costs a nickel, how many dimes will j)ay for a quart ? 12. If three dimes pay for a bushel of oats, how many nickels will pay for two pecks? 13. If one pound of seed costs a dollar, what part of a dollar will pay for four ounces ? 82 THE RATIONAL ARITHMETIC. 1. Name the days of the week. 2. How many days are there in one week? In tAvo weeks ? In three weeks ? In four weeks ? 8. What part of the week is one day? Two days? 4. How many school days are there in one week ? In three weeks? In ^ve weeks? 5. How many days of the week are not school days? 6. AVhat j)art of the week is the school days? 7. How many days of the week are called working days ? 8. What part of the week is the working days? 9. How many weeks are there in a month? 10. One week is what part of a month? Two weeks are what part ? Three weeks are what part ? 1 1 . Name the months of the year beginning with January. 12. How many months are there in the year? 18. What part of the year is one month ? Two months ? Six months? 14. What part is the winter months? The spring months? The summer months? The autumn months ? 15. During what months is school held? IT). What 2^ai't of the year is school held? 17. Dui'ing what months is there vacation? 18. AVliat part of the year is there vacation? 19. How many liours are there in a day? In two days? 20. AVliat part of a day is one hour? What part is two hours? Four hours? Ei£>:lit hours? Twelve hours ? 21. How many houi's are called "day"^ How many are called " sight "? PART FIRST. 83 1. Draw tlie face of a clock, and fasten to the center two mov- able hands. 2. Show how far the min- ute hand moves in an hour. Show how far the hour hand moves in an hour. 3. How many minutes are there in an hour? 4. How many minutes are there in half an hour ? Ho^v many in one-fourth, or one-quarter, of an hour? 5. Show where the hands are at one oVlock. 6. Show where the hands are at thirty minutes after one, or half past one. 7. Show where the hands are at fifteen minutes after one, or quarter j^ast one. 8. Move the hands to show the time of the opening of school in the morning; the beginning of recess; the closing of school at noon; the opening and closing of school in the afternoon. 9. If recess lasts fifteen minutes, what imrt of an hour does it last? 10. If a man works eight hours a day, what part of a day does he work ? 11. A boy starts for school at twenty minutes after eight and arrives there at ten minutes to nine. How long is he on the way ? 12. George went to school eight months one year. What part of the year did he attend ? 84 THE RATIONAL ARITHMETIC. 1. A train leaves one station at ten minutes after twelve, and arrives at tlie next at half past twelve; how many minutes does it take to go from one station to the other? What part of an hour ? 2. A man closes his store and starts for home at six o* clock. He walks home in a quarter of an hour. What time is it when he arrives ? 3. A man begins work at eight o'clock, and stops at half past five. How many hours a day does he work if he stops an hour at noon ? 4. Mary is six years old and Jennie is six and three - fourth years old. How many months older is Jennie than Mary? 5. School begins at nine o'clock and closes at half past three. How many hours are there between the opening and the closing? An hour and a half are allowed at noon, and half an hour for re- cesses; how many hours are the pupils in school during one day? 6. A farmer OAvned eighteen horses. He sold six; how many had he left ? What part had he left ? 7. A man mailed nine letters at one time and six at another. How many did he mail altogether ? 8. From a bunch of eighteen bananas, nine bananas were sold. How many remained on the bunch ? 9. There were twenty sheep in one pen, and ten m another. How many in both ? If ^ve were taken out, how many remained in the pens ? 10 A boy paid a dime for a bat, and a nickel for a ball. How many cents did he pay for both ? PART FIRST. 85 1. How long a string will reacli around the frame of a slate, tliat is twelve inches long and eight inches wide ? 2. A box two inches high is twice as wide as it is high. How wide is it ? Its length equals the sum of its mdth and height. How long is it ? 3. By cleaning walks, Edwin earned a quarter on Mon- day, a dime on Tuesday, and a nickel on Wednes- day. How much did he earn in the three days ? 4. One jar holds four pints, another holds six pints. How many pints do both hold? How many quarts do both hold ? 5. A ship leaves one port at noon on Monday and arrives at her next port at noon on Friday. How many days was she on the way? 6. In a class of nineteen pupils there was one more girl than there were boys. How many girls and boys were there in the class ? 7. A car goes eight miles an hour. How many hours will it take to go twelve miles ? Twenty miles ? Sixteen miles ? Twenty -four miles? 8. Sixteen acres of land are divided into two equal fields. How many acres are there in each field ? 9. When it is a quarter past nine o'clock, how many minutes past nine is it ? 10. How many pints of oil are there in a can holding twelve quarts? 11. A table is four feet long and two feet wide. What is the length of its perimeter ? What is its area ? 12. A piece of sidewalk seven feet long contains twenty- eight square feet. How wide is it? 8G THE RATIONAL ARITHMETIC. 1. If a peck of beans costs 40 cents, ^v^hat will one quart cost? 2. How many four-(|uai't pails can 1)e filled from seven- teen cpiarts of milk ? How many quarts Avill l)e left? 3. A man started for town at ten minutes to nine, and arrived at twenty minutes after nine. Ho^v many minutes Avas lie on the way? What part of an hour was he on the Avay ? 4. A garden five rods long is onedialf as wide as it is long. How many rods of fence will he recpiired to inclose it? 5. A grocer bought one tub of butter containing ten pounds, and another containing five pounds. How many pounds did he buy? How many jars hokb ing five pounds each coukl he fill with the butter? 6. Three five-dollar bills equal how many dollars? Four five-dollar bills? Five ten-dollar bills? 7. When 16 cents are paid for twelve eggs, how many cents must be paid for six eggs ? 8. There are twenty days of school in a month. Louis was absent ^ve days. What part of the school month was he absent? 9. How many shoes at 2 dollars a pair can be bought for 15 dollars? How much money will be left? 10. The rent of one house is 30 dollars a month; the rent of another is one -half as much. What is the rent of the second house? Of both houses? 11. One side of a signboard contains thirty-six square feet. If the signboard is six feet high, how wide is it? If it is nine feet high, how wide is it? PAKT FIRST. 87 1. From a jug holding one gallon of syru}), one (juart and one 2)int are taken. How much syrup is left in the jug? 2. How many Lags holding six pecks each ^\'ill he required to hold six Ijushels of corn? 3. A train leaves one station at fifteen minutes after one and arrives at the next station half an hour later. At Avliat time does it reach the second station ? 4. What is the Aveight of three packages, two of ^\ liich Aveigh ten ounces each, and one, five ounces? 5. A rectangular field containing sixty square yards, is twelve yards long. Hoav ^vide is it? (3. If one pound of coffee costs 32 cents, what Avill four ounces cost? 7. A boy left home at eight o'clock in the morning and returned at noon. Ho^v many hours was he a^vay \ What part of the day ^vas he a^vay ? 8. If a rope is cut into four equal parts, and each part is three feet long, ^vhat was the length of the entire rope? 9. In a basket of fruit there are two dozen j^ears. If half a dozen are taken out, ho^v many ^vill be left ? 10. The glass in a picture frame is two feet Avide and three feet long. How many s(piare feet are there in its surface ? 11. A clock is fifteen minutes fast. What is the correct time when the clock says half past three ? 12. With what three pieces of money can five 3 -cent car fares be paid ? 13. If one peck of potatoes costs 25 cents, what Avill three pecks cost? Four pecks? 88 THE RATIONAL ARITHMETIC. I A Jik & n 'T L JilJiL I] ■Pi mil IB iiraiii MiiMiiii*^^^^^^^^^^^^^^ ,1, T ft* »4i*i iiu 71 *++• F iJjjJijhlillillLIJlJ I ' 11 ' 1 1 I III *i4 JLdUil iMUJ UJJI irTTT ■■' e -n" 1. How many squares are there in A? 2. How many figures are used in writing the number? 3. How many squares are there in B? 4. How many figures are used in writing the number? 5. How many figures will represent C? D? E? F? G? H? I? 6. How many lO's in A and how many over? 7. How many lO's in C? 8. How many lO's in D and how many over? In F? InG? InH? In I? 9. Write 3 tens; 4 tens; 6 tens; 5 tens; 2 tens; 8 tens. 10. Write: 2 tens and 7. 3 tens and 7. 5 tens and 8. 8 tens and 2. 3 tens and 1. 4 tens and 2. 5 tens and 6. 7 tens and 5. 2 tens and 9. 5 tens and 1. 6 tens and 4. 9 tens and 1. PART FIRST. 89 1. Add A and B. A equals one 10 and 1, or 11. B equals 9. Place tlie 9 squares of B beside the 1 A=ll of A and wliat do we have? B= 9 C is the sum of A and B. C=20 2. Add D and E. Place E beside the 6 of D and what D=16 do we have? E= 6 F is the sum of D and E. F=22 3. Add G and H. Place the 3 of H by the 8 of G and G=18 what do we have ? H=13 I is the sum of G and H. 1=31 4. Add: A and D, 11 A and G, 11 A and H, 11 16 18 13 D and H, 16 C and D, 20 C and G, 20 13 16 18 C and H, 20 A and F, 11 A and E, 11 13 22 _6 D and F, 16 G and I, 18 H and I, 13 22 31 31 5. Read the following numbers: 21, 32, 44, 56, 27, 46, 29, 45, 64, 36, 25. 6. Which figure tells how many tens in each number? 7. The other figure we will call ones, as 1, 2, 4, 6, 7, etc. 00 THE RATIONAL ARITHMETIC. 1. Add: 11 19^ 10 [) ones and 1 are 10, or 1 ten. 2 1 ten and 1 ten are 2 tens. 80 o ^ tens and 1 ten are 8 tens oi* 80. 2. Add: 15 18 18 2 88 8. Add: 26 45 11 6 71 4. Add: 84 29 18 5 68 ) • 5. Add: 47 89 16 7 86 1 6. Add: 26 17 58 84 28 25 18 32 14 87 18 27 14 26 85 29 65 76 57 89 68 58 27 46 28 16 15 48 27 29 67 89 28 85 26 14 87 49 19 16 84 15 84 49 28 88 12 59 16 46 88 29 28 15 67 28 46 84 25 82 54 87 24 84 PART FIRST. 91 1. Write 11 tens. Read. IIoav many hundreds? Write 12 tens. Read. How many linndreds and how many tens over ? AVrite 15 tens. Read. How many hundreds and how many tens over? Write 4 tens and 4. Write 14 tens and 4. Read. How many hundreds, tens, and ones. 2. Add: 47 63 10 3 and 7 are 10, or 1 ten. 10 6 tens and 4 tens are 10 tens. 110 10 tens and 10 are 110. 3. Add: 27G 359 15 12 5 ()35 4. Add: 427 398 15 11 i 825 5. Add: 32 49 76 58 85 67 94 23 88 ()3 25 72 47 5-: 3(> 99 97 S() 78 63 5S 47 85 46 ('»4 57 59 8S 94 S7 76 76 44 54 5 .5 54 143 354 145 252 32 35 34 45 342 435 514 145 45 43 25 54 235 143 152 243 92 THE RATIONAL ARITHMETIC. 1. A farmer kept fifteen sheep in one field, twenty-four in another, thirty-one in another, and forty-three in another. How many sheep did he have in all the fields? 2. George earned 53 dollars in the winter, 43 dollars in the spring, 25 dollars in the summer, and 34 dollars in the fall. How many dollars did he earn in the whole year ? 3. A girl paid 35 cents for a book, 15 cents for paper, 3 cents for a ruler, and 23 cents for a box of paints. How much did she pay for all ? 4. A man traveled one hundred thirty -five miles the . first week, two hundred fifty -four miles the second week, and ^ve hundred forty -one miles the third week. How far did he travel in the three weeks ? 5. I paid 135 dollars for a horse, 154 dollars for a car- riage, and 23 dollars for a harness. How much did they all cost me ? 6. How long a line will it take to go around a house that is thirty-six feet long and twenty-eight feet wide ? 7. A man had 16 dollars, which was 15 dollars less than he needed to buy a suit of clothes. What was the price of the suit ? 8. Arthur earns 12 dollars in one month and William 10 dollars. If their father earns as much as both of them how much does he earn ? How much do the three earn ? 9. Mr. Stone bought a lot for 354 dollars. He built a fence around it at a cost of 103 dollars. What did the whole cost? PART FIRST. 93 1. From 43 54 67 89 354 597 728 Take 11 21 34 45 142 423 415 32 2. Eeacl 25, 37, and 78 as follows: 25 = 2 tens and 5 ones. (20+5.) 1 ten and 15 ones. (10+15.) 37 = 3 tens and 7 ones. (30 + 7.) 2 tens and 17 ones. (20+17.) 78 = 7 tens and 8 ones. (70+8.) 6 tens and 18 ones. (60+18.) 3. Read in the same way 32, 46, 54, 48, 67, 34, 74. 4. From 72 take 35. 5 ones cannot be taken from 2 72=60+12 ones. Change 72 to 6 tens and 35=30+5 12 ones. 5 ones from 12 ones are 30+ 7 = 37 7; 3 tens from 6 tens are 3 tens. 5. From 92 take 44. 92 = 80 + 12 44=40+ 4 40+ 8=48 ~ (]. From 131 take 43. 131 = 120+11 43 = 40+ 3 80+ 8 = :88 7. Subtract: 30 40 80 32 42 53 72 61 13 15 24 13 14 24 45 22 71 94 81 91 84 62 73 82 13 45 54 45 25 33 15 54 250 361 454 583 892 951 123 143 235 354 443 243 04 THE RATIONAL ARITHMETIC. 1. A man l;)oiTowed 73 dollars and returned 54 dollars. How mucli did lie still owe ? 2. In the morning there were ninety -one pounds of sugar in a barrel, and in the evening there wei*e forty -three pounds. How many j)ounds had been taken out during the day ? 3. A boy earned 82 dollars and spent 25 dollars for a ])icycle. How much money had he left? 4. One book contains three hundred eighty -two pages and another two hundred thirty-five pages. How many more pages are there in the first book than in the second? 5. A farmer sold a horse for 160 dollars, which was 24 dollars more than it cost. What was the cost of the horse ? C). It requires ninety feet of molding to go around a parlor and sixty-three feet to go around a din- ing-room. How much more is required for the parlor than for the dining-room? Hoav much is required for both rooms ? 7. Clara's j^urse contains ()3 cents. If she spends 46 cents for a ])ook, how^ much money Avill there 1)6 left? 8. In one school-room, there are six hundred seventy- two books; in another school -room, two h und I'ed forty-three books. Hoav man\' more l)ooks in the first room than in the second ? V). A cistern that will hold one hundred fifty-two barrels of water has only forty-thi'ee l)ai'r(ils in it. How many Larrels of water will 1)0 i'e(|iiired to fill it? PART FIRST. 95 1. Multiplication is tlie addition of equal numhers. 2. How many are tAVO 47 ^s, or 2 times 47 ? 47 47 47 _2 14 or 14 Two 7's are 14, or 1 ten and 4 ones. 8 8 Two 4 tens are 8 tens. 94 94 8 tens and 14 are 94. 3. How many are tliree 58's, or 3 times 58? 58 58 58 58 or 3 24 24 Tliree 8 's are 24. 15 15 Three 5 tens are 15 tens. 174 174 15 tens , and 2 4 are 174. 4. Multiply 36 • • 28 57 38 76 41 45 79 2 3 2 4 3 5 4 2 26 89 93 88 67 80 78 90 4 3 2 4 3 5 4 5. HoAv many are four 243 ^s, or 4 times 243 ? 243 12 Four 3's are 12. 16 Four times 4 tens are 16 tens. 8 Four times 2 hundreds are 8 hundreds. 972 Adding, 6 tens and 1 ten are 7 tens, 8 hun- dreds and 1 hundred are 9 hundreds, making 972. 96 THE RATIONAL ARITHMETIC. . Multiply: 325 438 147 235 268 470 138 1G7 295 3 2 5 4 3 2 5 4 2 179 489 249 304 169 230 294 157 109 3 2 4 3 5 43 5 4 2. A gardener set out four rows of trees, putting eighty -two trees in each row. How many trees (lid he set out? 3. If a person j^ays 4 dollars a Aveek for board, how much will he pay in a year, or fifty-two weeks? 4. There are twenty -four sheets of paper in a quire. How many sheets are there in five quires ? 5. How many bushels of wheat are there in ninety -six bags, if each bag contains two bushels ? 6. What will three pianos cost at 285 dollars each? 7. A family uses thirty-eight quarts of milk in a month. How much Avill the milk l)ill amount to at 5 cents a ( pi art? 8. There are one hundred ninety -six pounds of flour in a barrel. How many pounds in four barrels? 9. Mr. Gates sold his horse for 87 dollars. I sold mine for one -third as much. How much did I receive for my horse ? 10. If Mr. Field pays 36 dollars for one month's rent, what will his rent be for five months ? 11. One hundred ninety -six loaves of bread can be made from a barrel of flour. How many loaves can be made from five barrels of flour ? 12. Dr. Allen pays 75 dollars a year for his telephone. What will it cost him for four years ? PART FIRST. 07 1. Whiitis i of 42? 2)42 In 42 there are 4 tens and 2 ones. 21 tens is 2 tens; i of 2 ones is 1. ^ of 42 is 2 tens and 1, or 21. 2. Find: i of 24 2)24 Jr of 4 i of 28 2)28 i of 60 2)60 i of 36 3 )36 1 of 63 3)63 i of 39 3)39 i of 66 3)66 1 of 93 3)93 J of 96 3 )96 i of 48 4 )48 i of 84 4)84 i of 44 4 )44 i of 80 4 )80 i of 88 4)88 i of 120 4)120 -J of 55 5)55 4 of 50 5)50 | of 155 5)155 3. Kead 32, 54, and 88 as follows: 32-=3 tens and 2 (30 + 2). t 2 tens and 12 (20+12). 1 ten and 22 (10 + 22). 54 = 5 tens and 4 (50+4). 4 tens and 14 (40+14). 3 tens and 24 (30+24). 2 tens and 34 (20+34). 1 ten and 44 (10+44). 88 = 8 tens and 8 (80+8). 6 tens and 28 (60+28) 5 tens and 38 (50+38) 4 tens and 48 (40+48) 3 tens and 58 (30+58) 2 tens and 68 (20+68) 1 ten and 78 (10+78). 98 THE RATIONAL ARITHMETIC. 1. Read in as many ways as possible, 34, 56^ 72, 46, 68, 81, 96, 45, and 115. 2. Wliat is one-lialf of tliirty-two marbles? 2 )82^20+12 We cannot find i of 3 tens evenly. 10-f 6 = 16 Change 32 to 2 tens and 12. i of 2 tens is 1 ten; ^ of 12 is 6. 3. A boat sailed fifty -four miles in two hours; how far did it sail in one hour? In one hour it sailed | of 54 miles. 2 )54^:40+14 Change 54 to 4 tens and 14. ^ 20-h 7 = 27 of 4 tens is 2 tens; J of 14 is 7. 4. Seventy -five aj^ples are separated into three equal piles. How many aj)j)les are there in each pile ? In each pile there are J of 75 apples. 3 )75 = 60+15 Change 75 to 6 tens and 15. j. 20+ 5 = 25 of 6 tens is 2 tens; ^ of 15 is 5. -• 5. Find: i of 98 2)98 -I of 42 3)42 i of 54 2)54 i of 51 3)51 i of 92 4)92 | of 75 5)75 i of 68 4)68 i of 75 5)75 i of 56 4 )56 6. Ninety-six marbles are divided equally among four boys. How many marbles has each boy ? Each boy has J of 96 marbles. ^J^'^^ Change 96 to 8 tens and 16. i of 8 tens - — is 2 tens; 1 of 16 is 4. 24 PART FIRST. 99 1. There are one liundred fifteen scholars in five equal classes. How many scliolars are there in each class ? In each class there are i of 115 scholars. .xf-i^ Chano-e 115 to 10 tens and 15. \ of 10 tens is 2 tens; I of 15 is 8. 28 2. There are one hundred forty -four trees in four equal rows. How many trees are tliere in eacli row? In each row there are J of 144 trees. tens is 8 tens; J of 24 is 6. 86 8. A man walks three miles an hour. At the same rate, how many hours will it take him to walk one hundred sixty-two miles? It will take as many hours as there are 8's in 162. ox^V^ Read 162 as 15 tens and 12. There are 8)lb2 , . ^ , . 50 8 s m 15 tens; there are 4 8s m 12. 50 and 4 are 54. 4. Divide: 2)178 8)171 4)172 5)175 2)866 4)896 5 )150 5 )845 4)180 8)294 2)250 8)426 2)548 4 )188 8 )678 5)470 2)478 4)272 5)215 8)519 2)672 4)872 8)987 5)595 2)686 4)524 5)755 8 )648 4)886 5)485 2)946 8)819 4)296 5)875 8)201 100 THE RATIONAL APaTHMETTC. 1. What is tlie cost of one lot, if tliree lots cost 516 dollars ? 2. A farmer has three hundred fifteen bushels of pota- toes. If he puts them in barrels, each holding three bushels, how many barrels will he need? 3. A steamboat makes a trip of eight hundred forty- three miles in tliree days. How many miles does it run in one day ? 4. A clerk, selling cloth at 2 dollars a yard, received 506 dollars in one day. How many yards did he sell? 5. How many gallons in seven hundred twenty-eight quarts ? 6. A dealer bought five bicycles for 225 dollars. AVhat was the cost of one bicycle? 7. If a man saves 3 dollars a week, how many weeks will it take him to save enough money to pay for his house, on which he owes 879 dollars? 8. A farmer who has four hundred ninety-six acres of land, divides it into four farms of equal size. What is the size of each farm ? 9. A carjDenter receives 160 dollars for building five rods of fence. What was the cost per rod ? 10. There are three hundred sixty -five days in one year. How many days in one -fifth of a year? 11. A gardener has eight hundred twenty -eight ]3ounds of seed, which he puts into four-pound sacks. How many sacks will be required ? 12. In going to school and returning home, Henry has to walk nine hundred seventy -eight yards. How far does he live from the school house ? •> ■> > > > PAET SECOND. A B D 1. The above is the plan of a lot drawn to the scale, 1 iuch to 12 feet. This means that an inch in length in the drawing represents 12 feet in any line in the lot. 2. How many feet is it from A to B? 3. How many feet is it from A to F? 4. How many feet is it from F to E ? From D to E ? From B to C ? From C to D ? From A through B to C ? From A through F to E? 5. How many feet of fence are required to fence the lot? 6. There are 3 feet in a yard, how many yards from A to F:^ From A to B? How many yards around the lot? 101 Kk': THE RATIONAL ARITHMETIC. 1. I£.tli0 lot veie square with sides the length of A to F, how many yards around it? If square with sides the length of A to B, how many yards around it ? If square with sides the length of B to C, how many yards around it? 2. Taking steps 2 feet long, how many steps would one take in walking once around the lot described on page 101? 3. How many such steps would he take in walking halfway around the lot? In walking twice around the lot? 4. A car is 61 feet long, how long is a train of 1 such cars ? Of 5 such cars? 5. A block is 453 feet long. A lamp-post is 236 feet from one end of the block; how far is it from the other end? 6. A strip of wood 6 yards long is cut into pieces 2 feet long. How many pieces are there? 7. A girl rolled a hoop 12 yards at one time and 16 yards another time. How many yards did she roll it in all? How many feet? 8. A house is 54 feet high and a flag pole on top of the house is 24 feet high. How many feet from the ground to the top of the flag pole? How many yards? 9. A field is 240 feet wide, and 325 feet long. How many feet around it? 10. A block is 486 feet long, and 273 feet wide. What is the difference between the length and the width in feet? In yards? 11„ A boy lives 624 feet from the store. In going to the store and returning, hoAv many feet will he walk ? How many yards? If he goes to the store and returns once a day, 4 days in the week, how many yards will he walk? 12. A rail in the street car track is 10 yards long. How many rails in 50 yards of a single rail of track? In 2 rails of track? In all the rails of 2 tracks? PART SECOND. 103 27 ft ZIFT DINING ROOM ^ H 0-' PAP LOP • 1 KITCMEN ^ -n H rx3 5iTTIMG POOh T] H 1. The above plan is for tbe lower story of a house. 2. Howmany yards long is the parlor? Sitting-room? Dining- room ? Kitchen ? How many yards wide is each room ? 3. How many feel of mokling will reach around each room? How many yards? 4:. How many feet of molding will reach around all the rooms? How many yards? 5. How many strips of carpet, 1 yard wide, will cover the parlor floor ? How many yards long will each strip be ? How many yards in all the pieces for the parlor floor? f). How many strips of carpet, I yard wide, will cover the sitting-room floor? How many yards in all the carpet for the sittinsf-room ? 7. How many strips, 1 yard wide, will cover the dining- room floor? How many yards in all the carpet for the dinino:-room? 8. How many yards will be required for the 3 rooms together ? 104 THE RATIONAL ARITHMETIC. 1. Joe and Harry live 20 yards apart. How many feet of telephone wire do they need to connect the 2 houses, allowing 2 yards for connection at the ends? 2. The blackboard in the schoolroom is 24 feet long. It is divided into sections 24 inches wide, how many sec- tions are there? If there were 42 feet of blackboard, how many such sections would there be? 3. How many yards of border will be required to go around the walls of a parlor which is 15 feet by 18 feet? Around a bedroom which is 12 feet by 15 feet? 4. I Avished to carpet my stairs, and found I needed for that purpose 12 yards. It takes 18 inches for each step. How many steps are there in the staircase? 5. Mr. Benton had 4 book shelves which are 3 feet long. The first shelf he filled with books 4 inches thick. How many books did he put on the shelf? The second shelf he filled with books 3 inches thick. How many were there? The third shelf he filled with books 2 inches thick. How many were there? The fourth shelf, he filled with books 1 inch thick. How many did he put on the fourth shelf? How many books did he put on all the book-shelves? 0. Harold is 3 feet 9 inches tall and James is 4 feet tall. What is the sum of their heights? 7. George is 4 feet 9 inches tall and John is 3 feet 3 inches tall; how much taller is George than John? AVhat is the sum of their heights? 8. James is 3 feet 114^ inches tall and Jessie is 3 feet 7 inches tall; what is the difference in their height? 9. A room is 9 feet 8 inches high. The mantel is 4 feet 6 inches from the floor. How far is it from the mantel to the ceiling? PART SECOND. 105 D M H K 1. Tliis plan of a building is drawn to the scale of one inch to twelve feet. 2. How many feet is it from A to B ? From B to D through C ? From D to F through E ? From F to H through G ? From H to M through K and L ? 3. How many yards is it from P to O? From P to A? From D to E ? From G to K through H ? From F to L through G, H, and K? 4. How many yards is it from C to N through B, A, P and O ? 5. How many yards is it from N to G through M, L, K, and H ? 6. How many yards is it from G to C through F, E, and D? 7. How many yards is it around the entire building? 8. How many feet is it from B to O, following the dotted line? HoAv many yards is it? 106 THE RATIONAL ARITHMETIC. A 1 1 n U f- i 1 J o U — r^ La i^ \\ p\ U 1 1 ^ 1 1 1 L — 1. A is 6. How many 6's in B? How many in C? In D? E? F? G? H? I? J? K? L? 2. A equals (3, B equals 12. To what is C equal? D? F? G? H? I? J? K? L? 3. A equals wliat part of B ? What part of C ? 4 6 is what part of 12? What part of 18? 36? 42? 48? 54? 60? m? 72? 5. B equals how many A's? What part of C? F? G? H? I? J? K? L? Of D? Of 24? E? E? 30? OfD? E? PART SECOND. 107 1. 12 is how many 6's? What part of 18? Of 24? 30? 36? 42? 48? 54? 60? 66? 72? 2. C equals how many A's? How many B's? AVhat part ofD? OfE? F? G? H? I? J? K? L? 3. 18 is how many 6's? How many 12's? What part of 24? 30? 36? 42? 48? 54? 60? 66? 72? 4. D equals how many A's? How many B's? How many C's? What part of E? Of F? G? H? I? J? 5. 24 is how many 6's? How many 12's? How many 18's? What part of 30 ? 36? 42? 48? 54? 60? 72? 6. E equals how many A's? How many B's? How many C's? How many D's? AVliat part of F ? Of G? H? 7. 30 is how many 6's? How many 12's? How many 18's? How many 24's? What part of 36? Of 42? 48? 8. F equals how many A's? B's? C's? D's? E's? Etc. 2 12 22 32 6 42 52 62 72 6 16 26 36 6 48 56 66 76 O 13 23 33 6 43 53 63 73 7 17 27 37 6 47 57 67 77 4 14 24 34 6 44 54 64 74 8 18 28 38 6 48 58 68 78 5 15 25 35 6 45 55 65 75 9 19 29 39 6 49 59 69 79 Add the red figure to each number in the same large square. Subtract it from each larger number. Multiply and divide in the same way. Note. — Have pupils construct drill tables similar to those on pages 66 and 67, for this and following multiplication tables, pages 117, ]25, 135, 143, 149 and 153. 108 THE RATIONAL ARITHMETIC. 1. Add upward, downward, by lines to the right and to the left: 6 6 6 3 6 6 2 3 6 2 1 6 4 2 6 6 6 6 6 1 6 1 6 () 6 6 6 6 6 6 5 6 6 6 6 6 6 6 4 1 1 3 4 5 2 6 6 5 2. Add, subtract and multiply 12 18 24 30 36 42 48 54 60 66 72 6 6 6 6 6 6 6 6 6 6 i; 13 25 37 49 51 63 75 87 99 KH. 6 () 6 6 6 6 () 6 6 r, 3. Divide: 6)12 6)30 6)42 6)54 6)72 6V)^ 6)48' ^)i? ^)^ ^1^ ^^)^ ^'M ^)1?5 ^'H^ i 4. 12 equals how many 6's? 36 equals how many 6's? 24 equals how many 6'sV 42 equals how many 6's? 48 equals how many 6's? 66 equals how many 6's? 18 equals how many 6's? 30 equals how many ()'s? 54 equals how many 6's? 72 equals how many 6's? 6 is \ of 6 is I of 6 is 4f of _. 6 is J of 6 is tV of __• . 6 is 1 3 of 6 is 1 of 6 is 1 of 6 is 1 of 6 is 1 10 of PART SECOND. 100 1. 3 is I of 7 is « of 5 is I of . _. 8 is J of — 2 is J of 9 is I of __ 4 is ^ of 6 is I of . — 10 is ^ of 12 is -I of _ 2. How many 6's are there in 13? In 32? How many 6's are there in 57? In 51? How many O's are there in 25 ? In 45 ? How many 6's are there in 22? In 40? How many 6's are there in 75? In 63? The- sign for dollars is $; (> dollars is written $6. The sign for cents is ^; 25 cents is Avritten 25^. 3. At $6 a cord what is the cost of 5 cords of wood? 7 cords? 9 cords? 11 cords? 4. Six windows contain 48 panes of glass. How many panes are there in each window? In one-half of one window? 5. How many minutes are there in an hour? What part of an hour are 10 minutes? 20 minutes? 30 minutes? 40 minutes? 6. One man built a fence in 60 days. How many men could have built it in 6 days ? In 5 days ? In 3 days ? 7. One yard of braid is worth 6^, how much are 5 yards worth ? 8. At $6 a barrel, how many barrels of flour can be bought for $72? For $54? For $36? For $18? For $48? For $12? 9. In an orchard there are 54 trees in six equal rows. How many trees are there in one row? 10. Joe went to the store with 36^ and spent all but 6^. What part of his money did he have left? How much had he left ? 11. In going to school a boy rides 24 blocks and walks one- sixth as far as he rides. How many blocks does he walk ? How far does he travel ? no THE RATIONAL ARITHMETIC. 1. Tlie height of a tree is 72 feet, which is 6 times the dis- tance around it at the ground. How many feet around it at the ground? 2. If I buy 5 eight-cent postage stamps and give $1 in pay- ment, how much change should I receive? 3. Charles traveled 87 miles on his wheel in 3 days. At the same rate how far can he go in 5 days? In 6 days? 4. In one field a farmer has 96 sheep, which are one-sixth of his entire flock. How many sheep has he? 5. If $120 were divided equally among 6 men, how much money would each one receive? How much would 2 receive together? 3 together? 6. A piece of cloth is 54: yards long. One-sixth of it was sold at $2 a yard. How much was received from the sale? How much of the piece was left? How rnucli was it worth at the same rate? 7. If a man earns $71 a month and spends $52 a month, how much will he save in that time? How much will he save in months? 8. How many hours are there in 1 day ? In one-half a day ? In one-sixth of a day ? How many hours are there in 6 days? 9. A barrel holds 31|^ gallons ; how many gallons will 6 bar- rels hold? 10. A farmer owned 486 acres of pasture land. He bought one-sixth as many acres more. How many acres did he buy ? How many acres did he then own ? 11. A mile from north to south is 8 blocks, and from east to west 13 blocks. How many blocks will a boy travel in going 6 miles north and 6 miles west? 12. What is the cost of 27 yards of sewer pipe at $2 a foot? 13. How many weeks will it take a man to save $297 if he saves $3 each week? FART SECOND. Ill 1. How many square inclies in a rectangle that is 6 inclieh-- long and S inches wide? (See page 54.) One that is inches long and (j inches wide? One that is inches long and 8 inches wide ? One that is 6 inches long and 12 inches wide? 2. How many square inches in a G inch square? Draw one. 8. A 2 inch square equals what part of a 6 inch square? 4. A 3 inch square equals what part of a G inch square? 5. How many 4 inch squares in a G inch square? G. How many 5 inch squares in a 6 inch square ? 7. A 4 inch square equals what part of a G inch square? 8. A 5 inch square equals what part of a 6 inch square? 9. To what are 3 feet in length equal? 10. WJiat then may we call a figure 3 feet square? 11. On page 50 suppose each small square in the yellow fig- ure were one foot long. How long would the yellow figure then be? How wide? How many square feet Avould it contain? How many square yards? How many feet in the perimeter of a square yard? 12. On page 54 suppose each small square were one foot square. Hoav wide would the figure be? How long? How many square feet Avould it contain ? 13. How many square yards in a figure 2 yards square? How many feet long is one side of such a figure ? How many square feet does such a figure contain ? 14. How many square feet in 3 square yards? 5 square yards? (> square yards? 15. How many square yards in 18 square feet? 3G square feet ? 27 square feet ? 54 square feet ? 45 square feet ? IG. Turn again to the yellow figure on page 50. Suppose each side is one yard long. What part of a square yard is 3 square feet? 1 square foot? G square feet? 2 square feet? 5 square feet? 4 square feet? 112 THE RATIONAL ARITHMETIC. A 1 ^ ' / j 1 ^\ 1. How long is the box A? inches in one side? How deep? How many square ' PART SECOND. 113 1. B is a piece of paper the size from which to cut such a box without a cover. 2. How long is this paper? How wide is it? 3. The paper is then a rectangle of inches by inches. 4. What is the area of this paper? 5. A box is 2 inches long, 2 inches wide and 2 inches high. How many square inches in the sides and bottom of the box? 6. What are the dimensions of the piece of paper necessary to make it? What is its area? 7. What are the dimensions of the piece of paper necessary to make a box 3 inches long, 3 inches wide and 3 inches high, without a cover? What is the area of the paper? 8. What are the dimensions of a box that can be made from a piece of paper 12 inches long and 12 inches wide, without a cover? 9. A box is 4 inches long, 3 inches wide and 2 inches high. How large must the paper be in order to make it with- out a cover? How many square inches of paper are necessary ? 10. What are the dimensions of the piece of leather necessary to line a box that is 6 inches long, 2 inches wide and 2 inches high, without a cover? How many square inches? What will the leather for such a box cost at 6 cents a square inch? 11. How many square feet of cloth are needed to line a box 6 feet long, 3 feet wide and 2 feet high, with a cover? 12. The length of a room is 6 yards, its height 4 yards. How many square yards in one side of the room? In the 2 sides? The room is 5 yards wide, what is the area of one end wall? Of both? Of the ceiling? Of the floor? Of the entire inside surface of the room? 114 THE RATIONAL ARITHMETIC. I X 1 • rrr ZF a Y b e I PART SECOND. 11.3 1. The figure X is enclosed by the black irregular line. It is cut into four rectangles by the dotted lines. These rectangles are marked I, II, III, lY. 2. Measure the length and width of I. What is its area? AV^iiat are the dimensions of II? Its area? Dimen- sions of III? Its area? Dimensions of IV? Its area ? 3. Now what is the area of the figure X? into what other rectangles might X bo cut t(j find its area? What is the perimeter of X? 4. What part of the rectangle I equals II? III? IV? What part of II equals IV ? Ill ? 5. Suppose each inch in the dimensions of the figure X rep- resented 3 feei What would be the width of the rectangle I? Its length? How many square feet would it contain? How many square yards? (j. What would then be the dimensions of II? Its area? Dimensions of III? Its area? Dimensions of IV? Its area? 7. If I=S. what is II? III? IV? If 11-36, what is IV ? Ill ? I ? 8. The figure Y is made up of the rectangles c/, h, c. [). H-ow long is a? How wide? What is its area? ID. What are the dimensions of h? Its area? Dimensions of c? Its area? P* 11. What is the area of the figure Y? Is there more than one way to find the area of Y? 12. Suppose each inch in the dimensions of the figure Y rep- resented 3 feet. What would l^e the area of af !>? cf AVliat would be the area of the entire surface of Y in square feet? In square yards? 13. What is the area of X and Y together, in square feet ? In square yards? nc THE RATIONAL ARITHMETIC. At E — I n U r 1 1 J G K Pi D 1 1 1 1 1 l_ 1. A is 7. How many 7's in B? How many in C? In D? E? F? G? H? I? J? K? L? 2. A equals 7, B equals 14. To what is C equal? D? E? F? G? H? I? J? K? L? 8. A equals what part of B ? What part of C ? Of D ? E ? F? G? H? I? J? K? L? 4. 7 is what part of 14? What part of 21? Of 28? 35? 42? 49? 56? 63? 70? 77? 84? 5. B equals how many A's? What part of 0? Of D? E? F? G? H? I? J? K? L? 6. 14 is how many 7's? What paj-t of 21? Of 28? 35? 42? 49? 56? 63? 70? 77? 84? PART SECOND. 117 1. C equals how many A's? How many B's? What part o£D? 0£E? F? G? H? I? J? K? L? 2. 21 is how many 7's? How many 14's? What part of 2S? Of 35? 42? 49? 56? 63? 70? 77? 84? 3. D equals how many A's? How many B's? How many C's? What part of E? OfF? G? H? I? J? K? L? 4. 28 is how many 7's? How many 14's? How many 21's? What part of 35 ? Of 42? 49? 56? 63? 70? 77? 5. E equals how many A's? How many B's? How many C's ? How many D's ? What part of F ? Of G ? H ? I? J? K? L? 6. 35 is how many 7's? How many 14's? How many 21's? How many 28's? What part of 42? Of 49? 56? 63? 70? 77? 84? 7. F equals how many A's? How many B's? C's? D's? E's? What part of G? Of H? I? J? K? L? 8. 42 is how many 7's? How many 14's? How many 21's? How many 28's? Etc. 2 12 22 32 7 42 52 62 72 6 16 26 36 7 46 56 66 76 3 13 23 33 7 43 53 63 73 7 17 27 37 7 47 57 67 77 4 14 24 34 7 44 54 64 74, 8 18 28 38 7 48 58 68 78 5 15 25 35 7 45 55 65 75 9 19 29 39 7 49 59 69 79 Add the red figure to each number in the same large square. Subtract it from each number larger than itself. Multiply and divide in the same way. 118 THE RATIONAL ARITHMETIC. 1. Add upward, downward, by lines to the right and to the left : 7 7 6 4 5 3 2 7 7 1 2 4 () 7 7 5 G 7 3 7 4 7 4 7 7 7 (> 7 5 7 6 6 4 7 7 6 7 7 7 6 6 4 3 7 1 3 3 2 2 7 4 7 2. Add, subtract and multiply: 14 28 5G 21 42 84 35 70 63 78 59 7 r- < 7 7 7 7 7 7 7 7 7 83 <0 94 67 77 89 48 99 132 576 7 7 7 7 7 7 r- 7 7 7 3. Divide: 7)14 7)28 7)42 7)21 7)56 7)70 7)35 7)49 7)68 7)84 7)77 6)72 4. 14 equals how many 7's? 42 equals how many 7's? 28 equals how many 7's? 49 equals how many 7's? 56 equals how many 7's? 21 equals how many 7's? 35 equals how many T's? 77 equals how many 7's? 63 equals how many 7'sV 84 equals hoAV many 7'sV 5. 7 is ^5 of . 7 is \ of 7 is \ of .. 7 is \ of 7 is \ of 7 is -^ of TAKT SECOND. n'.) 7 is 1 2~ of 7 is I 1 of 7 is 1 12 > ot 4 is 1 8 of (•> is 1 of 8 is 1 T of is 1 5: of 7 is 1 9 of 7 is 1 1 t) of 6 is 1 of 7 is 1 1 of 4 is 1 of Ois 1 3 of 11 is 1 . ' of 111 29 ? Ill 45? In 25 ? Ill 48? Ill 78? Ill 82 ? 2. How many 7's are there in 15? How many 7's are there in 37? How many 7\s are there in 50? How many 7's are there in 57? How many 7's are there in 8B? How many 7's are there in 73 ? 3. One man digs 27 feet of ditch; another 17 feet, and a boy 7 feet. How many feet do all dig? 4. On one farm there are 754 feet of fence; on another 577 feet. How much more fence is there on the first farm than on the second? 5. A grain dealer bought 378 bushels of wheat in one place and 747 bushels in another. He sold 707 bushels; how many bushels had he left? 0. A man bought 7 horses at $65 apiece; how much did he pay for all? 7. A train travels 252 miles in 7 hours; how far does it go in 1 hour? 8. If 14 pails of butter weigh 42 pounds, what do 2 pails of the same size weisrh? 9. In making a well, 63 feet deep, 14 feet were dug through clay. If '}j of the well was dug each day, how many days were spent in digging through the clay ? 10. A farmer made a wire fence 14 yards long, he put in posts 7 feet apart, and 7 rows of -wire. How many posts were there? How many yards of wire did he use? 120 THE RATIONAL ARITHMETIC. PART SECOND. 121 1. The lower side upon which a triangle rests is called its base. The vertical side is called its height, or altitude. 2. What is the length of the base of the triangle A on the opposite page? What is the altitude? 3. Find the middle point of the altitude and the middle point of the long side of the triangle, and between these two points suppose the triangle cut and the upper part turned about to the side of A, as in B. 4. What do we call the figure B? What is its length? What is its width? What is the area of B? 5. What then is the area of the triangle A ? 6. Cut a 4-inch square. Draw a line between two opposite corners, and on this line cut the square in two. What is the altitude of one of the triangles thus formed? Its base? Find its area. 7. What are the dimensions of the triangle C? Draw a line from the center of the base to the center of the angle opposite. Suppose the left side of the triangle C to be turned about and laid upon the longest side of C as in the figure D. What is the figure D ? 8. What are the dimensions of D ? What is its area ? 9. What then is the area of the triangle C ? 10. Suppose the base of the triangle C were 6 feet and its altitude 6 feet, what would be the area of the triangle? 11. The area of such a triangle as C may be found in another way, as in the triangle E. 12. Find the middle point of the sides of the triangle, and suppose the triangle to be cut at these points and the top part equally divided and placed on the sides of the lower part of the triangle, as in the figure F. What figure do we then have? What are its dimensions? AVliat is its area? 13. What then is the area of the triangle E? 122 THE RATIONAL ARITHMETIC. 1. Draw the following 9 triangles and find the area of each: The base is (5 inches and the altitude 4 inches. The l)ase is 8 inches and the altitude 6 inches. The base is 9 inches and the altitude 4 inches. The base is 5 inches and the altitude 8 inches. The l)ase is 12 inches and the altitude 10 inches. The base is J 1 inches and the altitude 14 inches. The base is 18 inches and the altitude 12 inched. The base is 1^3 inches and the altitude 10 inches. The base is 15 inches and the altitude 14 inches. 2. A car contains 1) seats, each of which holds 7 persons. Ht)W many persons can be seated in the car? 8, There are 3 cars of this size in a train. How many per- sons can be seated in the train? 4. In front of a house there are 25 feet of sidewalk 7 feet wide. How many square feet in the sidewalk? 5. A door is 7 feet high and 8 feet wide. How many scj^uare feet in the door? How many square feet if the door were 3^ feet Avide? 6. How many books would there ])e in a bookcase containing 7 shelves, if there were 12 books on each shelf? 11 on each shelf? 9 on each shelf? 10 on each shelf? 20 on each shelf? 30 on each shelf? 7. A table is 7 feet long and 4 feet wide. What is its perim- eter? What is its area? 8. There are 35 pupils enrolled iii one schoolroom. If 5 are away, how many are present? What part of the whole number is absent? What part of the whole number is present ? 9. A fruit dealer sells pineapples at 34 cents apiece. How much money will he receive for 7 pineapples? 10. If I save 57 dollars a month for 7 months, how much more must I save to have $700? PART SECOND. 1-23 1. A piece of pipe is 80 feet long. How long are 7 such pieces together? 2. In a cellar there are 4 bins, each holding 7 bushels. How many sacks of apples, each holding 2 bushels, will be required to fill the bins? 3. The distance around a field is 63 rods. \ of the fencing around it is hedge, the remainder is board fence. How many rods of hedge? How many rods of board fence? 4. In a farm of 140 acres there are 7 acres of orchard. What part of the farm is the orchard? How much land l^e- side the orchard? 5. A grocer selling rice in 7 pound packages, sold 3 pack- ages to one man and 4 to another. How many pounds did he sell to both? 6. A florist sells roses which cost him 57 cents per dozen, for 95 cents per dozen. How much does he gain on 7 dozen? 7. 8S253 were divided equally among 7 children. How many dollars did each child receive? 8. Mr. Wood had $2891 and spent one-seventh of it. How many dollars had he left? What part of his money had he left ? 9. A lot cost $3747, a house $2735, a barn $878 and a side- walk f^l77. Wliat was the cost of all? 10. An army of 9287 men engaged in battle. 1375 were killed and 57 were made prisoners. How many were left in the army? 11. I bought 170 cameras for $7 each. I sold the wdiole number for $1100. Did I gain or lose, and how much? 12. Mr. Adams owned 19 horses; lie kept 12 and sold the remainder for $S9(). How much did he receive for each horse sold? 124 THE RATIONAL ARITHMETIC. A r-v r L 1 1 n U r- r 1 J p U /-N U !• r\ n LJ 1 1 1 1 1 L 1. A is 8. How many 8's in B? How many in C? In D? E? F? G? H? I? J? K? L? 2. A equals 8, B equals 10. To what is C equal? D? E? F? G? H? I? J? K? L? 3. A equals what part of B ? What part of C ? Of D ? E ? E? G? H? I? J? K? L? 4 8 is what part of 16? What part of 24? Of 32? 40? 48? 56? 64? 72? 80? 88? 96? 5. B equals how many A's? What part of C? Of D? E? F? G? H? I? J? K? L? 6. 16 is how many 8's? What part of 24? Of 32? 40? 48? 56? 64? 72? 80? 88? 96? 7. C equals how many A's? How many B's? What part of D? OfE? F? G? H? I? J? K? L? PART SECOND. 125 L 24 is how many 8's ? How many 16's ? What part of 32 ? Of 40? 48? 56? 64? 72? 80? 88? 96? 2. D equals how many A's? How many B's? Hoav many C's? What part of E? Of F? G? H? I? J? K? L? 3. 32 is how many 8's How many 16's? How many 24's? What part of 40 ? Of 48? 56? 64? 72? 80? 88? 96? 4. E equals how many A's? How many B's? How many C's? How many D's? What part of F? Of G? H? I? J? K? L? 5. 40 is how many 8's? How many 16's? How many 24's? How many 32's? What part of 48? Of 56? 72? 80? 88? 96? " " B's? C's? D's? E's? T7 r> T f» su : oo r yo r 6. F equals how many A's? B's? C's? D What part of G? Of H? I? J? K? L 1 O' O TT 1 ^1„ O TT „ equals now many ii s r .d s : v_/ s r u ni ^ » i What part of G? Of H? I? J? K? L? is how many 8's? How many 16's? How many 24's? How many 32's? Etc. 2 12 22 32 8 42 52 62 72 3 13 23 33 S 43 53 63 73 4 14 24 34 8 44 54 64 74 5 15 25 35 8 45 55 65 75 6 16 26 7 17 27 8 18 28 9 19 29 36 8 46 37 8 47 38 8 48 39 8 49 56 66 76 57 67 77 58 68 78 59 69 79 Add the red figure to each number in the same large square. Subtract it from each number larger than itself. Multiply and divide in the same way. l-2() THE RATIONAL ARITIL\FETJC. 1. Add upward, downward, by lines to the right and to fclie left: 8 8 8 8 8 8 8 8 8 7 8 5 8 1 7 8 7 4 8 6 2 7 8 5 8 2 8 5 3 G 8 4 3 7 G 7 4 G 8 3 4 . 8 3 4 8 2 8 8 7 8 6 4 7 1 8 8 7 3 2. Add, subtract and multiply: 32 24 IG 48 5G 72 G4 88 80 40 8888888888 13 8 25 8 37 8 49 8 79 8 88 8 G^ 8 98 8 38G 8 497 8 Divide 8)1G 8)32 8)48 8)24 8)5G 8)12 8)40 8)G4 8)88 X)9(i 8)80 7)84 4. IG equals how many 8'sy 32 equals how many 8's? 40 equals how many 8's? 5G equals how many 8's? 88 equals how many 8's? 80 equals how many 8's? 5. 8 is f^ of ._ 48 equals how^ many 8's? G4 equals how many 8's? 24 equals how many 8's? 72 equals how many 8's? 9G equals how many 8's? 49 equals how many 7's? 8 is I- of PART SECOND. 1-2? 0"? 1. 8 is 1 of 8 is 1 4 of 8 is 1 "9 of 8 is 1 1 of 8 is 1 1 1 of ) is 1 7 of 'J is 1 1 1 of 8 is 1 of 8 is G 1 8' > o 8 is 1 7 1 of 8 is of 7 is 1 2 1 of 4 is 1 9 of 3 is 1 8 of _ In 34? In 27? In (;3y In SI? In 42? • In (>7? In 30? In 98 ? 2. How many 8's are there in 17? How many 8's are there in 47? How many 8's are there in 50? How many 8"s are there in 71 ? How many 8's are there in 20? How many 8's are there in 59? How many 8's are there in 76? How many 8's are there in 85? 3. A boy picked 38 quarts of berries in one week, 42 in the second, 28 in the third, and 18 in the fourth. How many quarts did he pick? 4. In one school there are 858 scholars; in another there are 684. How many more are there in one than in the other ? A man traveled 284 miles by rail and 8 times as far by boat; how far did he travel by boat? During the summer a family used 248 quarts of milk. During the winter they used g as much. How many quarts did they use during the winter? 7. If one boat holds 5 persons; how many boats will be needed for a party of 40 people? 8. In an orchard there are 56 trees in each row, and \ as many rows as there are trees in each one; how many rows are there? How many trees in all? 9. If 32 bushels of wheat make 8 barrels of flour ; how many bushels will be needed to make 64 barrels? o (J. 128 THE RATIONAL ARITHMETIC. 1. In the first layer of blocks in this solid, how many rows of 4 blocks each? How many blocks in the layer? How did you find this? In all 3 layers, or the entire solid, how many blocks are there? How did yon find this? How then do yon find the number of cubic feet in any solid ? 2. How many inch cubes are there in a block 2 inches long, 2 inches wide and 1 inch high? See ])age 68. How many inch cubes are there in a block 4 inches long, 2 inches wide and 1 inch high? 3. HoAV many inch cubes are there in a block 6 inches long, 4 inches wide and 1 inch high? How many inch cubes are there in one row? How many of these rows are there in the block? 4. How many cubic inches are there in a box that is 4 inches long, 3 inches wide and 1 inch high ? 2 inches high ? 3 inches high? 5. How many cubic inches are there in a box 4 inches long, 2 inches wide and 2 inches high? 6. A block containing 12 cubic inches is 3 inches long and 2 inches wide; how high is it? PART SECOND. 129 1. A pencil box containing 2-1: cubic inches is 8 inches wide and 1 inch high; how long is it? 2. A block is 3 feet long, 3 feet wide and 3 feet high ; how many cubic feet does it contain? What is the area of one side of such a block in square feet? In square yards? How many cubic yards in a block 1 yard long, 1 yard wide and 1 yard high? How many cubic feet in such a block? 3. A room is 5 yards wide, 7 yards long and 4 yards high. How many cubic yards are there in the room ? 4. A cellar is 7 yards long, 6 yards wide and 3 yards deep. How many cubic yards of earth were taken out in diijficimj: the cellar? 5. The foundation of a house is equal to a straight wall 65 feet long, 4 feet high and 1| feet wide. How many cubic feet does it contain? 0. A box is 7 feet long, 3 feet wide and contains 03 cubic feet. How long is it? 7. A bin is 3 feet wide, 4 feet high and contains 72 cubic feet. How long is it? 8. A coal-bin is 12 feet long, feet wide and 7 feet high. How many cubic feet of coal will it hold? 9. A car is 7 yards lon <]uarts of milk. How many gallons did he have? 9. How many gill cups can be filled from 2 quarts and 1 pint of vinegar? From 5 gallons? 10. Tliere are 314^ ii^allons in a barrel. How nuury iJ^allons are there in 4 barrels? In G barrels? In 8 barrels? 3 barrels? 5 barrels? 11. A barrel holds 31^ gallons? How^ many quarts in it? 12. From a barrel of gasoline how many cans may be filled if each holds 3 quarts? How many if each holds ^ a U-allon ? Ih trallon ? Id. A milk-man starts in the morning Avith 48 gallons of milk. How many customers can he serve if each takes 3 quarts? How many, if each takes 2 quarts? If each takes 3 pints? PART SECOND. L'U 1. Review page 76. 2. At 9^ a peck, what Avill 2 bushels of oats cost? 8. What is 1 quart o£ beans worth if a peck is worth 72^? 4. At $2 a peck, how many bushels of clover seed can be bought for §?88? 5. A fruit dealer sold 3 pecks of nuts at 8^ a quart. What did he receive for them ? f). A farmer picked 2 bushels of apples from one tree and 3 bushels from another. How many pecks did he pick from both together? 7. A grain bin holds 2 bushels. How many pecks do 7 such bins hold? 8. During the summer a boy picked 64 quarts of berries. How many pecks did he pick? How many bushels? 9. From a bushel of beans 2 quarts and 1 pint are taken. How many quarts are left? 10. How many pint boxes of cherries may be filled from a peck ? 11. A man paid 60(^ for 14 bushels of apples. He sold them at 15^ a peck. How much did he receive? How much did he gain? 12. 2 boys gathered 6 bushels of nuts. They sold 5^ bushels by the peck. How many pecks did they sell? The remainder they sold by the quart. How many quarts did they sell? 13. A wheat bin holds 144 bushels. If 340 pecks are taken out, how many pecks remain? How many bushels? 14. A farmer's apple orchard yields an average of 5 bushels per tree. If there are 75 trees in the orchard, Avliat is the entire yield? If he packs them in barrels, allowing 3 bushels to a barrel, how many barrels would he require ? 132 THE RATIONAL ARITHMETIC. 1. How long will it take to travel 592 miles on a bicycle at the rate of 8 miles an hour? 2. A squirrel carried into his hole 8 acorns every day. How many did he carry in 8 Aveeks? 3. Find the cost of 2 bushels, 3 pints of cherries at 4^ a pint. 4. AVhat is the weight of 8 tubs of butter, each weighing 56^ pounds? 5. What is the cost of 12 pecks, 3 quarts of peas at 8^ a quart ? 6. What is the cost of 8 sacks of barley, each weighing 112 pounds, at 8^ a pound? 7. How many pints in 53G gallons? In 987 gallons? 8. How many quarts in 498 pecks? In 789 pecks? In 586 pecks? In 379 pecks? 9. How many months will it take a man to save $1,000 if he saves $8 a month? 10. How many pecks in 2708 quarts? In 7912 quarts? In 6856 qiiarts? 11. How many gallons in 4584 pints? In 9728 pints? In 8136 pints? 12. How long will a barrel of oil containing 504 pints last, if 8 pints are burned each week? 13. Find the weight of 8 barrels of oat meal, each containing 192 pounds. 14. A fruit-dealer bought 8 barrels of apples at $2 a barrel, each barrel containing 3 bushels. He sold them at $1 a bushel. How much did he get for them? How much did he gain? 15. Allowing 30 days to a month, how many days are there in 8 months? 16. A farmer had 420 bushels of wheat. He sold J of it to one man and 304 pecks to another. How many bushels had he left ? PART SECOND. 133 1. There are 9 horses in each of 8 fields; how many horses are there in all? 2. If a person works 8 hours a day, how many hours will he work from Monday morning until Saturday night? 3. A boy was asked how many marbles he had, and replied that if he had 8 times as many he would have 56. How many had he? 4. A ship sails 8 miles an hour. At the same rate, in how many hours will it sail 88 miles? 5. At ^12 a month, how much is the rent of a house for 8 months ? 6. A clerk receiving $12 a week, spends $4 for board. If he saves the rest, how much will he have in 8 weeks? 7. A man being asked the value of his horse, said he would take $96 dollars for him although he was worth one- eighth more. What was the horse worth? 8. Mabel is 20 years old, and her sister's age is three-fourths of hers. How old is her sister? 9. At 8^ a quart, what will 6 quarts of cranberries cost? 10. A horse goes 9 miles in 2 hours; a train runs 8 times as fast. How many miles will the train run in the same time ? 11. How much is hay per ton when $88 is paid for 8 tons? 12. A horse is fed a peck of oats a day. How many weeks will 42 pecks last him? 13. If a family uses 2 quarts of milk a day, at 4^/ a quart how much will the bill amount to in 8 days? 14. How many days are there in 32 weeks? 15. If 1 jumping-rope is 6 feet long, how long are 8 such ropes together? How many yards long? 16. If 1 pint of oil costs 3^, what will 4 quarts cost? IT. A family uses 6 pints of mineral water a day. How many gallons will they use in 32 daj^s? 134 THE RATIONAL ARITHMETIC. W R t5 e E ^ G K n u 1 1 1 1 1 L^ 1. A is 9. How many 9's in B? How many in C? In D? J? K? L? To what is C equal ? D ? E ? K? L? What part of C ? K? L? E? F? G? H? I? 2. A equals 9. B equals IS. F? G? H? I? J? 8. A equals what part of B ? F? G? H? I? J? 4. 9 is what part of 18 ? What part of 27 ? 54? 63? 72? 81? 90? 99? 108? 5. B equals how many A's? What part of C? F? G? H? i? J? K? L? (). 18 is how many 9's? What part of 27? 54? 63? 72? 81? 90? 99? 108? 7. C equals how many A's? How many B's? D? OfE? F? G? H? I? J? K? L? 8. 27 is how many 9's? How many 18's? What part of 36? Of 45? 54? 63? 72? 81? 90? 99? 108? Of D? Of 3()? Of D? Of 36? E? 45? E? 45? What part of PART SECOND. 135 1. D equals how many A's? How many B"s? How many C's? What part of E? Of F? G? H? 1? J? K? L? 2. 36 is how many9's? How many 18's? How many 2T's? What part of 45 ? Of 54? 63? 72? 81? UO? 99? 108? 3. E equals how many A's? How many B's? How many C's ? How many D's ? Wliat part of F ? Of G ? H ? I? J? K? L? 4. 45 is how many 9's? How many 18's? How many 27's? How many 36's? What part of 54? Of 63? 72? 81? 90 ? 99 ? 108 ? 5. F equals how many A's? How many B's? How many C's? How many D's? How many E's? What part of G? Of H? I? J? K? L? 6. 54 is how many 9's? How many 18's? How many 27's? How many 36's? Etc. 2 12 22 32 9 42 52 62 72 6 16 26 36 9 46 56 66 76 3 13 23 33 9 43 53 63 73 7 17 27 37 9 47 57 67 77 4 14 24 34 9 44 54 64 74 8 18 28 38 9 48 58 68 78 5 15 25 35 9 45 55 65 75 9 19 29 39 9 49 59 69 79 Add the red figure to each number in the same large square. Subtract it from each number larger than itself. Multiply and divide in the same way. 136 THE RATIONAL ARITHMETIC. 1. Add upward, downward, by lines to the right and to the left: 9 9 9 9 9 9 9 9 9 8 9 7 6 9 4 3 2 3 7 8 9 6 5 9 9 8 4 6 9 7 9 9 4 3 9 6 5 8 9 6 9 9 9 2 5 4 9 7 9 5 9 3 9 8 3 8 9 6 9 4 9 2 7 2 9 7 9 5 9 3 9 9 1 8 9 () 9 4 9 2 8 2. Add, subtract and multiply 47 68 45 89 93 77 90 64 99 9 9 9 9 9 9 9 9 9 39 88 92 46 80 209 398 768 908 9 _^ _^ Jl, _^ _^ __?. _^ _5 3. Divide: 9)27 9 )45 9 )63 9 )36 9 )54 9 )18 9)72 9)108 9)90 9)81 9)99 8)96 4. 27 equals how many 9's? 54 equals how many 9's? 63 equals how many 9's? 18 equals how many 9's? 72 equals how many 9's? 99 equals how many 9's? 45 equals how many 9's? 36 equals how many 9's? 81 equals how many 9's? 90 equals how many 9's? 108 equals how many 9's? 72 equals how many 8's? PART SECOND. 137 1. 9 is 1 T of 9 is 1 2 of 9 is 1 of 9 is 1 '9 of 9 is 1 1 of 9 is 1 1 1 of 2. How many 9's in 19? In 29? How many 9's in 48 ? In 56 ? How many 9's in 39? In 65? How many 9's in 76? In 109? How many 9's in 84? In 98? 3. At siglit, name the sums: 5 6 7 8 9 4 4 7 8 9 3 9 9 is J of 9 is J- of 9 is i of 9 is 4 of 9 is ^ig- of 8 is i of 8 6 7 7 7 9 5 9 5 6 3 7 2 3 9 5 8 6 4 7 8 6 6 9 5 5 7 4 6 6 9 9 8 3 9 7 10 41 22 53 84 75 30 67 98 59 6 6 6 () 6 6 (> (> 6 6 4. At sight, name the differences: 12 15 18 17 19 16 29 25 28 29 4 6 4 6 5 4 9 3 7 10 24 26 28 26 27 25 23 28 27 29 13 12 15 14 16 14 11 15 13 16 21 22 23 24 25 27 28 26 25 24 9 6 7 8 6 9 8 9 7 1 ' 6 138 THE RATIONAL ARITHMETIC. 1. What is the cost of 4 dozen eggs at 9^ a dozen? 2. What is the cost of 6 feet of mokling, if 9 feet cost 81^? 3. How long Avill it take 1 man to do the work that 9 men can do in 11 days? 4. William earns one-ninth as much money as his father whose wages are $08 a month ; how much does William earn a month ? 5. In the front of a building there are 72 windows. In each story there are 9 windows; how many stories high is the building? 6. Jane's grandfather is 72 years of age, and Jane is one- ninth as old ; in how many years will she be 17 ? 7. How much more than $36 should a man have in order to buy 9 tons of coal at $5 a ton? 8. There are 8 rows of seats in a school-room, and 9 seats in each row; how many seats in the room? 9. Find the cost of 17 barrels of rice at $9 a barrel. 10. I Ixad 9 dozen buttons and used 88 buttons. How many were left? How much did I pay for all of them at ()^ a dozen ? 11. A steamer sails 298 miles a day. How far will it sail in 9 days ? * 12. I bought 12 barrels of flour at $9 a barrel, and sold the flour for $95. How much did I lose ? 13. At $158 an acre, what will 9 acres of land cost? 14. Alice has $11 and her father has 9 times as much and $S more. How many dollars have both? 15. A certain line of telegraph costs $985 a mile. How much would 9 miles cost? 16. What is a man's income in 9 years at $2385 a year? 17. A gentleman earns $9 a day for 8 days, and spends $8 a day for 8 days. How much has he left? PART SECOND. 139 1. How many square feet in a square yard? 2. A blackboard is 4 feet wide and 9 feet long. How many square feet in it? How many square yards? 3. Each window in a scliool-room contains 9 square feet. In 6 sucli windows there are how many square feet? How many square yards? 4. There are 9 sheh^es in a book-case; each one contains 12 books. How many books in the case? 5. One end of a desk is 9 feet from the wall, the other end is 7 feet from the opposite wall. The desk is 3 feet and 6 inches long. How far is it from one side of the room to the other? 6. A horse travels 6 miles an hour. How far will it go at the same rate, in 9 hours? 7. John has 83^. How many 9^ books can he buy, and how much money will he have left? 8. A boy pays 12^ for 3 pencils. At the same rate what will 9 pencils cost? 9. In each of 9 cars there are 57 persons. How many per- sons in the 9 cars? 10. There are 322 rails to the mile of railroad track. Plow many rails in 9 miles of track? 11. There are 9 equal lots fronting on a street 378 feet long. How wide is each lot? 12. A man owns 5 lots. The first is worth $1,929, the second $959, the third $1,195, the fourth $1,699, and the fifth $989. What is the value of the 5 lots? 13. A boy takes 9 subscriptions to the Youth's Companion at $1.75 each. How much money did he receive for them all? 11. A manufacturer sold 9 carriages at $195 each. How much did he get for them? 140 THE RATIONAL ARITHMETIC. 1 ounce 2 ounces 4 ounces 8 ounces 16 ounces 1 pound 1. Review page 78. 2. How many ounces are there in 1 pound? In 2 pounds? 3 pounds? 4 pounds? (3 pounds? 3. What part of 1 pound is 8 ounces ? 4 ounces ? 2 ounces ? 12 ounces? 4. Which weight shown on this page equals J- a pound? Which one equals -j^ of a pound ? Which ^ ? Which ^ ? 5. Which 2 weights together equal f of a pound? AVhicli 2 together | of a pound? 0. The 8 ounce weight equals Avhat part of 2 pounds? Of 3 pounds? 7. The 4 ounce weight equals Avhat part of 2 pounds? Of 3 pounds? 8. The 8 ounce and the 4 ounce weight together equal what part of 2 pounds? Of 3 pounds? 9. 100 pounds are called a hundredweight. 10. How many hundredweights are there in 200 pounds? In 400 pounds? 11. How many pounds are there in i of a hundredweight? i- of a hundredweight? |-? 12. If a grocer has different weights, as shown in the picture, which ones will he use in weighing |- of a pound of tea ? Which in weighing |- of a pound ? -^\ of a pound ? y\ ? 19 5 9 19 19 19 119 59 i 5 9 7. 9 X 3 9 "3" • T"6 • ¥ • T • T^ • T 6 • 8 * 16' 8 * 16- 13. Which different weights may he use in weighing 1 J- pounds of rice? In weighing 1] pounds? IJ- pounds? 11 pounds ? If ? PART SECOND. 141 1. There are 60 pounds of wheat in 1 bushel. How many pounds in 9 bushels V In 7 bushels? In 5 bushels? 2. 1 hundredweight of metal costs $6. What will 50 pounds cost? 75 pounds? 25 pounds? 3. What is the postage at |^ an ounce on a package weigh- ing 4 ounces? On 1|- pounds? On 3 pounds? 4. A bushel of oats weighs 32 pounds, how many pounds in a peck? In a quart? In 3 pecks? 5. A grocer weighs out 1| pounds of butter. What weights does he use? How many 4 ounce weights will he use to weigh li pounds? I pound? 2 pounds? 6. Find the value of 4 pounds and 8 ounces of pepper at 20^ a pound. 7. A grocer sells 8 packages of tea, each weighing 6 ounces ; how many ounces do all weigh together? How many pounds ? 8. A man bought GO bags of flour, each weighing 5 pounds. HoAV many hundredweights did he buy? 9. If a man buys old iron at 14^^' a pound, what will lie pay for 24 pounds? For | a hundredweight? 10. How many ounces are there in 12 pounds? 11. A farmer sold G tubs of butter averaging in weight I a hundredweight each. How many pounds did he sell ? How many ounces? 12. What is the weight in pounds of 3 packages, one weighing 2^ pounds, one ^ a pound and the other 3 pounds? What is the weight in ounces? 13. A man bought 3 packages of beans weighing 8 pounds each ; he made them into 8-ounce packages. How many packages did he have? 14. A grocer sold |^ of a pound of tea, ^ a pound of butter, f of a pound of coffee, and 1^ pounds of sugar. How many ounces in the entire sale? 142 1. THE RATIONAL ARITHMETIC. 1 X 10 — 10 X 1 2 X 10 10 X 2 — 3 X 10 10 X 3 4 X 10 10 X 4 — 5 X 10 — 10 X 5 6 X 10 10 X 6 i X 10 10 X 7 8 X 10 — 10 X 8 9 X 10 10 X 9 — A /\ n U r> ■1 ^ 2. How many lO's in A ? In B ? In C ? 3. A equals what part of B ? Of C ? 4. B equals how many A's? What part of C? 5. C equals how many A's? How many B's? 6. 10 is what part of 20? Of 30? 40? 50? 60? 70? SO? 90? 100? 110? 120? 7. 20 is how many lO's? What part of 30? Of 40? GO? 70? 80? 90? 100? 110? 120? 8. 30 is how many 20's? AVhat part of 40? Of 50? 70? 80? 90? 100? 110? 120? 9. 40 is how many 20's? How many 30's? What part of 50? Of 60? 70? 80? 90? 100? 110? 120? 10. 50 is how many 20's? How many 30's? How many 40's? What part of 60 ? Of 70? 80? 90? 100? 110? 120? 50? 60? PART SECOND. 143 1. 60 is how many 20's? How many 30's? 40's? 50'sV What part of 70? Of 80? 90? 100? 110? 120? 2. 70 is how many 20's? How many 30's? 4:0's? 50's?* 60's ? What part of 80 ? Of 90 ? 100 ? 110 ? 120 ? 3. 80 is how many 20's? How many 30's? 40's? 50's? 60's? 70's? What part of 90? Of 100? 110 120? 4. 90 is how many 20's? How maiiy 30's? 40's? 50's? 60's? 70's? 80's? What part of 100? 110? 120? 5. 100 is how many 20's? How many 30's? 40's? 50's? 60's? 70's? 80's? 90's? What part of 110? Of 120? 6. 110 is how many 20's? How many 30's? 40's? 50's? 60's? 70's? 80's? 90's? lOO's? What part of 120? 7. 120 is how man 20's? How many 30's? 40's? 50's? 60's? 70's? 80's? 90's? lOO's? llO's? 8. Add, subtract and multiply: 12 15 23 30 36 42 47 53 59 61 68 10 10 10 10 10 10 10 10 10 10 10 74 79 80 83 88 91 98 87 59 67 99 10 10 10 10 10 10 10 10 10 10 10 8. Divide : 10)30 10)50 10> 46 10)60 10 )75 10)29 10)80 10)67 10)90 10)38 10)100 10) 99 10)110 10)120 10. 30 equals how many lO's? 50 equals how many lO's? 40 equals how many lO's? 70 equals how many lO's? 60 equals how many lO's? 20 equals how many lO's? 90 equals how many lO's? 110 equals how many lO's? 80 equals how many lO's? 100 equals how many lO'sr 120 equals how many lO's? 81 equals how many 9's? 144 THE RATIONAL ARITHMETIC. 10 is 1 3 of 10 is 1 75 of 10 is 1 7 of 10 is 1 6 of 10 is 1 11 of 10 is 1 T2 of 7 is 1 7 3 or 6 is 1 1 of 4 is 1 of R i« 1 of 1 2 10 is i- of 10 is i of 10 is i or 10 is 1 of 10 is ^v of 9isl of 8 is i of 5 IS i\ of 7 is i of 9is,V or In 50 ? In 47 ? In 70? In 100? In 125 ? 2. How many lO's are there in 34? How many lO's are there in 29? How many lO's are there in 0(3? How many lO's are there in 85? How many lO's are there in 99? 3. What is the sum of three lO's and five lO's? What is the sum of four lO's and five lO's? What is the sum of six lO's and five lO's? What is the sum of five lO's and five lO's? What is the sum of six lO's and six lO's? 4. Wliat is the sum of 40 and five lO's? What is the sum of 70 and three lO's? What is the sum of 85 and two lO's? What is the sum of 33 and six lO's? What is the sum of 110 and nine lO's? What is the sum of 130 and four lO's? 5. What is the difference between 121 and six lO's? What is the difference between 111 and seven lO's? What is the difference between 98 and three lO's ? What is the difference between 143 and nine lO's? What is the diff'erence between 110 and eiofht lO's? What is the difference between 85 and six lO's? What is the difference between 93 and four lO's? PART SECOND. 145 1. If a mail works 10 hours a day, how many hours does he work in one week not inchiding Sunday? 2. How many inches in 10 feet? 3. How many eggs in 10 dozen? 4. How many months in 10 years? 5. How many square feet in 1 square yard? In 10 square yards ? 6. If there are 10 square feet of window glass in one win- dow, how many in 8 windows? 7. Mr. Reed had 70 sheep. Wolves killed three- tenths of them. How many were left? 8. How many square inches in a 10 inch square? 9. How many blocks of wood 1 foot square will be required to pave a hall that is 10 feet wide and 11 feet long? 10. How many square feet in the walls of a room that is 10 feet high and 10 feet square? 11. It is 6 miles to a village. A man goes and returns 5 days each week. How^ far does he travel in 1 week? In 3 weeks? 6 weeks? 10 weeks? 12. There are 10 rooms in a house. In each room there are 2 pictures and 3 wdndow-s. How many pictures and win- dows in the house? 13. In one car each seat will hold 5 persons, in another 6 per- sons and in another 3. In each car there are 10 seats. How many persons may be seated in the 3 cars? 11. A train of 4 cars has in the first car 45 persons, in the second 54, in the third 65, in the fourth 59. How many persons are in the train? 15. A ten story building has 10 windows in each of the first 6 stories, and 8 wdndows in each of the remaining 4 stories. How^ many windows in the entire buildiug? 16. A table is 10 feet long, 4^ feet wide. What is its peri- meter? Its area? 146 THIO NATIONAL ARITHMETIC. 1. Review page 80. 2. One dollar is written $1 or $1.00. One dollar and fifty cents is written $1.50. 3. Tlie point after tlie $1 shows that the two figures on the right stand for cents, and the figure or figures on the left stand for dollars. 4. Two dollars and twenty-five cents is written $2.25. Tliree dollars and six cents is written $3.06. Ten dollars and sixty cents is written 110.60. 5. Head: ;5.01 $9.10 $7.09 $10.20 $36.50 $30.03 $20.19 S.02 14.15 $9.13 143.75 $84.62 $13.40 $12.05 6. If any number of cents, as, for example, 25, stands alone with no dollars, it may be written 25(^, or $.25. 7. Read, $.40, $.16, $.35, $.50, $.07, $.10, $.09. 8. Write in figures: Nine dollars and twenty -five cents; forty dollars. Twenty-six dollars and six cents; fourteen cents. Ninety dollars and ninety cents; seven cents. Tliirt)^ dollars and five cents; one hundred dollars. 9. What is the sum of 1 quarter, 2 dimes and 1 nickel? Write the answer. 10. What is the sum of 3 half-dollars, 1 quarter, 2 dimes and 5 pennies? AVrite the answer. 11. If you pay for a 3-cent car fare with a quarter, in what coins may your change be given you? 12. A street-car conductor collects 72 five-c(^nt fares in one trip. How much money does he collect? 13. A girl buys flowers worth 40^/. If she has quarters, dimes, nickels and pennies, with what different coins may she pay for them ? Note. — Have dollars, half dollars, quarters, dimes, nickels and pen- nies where they may be observed and handled. Toy money will serve the purpose. PART SECOND. 14^ 1. Add: $1.55 .08 4.50 5.17 8.69 $9.76 3.72 1.31 7.75 .87 $9.30 12.10 17.68 24.33 9.77 $25.71 20.04 47.37 .75 8.10 $85.94 57.38 19.99 6.43 .98 2. Subtract: $56.29 15.25 $54.54 24.32 $13.74 7.53 $99.99 93.94 $107.60 89.10 $10.34 7.25 $45,32 22.50 $77.55 35.95 $321.76 . 145.09 $446.82 128.72 3. Multiply: $2.63 2 $16.24 3 $37.58 4 $56.17 5 $10.29 5 $207.20 7 $450.75 6 $327.06 7 $525.50 8 $290.40 9 4. Divide: 2 )$56.24 2 )$38.56 3 )$27.96 3 )$45.21 4 )1416.72 4)$892.64 5 )$125.75 5 ) $530. 50 6 )$426.84 6 )$558.72 7 )$637. 84 8 )$968.72 8 ) $656. 32 9 ) $468. 63 5. I bought a horse for $97.00, kept him at a livery stable for six months at $12.00 a month, and then sold him for $175.00. Did I gain or lose, and how much? 6. Mr. A. had $756.48. Mr. B. had $327.16 and Mr. C. had $258.92. How much did they all have together? 148 THE RATIONAL ARITHMETIC. 1 X 11 2 X 11 3 X 11 4 X 11 5 X 11 6 X 11 7 X 11 8 X 11 9 X 11 10 X 11 11 X 1 = - 11 X 2 =: _ 11 X 3 = . 11 X 4 =^ _ 11 X 5 =^ _ 11 X 6 = - 11 X 7 == _ 11 X 8 = _ 11 X =^ _ 11 X 10 = — - A /\ n U 2 How many ll's in A? In B? 3. A equals what part of B ? 4. B equals liow many A's?. n. 11 is what part of 22? Of 33? 44? 55? 66? 77 88? 99? 110? 121? 132? (;. 22 is how many ll's? What part of 33? Of 44? 55? 06? 77? 88? 99? 110? 121? 132? 7. 33 is how^ many ll's? How many 22's? What part of 44? Of 55? 66? 77? 88? 99 110? 121? 132? 8. 44 is how many ll's? How many 22's? How many 33's? What part of 55? Of m? 11? 88? 99? 110? 121? 132? TART SECOND. 149 1. 55 is how many ll's? How many 22's? 33's? 44's? What part of 66? Of 77? 88? 99? 110? 121? 132? 2. 66 is how many ll's? How many 22's? 33's? 44's? 55's? What part of 77? Of 88? 99? 110? 121? 132? 3. 77 is how many ll^s? How many 22's? 3B's? 44's? 55's? 66's? What part of 88?' Of 99? 110? 121? 132? 4 88 is how many ll's? How many 22's? 33's? 44's? 55's? 66's?'77's? AVhat part of 99? Of 110? 121? 5. 99 is how many ll's? How many 22's? 33's? 44's? 55's? ^66's?' 77's? 88's? What part of 110? Of 121? 132? 0. IIU is how many ll's? How many 22's? 33's? 44's? 55's? 66's? 77's? 88's? 99's? What part of 121? Of 132? 7. 121 is how many ll's? How many 22's? 33's? 44's? 55's? 66's? 77's? 88's? 99's? llO's? What part of 132? 8. 132 is how many ll's? How many 22's? 33's? 44's? 55's? 66's? 77's? 88's? 99's? llO's? 121's? 9. Add, subtract and multiply: 39 45 50 23 47 56 73 65 89 29 99 n nnnnniiiiiiiiii 93 70 84 38 87 49 96 27 71 59 77 11 11 11 11 11 11 11 11 11 11 11 10. Divide: 11)33 11)55 11)77 11)^ 11)44 11)66 11)59 11)77 11)69 11)110 11)88 11)121 11)99 11)132 150 THE RATIONAL ARITHMETIC. 1. 33 equals how many ll's? 66 equals how many ll's? 44 equals how many ll's? 99 equals how many ll's? 110 equals how many ll's? 88 equals how many ll's? 55 equals how many ll's? 22 equals how many ll's? 77 equals how many ll's? 121 equals how many ll's 132 equals how many ll's? 84 equals how many 7's? 2. 11 11 11 11 11 11 (] 7 5 7 s J of s I of s I of s 4- ol S yV of S yV ^^ s I of s tV of s^of s -iV of 3. How many ll's are there in 35? How many ll's are there in 28? How many ll's are there in 61? How many ll's are there in 89? How many ll's are there in 111? 4. How many ll's are there in 88? How many ll's are there in 66? How many ll's are there in 99? How many ll's are there in 55? How many ll's are there in 39? 5. What is the difference between five ll's and three ll's? What is the difference between seven ll's and four ll's? What is the difference between eight ll's and five ll's? What is the difference between nine ll's and seven ll's? What is the difference between six ll's and two ll's? 11 is J of 11 is l- of 11 is i of His i of 11 is ,V of 8 is 1 or 9 is -t of 6 is 3^2 of 8 is i of 9is i of In 57 ? In 45 ? In 79 ? In 100? In 125? In 74? In 85? In 76 ? In 65 ? In 43 ? PART SECOND. 151 1. What is the perimeter of an 11 inch square? 2. What is the area of an 11 inch square? 3. 3 loads of hay will winter one cow. How many cows will 33 loads winter? ■4. How many inches in 3 feet? In 5 feet? 7 feet? 11 feet? 5. How many square inches in a rectangle that is 11 inches long and 3 inches wide? 11 inches long and 5 inches wide? 11 inches long and 7 inches wide? 11 inches long and 9 inches wide? 11 inches wide and 12 inches long? 6. How many days in 11 weeks and 4 days? 7. Find the cost of one-eleventh of 55 sheep at 5 dollars each ? 8. What is the cost of three-elevenths of 121 cords of wood at ^5 a cord? 9. Find the cost of one-eleventh of 22 sheep at $7 each. Of three-elevenths at $9 each. 10. I paid §110 house rent and one-eleventh as much for gas. How much did I pay for both? 11. Isaac planted 132 seeds in 11 hills. How many seeds did he put in one hill? 12. How many square inches in the top of a mantel that is 11 inches wide and 48 inches long? 13. All but one-eleventh of §99 was divided among 3 people. How much did each receive? 14. How many feet of ribbon Avill be required to bind a port- folio that is 11 inches square, allowing 4 inches extra for corners? How many yards? 15. What is the perimeter of a rectangle 7 by 11 inches? What is its area? 16. It is 11 miles from A to B. How far will one travel in making 4 round trips? 152 THE RATIONAL ARITHMETIC. 1. 1 X 12 = 2 X 12 = 3 X 12 = 4 X 12 . 5 X 12 = 6 X 12 = 7 X 12 = 8 X 12 = 9 X 12 = 10 X 12 - 11 X 12 = 12 X 1 = 12 X 2 = 12 X 3 :: 12 X 4 r 12 X 5 3 12 X 6 = 12 X 7 :: 12 X 8 r 12 X 9 -- 12 X 10 12 X 11 A /\ 2. How many 12's in A? 3. 12 is what part of 24? Of 86? 48? (U)? 72? 84? 96? 108? 120? 132? 144? 4. 24 is how many 12's? What part of 36? Of 48? 60? 72? 84? 96? 108? 120? 132? 144? 5. 36 is how many 12's? How many 24's? What part of 48? Of 60? 72? 84? 96? 108? 120? 132? 144? 6. 48 is how many 12's? How many 24's? How many 36's? What part of 60? Of 72? 84? 96? 108? 120? 132? 144? PART SECOND. 153 1. GO is how many 12's? How many 24"s? 36's? 48's? AVliatpartof72? OfS4? 96? 108? 120? 132? 144? 2. 72 is liow many 12's? How many 24's? 36's? 48's? 60's? What part of 84? Of 96? 108? 120? 132? 144? 3. 84 is how many i2's? How many 24's? 36's? 48's? 60's? 72's? What part of 96? Of 108? 120? 132? 144? 4. 96 is how many 12's? How many 24's? 36's? 48's? 60's? 72's? 84's? What part of 108? Of 120? 132? 144? 5. 108 is how many 12's? How many 24's? 36's? 48's? 60's? 72's? 84's? 96's? What part of 120? Of 132? 144? 6. 120 is how many 12's? How many 24's? 36's? 48's? 60's? 72's? 84's? 96's? 108's? What part of 132? Of 144? 7. 132 is how many 12's? How many 24's? 36's? 48's? 60's? 72's? 84's? 96's? 108's? 120's? What part of 144? 8. 144 is how many 12's? How many 24's? 36's? 48's? 60's? 72's? 84's? 96^s? 108's? 120's? 132's? 9. Add, subtract, and multiply: 28 53 45 33 48 57 74 66 90 38 • 99 12121212 12 121212121212 67 89 78 49 96 50 87 29 82 59 88 12 12 12 12 12 12 12 12 12 12 12 10. Divide: 12)36 12)60 12)72 12)_28 12)49 12)_56 12)66 12)71 12)108 12)99 12)120 12)84 12)144 12)132 154 THE RATIONAL ARITHMETIC. 1. 86 equals how many 12's? 48 equals how many 12's? 24 equals how many 12*s? 108 equals how many 12's? 96 equals how many 12's? 144 equals how many 12's? 60 equals how many 12's? 72 equals how many 12's? 84 equals how many 12's? 132 equals how many 12's? 120 equals how many 12's? 121 equals how many ll's? 12 is 1 or 12 is 1 (5 or 12 is 1 8 of 12 is 1 1 of 12 is 1 1 1 of 12 is 1 1 2 of 10 is 1 9^ of His 1 8 of 7 is 1 10 of 9 is 1 7 of 12 is 1 "2 of 12 is 1 '4 of 11 is 1 6 of 12 is 1 9 of 12 is 1 1 of 9 is 1 •8 of 11 is 1 8" of 9 is 1 12 of 11 is 1 IT of 10 is 1 1 of In 4( )? In 52? In 74? In 107? In 142? 3. How many 12's are there in 49? How many 12's are there in 29? How many 12's are there in 65? How many 12's are there in 87 ? How many 12's are there in 112? 4. What is the sum of 40 and two 12's? What is the sum of 21 and four 12's? What is the sum of 23 and six 12's? What is the sum of 104 and eight 12's? What is the sum of 36 and fiA^e 12's? What is the sum of 16 and seven 12's? 5. What is the difference between 72 and two 12's? What is the difference between 96 and seven 12's? What is the difference between 100 and five 12's? What is the difference between 104 and six 12's? What is the difference between 144 and four 12's? What is the difference between 236 and three 12's ? PART SECOND. 155 1. Keview pages 82 and 83. 2. How many months old is a boy who is 7 years old? How many Aveeks old is one who is 11 months old? 3. How many months old is a boy who is 11 years old? 12 years old? 4. How many weeks in 6 months? 5. How many minutes in one-half a day? 6. How many minutes from 7.15 a. m. to 8 o'clock a. m. ? 7. How many minutes from 8 o'clock p. m. to 9.15 p. m. ? 8. How many hours from 5 in the morning until 9 at night? 9. A boy goes to bed at 9 o'clock and gets up at 6. How long is he in bed? 10. A boy plays ball in the morning from 7 until 9, and in the afternoon from 1 until 6. How many hours does he play? 11 A train leaves Chicago at 9 o'clock in the morning and arrives in Cincinnati at 6 in the evening. How many hours is it on the way? 12. A train leaves Chicago at 10.30 in the morning and reaches Buffalo at 12.20 at night. How many hours is it on the way? 13. A train leaves Burlington at 9 o'clock in the morning, and reaches Chicago at 2.15 in the afternoon. How many hours is it on the way? 14. A train leaves Peoria at 11.40 a. m., reaches Streator at 1.33 p. m., and Chicago at 4.30 p. m. How long is it on the way from Peoria to Streator? How long from Peoria to Chicago? 15. A boat leaves Chicago at 8.30 in the morning, reaches Milwaukee at 11.30, and leaving Milwaukee at 6.15 in the evening, reaches Chicago at 9.15. How many hours does it take to make the round trip? How many hours from the time the boat leaves Chicago until it returns ? J 56 THE RATIONAL ARITHMETIC. 1 hour 1 day 1 week 1 year 60 minutes 24 hours 7 days 365 days 52 weeks 12 months 1. How many minutes in 1 hour? In 2 hours? 3 hours? 5 hours? 8 hours? One half an hour? One-fourth of an hour? Three-fourths of an hour? 2. What part of an hour are 10 minutes? 30 minutes? 45 minutes? 15 minutes? 3. How many hours in a week? 4. How many weeks in 147 days? 5. A boy is 8 years and 4 months old. How many months okl is he? 6. The train leaves the station at 8.05. It is a 12 minutes' walk to the station. At what time must one start in order to catch the train ? 7. A boy leaves home at 7.30 each morning and returns from work at 6.15 in the evening. How long is he away from home? How long is he away in 6 days? 8. A train leaves the station at 7.15 and arrives in the city at 7.42 in the morning. Returning, it leaves the city in the evening at 5.40 and arrives at 6.11. How long does a man spend on the train who goes back and forth each day for 10 days? 9. A boy leaves home for school at 8.35 and reaches the school room at 2 minutes before 9. He returns home for lunch at noon, taking the same time on the way each trip. How long is he on the way in 1 day? In 5 days? 10. School begins at 9 o'clock and dismisses at 15 minutes before 12; opens at 1.30 and closes at 3.45. How long is the forenoon session? How long is the afternooB session? How long are both together? 11. If 15 minutes were allowed for recess both morniug auC afternoon, how long would the sessions be together? PART SECOND. 15 ■*/ 1. The months of the year are: 1. January (Jan.) 5. May 9. September (Sept.) 2. February (Feb.) 6. June 10. October (Oct.) 3. March (Mar.) 7. July 11. November (Nov.) 4. April (Apr.) 8. August (Aug.) 12. December (Dec.) 2. What is the second month ? Fifth month ? Ninth month ? Sixth month? Eighth month? Eleventh month? Twelfth month ? 3. Learn the order of the months by number and name. 4. Seven of the months have 31 days each, four have 30 days each and one 28 days. How many days in the year? 5. The first, third, fifth, seventh, eighth, tenth and twelfth months have 31 days, the others have 30 days, except February which has 28 generally, but in Leap year 29. 6. How many days in all of the months containing 31 days? How many days in all the months containing 30 days? 7. How many days in January? April? March? Feb- ruary? June? August? Septeml)er? July? Octo- ber? November? December? 8. How many days in the first 3 months of the year? In the last 3 months of the year? 9. How many days in the first 6 months of the year ? In the last 6 months of the year? 10. How many days difference between Ihe first 6 months and the last 6 months of the year? 11. How many days in February, March and xlpril together? 12. In April, May and June together? 13. In July and August together? 14. In September, October and November together? 15. A man left home in the morning the first day of April and returned home in the evening the last day of July. How many days was he away from home? 16. How many days in the first, third, fifth, seventh and eighth months together? 158 THE RATIONAL ARITHMETIC. 1. If $24 pays for 8 yards of silk, how many yards can be bought for $12? 2. What 5 equal numbers make 75? 3. How many oranges worth 4^ each must be given in exchange for 16 lemons worth 3^ each? 4. William paid half a dollar for a reader, a quarter of a dollar for a music book and a dime for a tablet. How much did he pay for all? 5. If 4 lemons cost 3^, what will two dozen lemons cost? 6. In 800 pints how many quarts are there? Hov/ many gallons ? 7. It requires 64 rods of fence to go around a square lot. How long is one side of the lot? 8. What is the rent of a house for a year at $12 per month ? 9. What is the cost of 3 bushels of corn at 10^ a peck? 10. A boy worked 8 days for 50^ a day and then had |6. How much had he before beginning the work? 11. Edward can make a kite in 8 days, working 3 hours a day. How many days will it take him if he works 6 hours a day? 12. How much did it cost Lewis to visit the World's Fair 12 days, if he paid each day, 20^ for car fare, 50^ f(^r his admission ticket and 40^ for lunch ? 13. How many feet are there in 5044 inches? 14. Find the entire cost of 11 pounds of tea at 60^ per pound; 25 pounds of sugar at 7^; 124 pounds of soap at 10^; and 18 barrels of flour at $8.37 per barrel? 15. A man bought a horse for $85.50, and a carriage for $53.80 more than the cost of the horse. What was the cost of both? 16. A farmer raised 8750 bushels of wheat. He sold one half of it to one man and 4200 bushels to another man. How many bushels did he have left? PART SECOND. 150 1. Harold has 86 specimens in liis stamp album. His father gave him 12 more. How many had he then ? 2. A street car conductor collected 12 5 -cent fares and 12 3-cent fares on one trip. How much did he collect? 3. One l3oy can jump 3^ feet high; another boy can jump 12 inches Jiiglier. How high can the second boy jump? 4. A railroad track is made at the rate of 12 miles a month. How many miles of track can be made at the same rate in one year? In IJ years y In 2^ years? 5. '.>Tn ball cartridges were distributed among the members of a com])any of soldiers. Each received 12 car- tridges and there were 10 left. How many soldiers were there in the company? 0. A lady spent 54 months away from home. How many years was she away ? 7. How many minutes from (5 o'clock in the morning until 6 at night? 8. How many yeai's are 9,87G months equal to? 9. A boy left home at tlie age of 13. He was gone until he was 55. How many months was he away from home? 10. At 11 cents a dozen, what will 180 Inittons cost? 11. A tailor uses 000 buttons every month, and puts 12 on each garment. How many garments does he make? 12. Mr. Brown's salary is ^2,500 a year. How much is it a month ? 13. Find the cost of 12 gallons and 2 quarts of syrup at 11 cents a quart. 14. On each side of the street there are 09 trees. What did it cost to plant them, at 12 dollars each? 15. For 7 yoke of oxen I paid $84 a yoke and sold them all for .^875. Did I gain or lose, and how much? 16. 12 dozen eggs cost $2.40. What will 5 dozen cost? 17. How many square inches in a square foot? 160 THE RATIONAL ARITHMETIC. 1. If 4 tons of coal cost $24, what will be the cost of 2 tons ? 2. How many bushels are | of 54 bushels? 3. In how many days can 4 men dig a ditch that 2 men can dig in 12 days? 4. What is the cost of 2 pecks of beans at 3^ a quart? 5. George now has $50. How much will he have if he saves $7 a week for 4 weeks ? 6. If a man buys old iron at ^^ a pound, how much will he pay for 48 pounds ? 7. What are 4 pecks of cherries worth at 10^ a quart? 8. At 10^ a pound, how many pounds of grapes can be bought for 90^' and 30^' together? 9. John earned | as much as Henry. If Henry earned 32^, how much did both earn ? 10. What will 2 gallons of oil cost at 6(K/ a quait? 11. How many feet in a line 512 inches long? 12. I sold a watch that cost $75 so as to gain | of the cost. How much did I sell it for? 13. Find the difference between nine thousand eighty and seven thousand seven hundred six. 14. How many tablets at 9^- each can be bought for $82.08? 15. How many years will it take a man to save $2880, if he saves $12 a month? 16. A building is 240 feet long and 200 feet wide. How many yards is it around the building? 17. What is the difference in value between 12 lots at J^225 each and a house at $9500? 18. There are 96 boxes of soap, each containing 60 pounds. How many ])ackages of 4 pounds each (^an be made from the soap? 19. How long will a barrel of oil, containing 51 gallons, last, if 2 quarts are burned each day ? PART SECOND. IBl L What will be the cost of 50 feet of rope at 4^ a foot? 2. I pay for room rent $S a month, and for office rent 19 a month. How much do I pay a year for both? 3. How many r)alls weighing 8 pounds each will equal in weight (i balls weighing 12 pounds each? 4. How many pounds of grapes at 4^ a pound must be given for a dozen apples worth 3^ each? 5. AVhat will be the cost of 6 sheep, if 12 sheep cost $60? 0. How loni; will it take 6 men to do the work that 5 men can do in 12 days? 7. A bushel of wheat weighs 4 pounds more ihan a bushel of corn. What is the difference in weight between 845 bushels of wheat and 845 bushels of corn ? 8. Four loads of coal weigh respectively, 194H pounds, 2104 pounds, 1852 pounds and 2468 pounds. If the coal were divided equally among 5 families, how many pounds will each family receive? 9. In tiling a hall, 4878 tiles were l)ought, but two-ninths of them were returned. How many tiles were used in tiling the hall ? 10. How many strips of carpet one yard wide will be required to cover a floor that is 27 feet long and 18 feet wide? How many yards of carpet? 1 1 . How many square inches in the top of a table three feet square ? 12. AVliat will 11 copies of Robinson Crusoe cost at 38 cents per copy? 13. How many pews in a church that will seat 760 persons, if 5 persons can be seated in each pew? If each pew will hold only 4 persons? 14. I can buy a quart of cherries for 12 cents. At that rate, what should I pay for 7 bushels? 162 THE RATIONAL ARITHMETIC. AVEITING AND READING NUMBERS. 1. 0, I, 2, 3, 4, 5, (), 7, S. 1) 2. How many diffei-ent ciiaracters are given above? All numbers, no matter liow large, may be represented by these figures. 3. 243 Reading tlie 3 alone we say 3 ones. Reading tlie 4 alone we say 40 or 4 tens. Reading the 2 alone we say 200 or 2 hundreds. 4. If we were to write above each figure a separate name it would appear:) i/i a i/i w n p] oj w ^ § 2 4 :^ But if we were to call these all ones, we would read it as 243 ones or units. 5. How Avould you read 3,243? (1 This new figure, 3, placed before the other nundjer, we call thousands. How then would you read 10,243? 7. Large numbers are divided into periods of 3 places each, thus 243 is one period. 3,243 has 2 periods. These periods are separated l)y commas, for convenience, as f olloAvs : OlK'S a 111 C!j (H Ifl ^3 , P! fl W w O J5 3 lace the 8 in the ones' column of the sum, 1879 and the 1 ten above tens' column. 4195 Adding tens, 9 + 7 + (J + 1 = 23 tens, or 2 8638 hundreds and 3 tens; ])lace the 3 tens in tens' column in tlie sum, and the two hundreds above hundreds' column. Adding hundreds, l-\-H-\~^-\-2=W hun- dreds, or 1 thousand and 6 hundreds; place the 6 hundreds in hundreds' column in the sum, and the 1 thousand above thousands' column. Adding thousands, 4 + 1 4- 2 + 1 ~ 8 thous- ands, which place in thousands' column in the sum. 2. In the same way add : 1729 3546 1892 1563 2623 1089 2703 2354 1273 4203 2427 1206 721 3145 4162 2098 461 5314 4257 5147 605 1431 1754 2574 256 1714 2425 2804 947 6126 1245 4678 6924 3987 3004 2753 825 3256 963 728 4058 289 1388 1268 1367 2837 1256 874 1452 5234 1834 2756 1234 473 1498 3257 3. A man had 5 farms. In the first there were 160 acres, in the second 88 acres, in the third 275 acres, in the fourth 96 acres and in the fifth 324 acres. How many acres in the fiA^e farms? 4. There are 375 pupils in one school building, 640 in another, and 583 in anotiier. How many in the three buildings ? 166 THE RATIONAL ARITHMETIC. 1. A man paid $2684 for a house, $398 for fiirnitiire and $265 for a horse and carriage. How much did he pay for all ? 2. A lot cost $1540, the sidewalk $116, the house $6535, the barn $975. How much did they all cost? 3. A ship sailed 234 miles the first day, 275 miles the second day, and the third day as far as in the first two. How far did it sail in the three days? 4. Three vessels are loaded with copper. The first carries 347 tons, the second 1256 tons, the third 4384 tons. How many tons do they all carry? 5. From Chicago to Detroit it is 284 miles; from Detroit to Buffalo, 251 miles; from BufPalo to New York City, 410 miles. How far is it from Chicago to Buffalo? How far is it from Chicago to New York? 6. From Chicago to St. Louis it is 282 miles; from St, Louis to Kansas City, 277 miles. How far is it from Chicago to Kansas City by the way of St. Louis? 7. From Chicago to Burlington it is 206 miles; from Bur- lington to Omaha, 296 miles; from Omaha to Lincoln, 39 miles; from Lincoln to Denver, 484 miles. How far is it from Chicago to Omaha? From Chicago to Lincoln? From Chicago to Denver? 8. From Chicago to Milwaukee it is 85 miles; from Mil- waukee to La Crosse, 281 miles; from La Crosse to St. Paul, 131 miles; from St. Paul to Minneapolis, 10 miles. How far is it from Chicai^^o to La Crosse? From Chicago to St. Paul? From Chicago to Minne- apolis? From Milwaukee to St. Paul? 9. From the above distances, find how far it is through Chi- cago from New York to St. Louis. From New York to Kansas City. To Omaha. To Denver. To St. Paul. To Milwaukee. PART SECOND. 167 1. A man IiRvS 156 books in one case, 275 in another and in a third 145 more than in both of the others. How many books has he in the B cases? 2. A factory made 540 bicycles in January; 87 5 in Febru- ary; 643 in March, and 856 in April. Hoav many did it make in the 4 months? 3. A man delivered 4 loads of coal. In the first were 2150 pounds; in the second, 1975 pounds; in the third, 2260 pounds, and in the fourth, 2315 pounds. How many pounds were delivered in the 4 loads? 1. A carpenter was paid it^l375.50 for building one house; $3240.75 for another; '^1658.50 for a third. How much did he receive for building the 3 houses? 5. The cash sales of a certain merchant were on Monday, $253.25; Tuesday, $167.54; AVeduesday,- $365.80; Thursday, ^453.65; Friday, $385.42, and on Saturday, $563.85. Wliat were the cash sales for the week? 6. A man bought a lot for $2154. He paid $453 for grading and digging a cellar, and $165.40 for a sidewalk. He built a house to cost the same amount that he had spent for the lot and all improvements. How much did he invest in the lot and house? 7. A man's salary was $2300 a year. He also received $135 interest, $426 rents, and from all other sources a sum equal to these three amounts. AVhat was his annual income ? 8. The yield from one field of wheat was 275 bushels; from a second, 562i bushels; from a third, 458 bushels, and from a fourth, 346|- bushels. What was the entire yield from the 4 fields? 9. From A to B is 416 feet and 6 inches; from B to C, 375 feet; from C to D, 456 feet and 6 inches. How far is it from A to D ? 168 THE RATIONAL ARITHMETIC. 1. Eeview page 93. 2. Subtract 247 from 5() i. ' 7 ones cannot be subtracter! 564 = 550 + 14 from 4 ones. Change 564 to 247 = 240 + 7 550 + 14. Subtracting, 7 3jQ _l_ rj __ p^^^ from 14 irr 7; 240 from 550 =:310. 310 + 7 = 317. 3. A simpler way to wiite the numbers in subtraction is to place above each figure that figure to which it is to be changed. 4. In this way subtract the above numbers, 5 j4 7 cannot be subtracted from 4. 564 must be 564 changed to 550 -+- 14. The 5 in hundreds' place 247 stays unchanged; the 6 tens become 5 tens, — 317 place the 5 above the 6 tens; the 1 ten left from the 6 tens is added to the 4 to make 14,— so place the 14 above the 4. Subtracting: 7 from 14 = 7; 4 tens from 5 tens = 1 ten; 2 liundreds from 5 jiundreds = 3 hun- dreds. 5. Subtract 4526 from 6352. 5,i3,4,r2 ^> cannot be subtracted from 2. 5 tens and 2 6352 must be changed to 4 tens + 12; place the 4 452() above the 5 tens, and the 12 above the 2. 1826 Snl)tracting: 6 from 12 = 6; 2 tens from 4 tens = 2 tens. But 5 hundreds cannot be subtracted from 3 ]iu)idreds. 6 thousands and 3 hundreds must be clianged to 5 thousands + 13 hundreds; place the 5 above the 6 thousands and the 13 above the 3 jiundreds. Again subtracting: 5 hun- dreds from 13 hundreds = 8 hundreds; 4 thous- ands from 5 thousands = 1 thousand. PART SECOND. ini) 1. Subti'Hct: 572 744 683 567 452 334 695 246 527 256 439 326 128 478 2. Subtract: 4283 3172 7395 6476 5746 8374 9547 2657 1854 5868 3849 2828 5407 5618 .S12 2 16 Subtract 4687 from 9374. T cannot ])ft subtracted from 4. 7 tens and 4 ^,fi4 must be changed to 6 tens + 14; place tlie () 9 3 7 4 above tlie 7 tens, and the 14 above the 4. 46 8 7 Subtracting: 7 from 14 = 7. 4 () g 7 But 8 tens cannot be subtracted from 6 tens. 3 hundreds and 6 tens must be changed to 2 liundreds -\- 16 tens; place the 2 above the 3 Jiundreds and tlie 16 above the 6 tens. Subtracting: 8 tens from If) tens = 8 tens. But 6 liundreds cannot be subtracted from 2 hundreds- 9 thousands and 2 hundreds must be changed to 8 thousands + 12 hundi'eds; place the 8 above the 9 thousands and the 12 above tlie 2 hundreds. Subtractino-: 6 hundreds from 12 hundreds = 6 hun- CD dreds; 4 thousands from 8 thousands = 4 thousands. 4. Subtract: 4352 6234 8132 9457 5321 3324 7563 2676 1395 5786 3869 1867 1657 2786 8967 8241 7241 7294 7182 9256 6842 3429 3819 39s 5076) 3647 7498 3715 7586 6493 4250 8593 5721 5345 3248 4729 7279 3809 2675 3629 170 THE RATIONAL ARITHMETIC. 1. A farm cost $3215. The buildings cost $627 less than the farm. How much did the buildings cost? 2. One railroad has 5214 miles of track; another has 2767 miles of track. How much more track has the first than the second? o. A gentleman's income one year w^s $1985 and the next year it was $2140. How much greater was his income the second year? 4. Two vessels start fi'om tlie same point at the same time and in the same direction. The. one travels sf|iiHre feet less; how many square feet in the second room? 2. A gentleman's salary is $2(>5() a, year; it' liis expenses for the same time are §2025, liow much does he save in one year ? o. The land of a farm is valued at $5785 and the huildiiigs on it at §2450. How inucli more is the land worth than the buildings? 4. One farmer raises 7519 bushels of corn; another i)H[H') bushels; how much more corn does the first man raise than the second? 5. One soldier spent 8 years and 5 months in the army; another spent 2 years and 7 months; how many months longer was the first soldier in the army than the second? 0. In buying horses a man paid §120 each for two horses and $105 each for three others. How^ much less did the first two toi^ether cost than the last three toirether? 7. One tank of water holds 200 barrels; a second taidv holds 185 barrels; a third 150; how much more does the first tank hold than the second? Than the third? How much more do the first and second together hold than the third? The second and third together than the first? 8. If on(5 ship sails 045 miles in 3 days, and another sails 717 miles in the same time, how mach farther does the second sail than the first? At the same rate, how much farther would it sail in one day ? In 9 days ? 9. The expenses of one boy in college were $755 a year; the expenses of another boy for the same time were §105 less; of a third boy for the same time §150 less than those of the second. What were the expenses of the second and third boys? 173 THE RATIONAL ARITHMETIC. 1. Beview page 95. 2. Multiply 4, 6, 8, 10, 3, 5, 7, 9, 11, each by 10. In each case, wlnit do you do when multiplying by 10? n. Multi[)ly 14, 25, 73, 243, 549, each l)y 10. 4. To niulti|)]y one nund)er by finother number ending with on(? or more ciphers, is (M]uh1 to multiplying by the left hand figures and adding the ci})hers to the answer. 5. In this way multiply 24 by 20. Place the 20 so that the 2 comes beneath the 4 of 24 24, leaving the ci])her to the right, to be placed at 20 tlio right ot* the answer. 480 Multiplying: 2 X 4 == 8; 2x2 = 4; add the cipher, and we have 480. ('). Multiply: 84 90 75 68 237 485 379 946 20 ;'>() 40 50 00 70 SO 90 37 49 54 124 272 234 563 847 200 300 400 500 600 700 800 900 7. Multiply 24 by 13. 24 Since 13 is 10 + 3, multiplying 24 by 13 13 e(j[uals the sum of 24 X 3 and 24 X 10. 72 24 X :^> 240 24 X 10 312 8. Multiply 76 by 15. 76 76 X 15 = 7(] X 5 and 7() x 10. 15 380 76 X 5 760 76 X 10 1140 PART SECONIJ. 173 1. Multiply 53 by 24. 53 53 X 24 = 53 X 4 and 53 x 20. 24 212 53 X 4 1060 53 X 20 1272 2. Multiply 134 by 45. 134 134 X 45 = 134 X 5 and 134 x 40. 45 070 134 X 5 5360 134 X 40 6030 3. 67 35 50 76 145 476 308 714 974 23 32 43 53 37 27 83 75 523 416 312 206 102 560 345 234 630 67 22 51 34 27 46 35 18 42 297 267 285 526 808 132 114 125 863 28 35 19 25 36 47 66 48 62 169 273 286 299 473 308 315 651 943 13 44 88 120 62 73 160 23 92 4. School is in session 6 hours a day. How many hours is it in session during 26 weeks of 5 days each? 5. There are 95 rows in a potato field,- if it takes 2 bushels to plant one row how many bushels will it take to plant the entire field? 6. A ship can sail 225 miles a day in fair weather, and 160 miles a day in stormy weather. How many miles can it sail in 7 days if 3 of these days are stormy ? 174 THE RATIONAL ARITHMETIC. 1. A merchant buys 4 dozen pairs of slioes at $2.25 per pair. How much did they cost? 2. A boy reads one book of 31 G pages every 2 weeks during the year. How many pages does he read in the year? 3. There are 189 teachers in the schools of a city. Each one lias 49 scholars enrolled. How many scholars are there in the city? 4. A lot is 195 feet long and 53 feet wide. How many square feet does it contain? 5. A train runs 37 miles in an hou)-. How far will it run in two days at the same rate? 6. A man bought 37 horses at $09 each. How ranch did they cost him ? 7. A merchant bought 149 rolls of carpet. Each roll con- tained 68 yards. How many yards of carpet did he buy ? 8. There are 8 cars an hour on a street car line, and each carries 3G persons. How many persons ride on the road from (> o'clock in the morning until G in the evening ? 9. A conductor collects 27 5^' fares, and G 3^^ fares on each trip for 9 trips. How much money does he collect? 10. A ]>oy gets $3.75 a week and spends 2V)^' each week. How • much money will he have at the end of IS weeks at the same rate? 11. A boy sells 29 papers each day G days in a week. How many papers does he sell in a year? 12. If there are 17 apples in half a peck, how many apples are there of the same size in 13 bushels? 1)^ A miller bought 118 bushels of wheat at 78^/ a bushel. How much did it cost him? 14. A boy makes up a club of 17 subscribers for Har])er's Young reo])lo at $1.G5 each. How much money should he collect? PART SECOND. 175 What is the cost of the foHowiiig articles? 1. 138 pounds of creamery butter at 18^/ a pound? 2. 215 pounds of dairy butter at ITr/- a pound? 3. 348 dozen strictly fresh eggs at 9^f a dozen ? 4. 48 bushels of new potatoes at 85^/ a bushel? 5. 464 pounds of turkeys at 8?// a pound? (*). '-*>7S pounds of chickens at D^- a pound? 7. 17 barrels of choice apples at $3.25 a bai-rel? 8. 21) barrels of common apples at Jjj>2.35 a barrel? *). ()7 bunches of bananas at 78^- a bunch? 10. 29 boxes of lemons at |2.75 a box? 11. 19 boxes of California oranges at $1.95 a box? 12. 13 crates of pineapples at $3.75 a crate? 13. 23 crates of tomatoes at $2.35 a crate? 14. 17 barrels of sweet potatoes at $3.75 a barrel? 15. 378 pounds of white sugar at 44^/ a pound? If). 456 pounds of yellow sugar at 4y- a pound? 17. 17 bags of coffee at $5.83 per bag? 18. 14 tons of timothy hay at $9.50 a ton? 19. 275 bushels of barley at 43^- a Imsliel? 20. 58 bushels of No. 1 wheat at $1.05 a bushel? 2i. (;5 bushels of No. 2 wheat at 98^/ a ])usJiel? 22. 165 bushels of No. 1 corn at 42^/ a busliel? 23. 235 bushels of No. 2 corn at 39^- a bushel ? 24. 256 bushels of white oats at 344^' a bushel. 25. 27 bales of cotton at $6.34 a bale? 26. 47 barrels of flour at $(> 50 a barrel ? 27. 39 bags of bran at $1.35 a bag? 28. 464 pounds of corn meal at 1^^ a pound? 29. 19 barrels of buckwheat flour at $3.25 a barrel? Note. — These problems may be varied each week, or (nich month, Ijy taking the market quotations in the newspapers and substituting the prices quoted for those given in the problems. 176 THE RATIONAL ARITHMETIC. 1. Review pages 98 and 99. 2. What is i of 992 ? 16,32 Change 9 hundreds and 9 tens to 8 hundreds ft\^QQQ ^^^^ ^^ tens. 1^ of 8 hundreds is 1 hundred. — - — Change 19 tens and 2 to 16 tens and 32. -J of 1-"^ 16 tens is 2 tens; J of 32 is 4 3. What isyV«f ^9^2? Chansre 59 hundreds and 6 tens to 55 hun- 44, 22 55, 46 ^ -i \ ,^f^r>,^ dreds and 46 tens. -:rV of 55 hundreds is o 11) 5952 111 hundreds. ^^^ Change 46 tens and 2 to 44 tens and 22. -^ of 44 tens is 4 tens ; y^y of 22 is 2. 4. What is J^r of 7741 ? Change 77 hundreds and 4 tens to 72,^^^ 72 hundreds and 54 tens. J.- of 72 12)7741 hundreds is 6 hundreds. 645 1 xem. Change 54 tens and 1 to 48 tens and 61. ^ of 48 tens is 4 tens. Change 61 to 60. -^.^ of 60 is 5. The figure that is left over in an uneven division, as the 1 here, is called the remainder, and is placed to the right of the answer. 5. Divide: 6 )1764 7)2269 8 )2936 6 )2514 7 )1624 8 )3387 9 )2925 6 )1318 7 )2338 8 )3656 9 )8892 6 )5544 7)6475 8)7576 11)4631 10)2670 8)9352 9)3978 9 -* • 12 )2785 11 )7857 10 )4763 9 )3565 10 )5780 12 )5256 8)1032 11)7078 12)6888 11)8613 9)3288 12)8676 PART SECOND. 177 1. At 80^' a gallon, what is the value of one quart? 2. How many years do 1728 months equal? 3. If 8 gallons of syrup cost §^12. 80, what does 1 gallon cost? One pint? •i. A boy in school for 7 years and -t montlis studies history during one-eighth of the time. How many months does he study history? 5. A man pays $50 a month for rent, and J as much for gas. How much does he pay for both? 6. A grocer sold 6 pounds of tea for $4.80. How much did he get a pound for it? How much an ounce? 7. A person bought land for $4572, he sold it for ^r more than it cost; for how much did he sell it? 8. How many cans holding 5 pounds each can be filled frojn 2 hundredweights of coffee? D. A girl divided one-third of 195 nuts e(|ually among 5 friends. How many did each re(;eive? 10. How many feet long is a platform 720 inches long? 11. In a fire a man lost one- twelfth of his goods, all of which were valued at $9,876. How many dollars worth uii goods did he lose? 12. A farmer owning 1,272 acres of land divided it into 2 equal parts; one of these parts he again divided into 3 equal parts, giving one of these parts to each of his 3 sons, and keeping the rest himself. How many acres had he left? How many acres had each son? 13. A book case contained 203 books, each of the 7 shelves containing the same number of books. How^ many books were there on a shelf? II. A man sold 11 bicycles for $195. They were all sold for the same price. For how much did he sell each one? 15. A man sold 9 horses .iov $783, receiving the same price for each one. For how much did he sell each horse? ITS THE RATIONAL ARITHMETIC. 1. 2. 3. 4. 0. (). 7. 8. 1). 10. 11. 12. 13. 14. 15. 16. 17. 18. 11). 20. 21. 22. 23. 24:. 25. 26. How many ^'s? ^"s? tV/^? What part of O = A ? AVliat part of A = B ? What part of B = C ? What part of C = D ? B = Avhat ])art of O? C = wha,t part of OV 1) = what ])art of O? How many A's — ()? How many B's — O? HoAv many O's = O? How many D's = O? In 1 how many 4'sV What part of 1 is 4^ ? AYhat part of 4^ is ^? What part of -J- is |? What part of I is J ? AVhat part of J is y\; ? WJiat part of |- is -/,. ? What part of l- is -^^^ ? J- = how many |'s? How many -^'s? What is the sum of I and ^? AVhat is the sum of |- and J ? What is the sum of 4, \ ai]d ^ ? What is the sum of \ and y\. ? AVhat is the sum of 4 . J, \ and y^g ? Wliat is the sum of \ and -^^ ? 1 'q9 T 6 S ' PART SECOND. 179 1. E is what part of O? 2. F is what part of E? What part of O? 3. G is what part of E? Of E? Of Oy 4. How many E's = O? 5. How many E's — O? (). How many O's — O? 7. In 1 liow many ^'sV J's? ^Vs? 8. .V — how many J.'s? 1). V — how many ^'s? 10. i = liow manv ,'.,'s? 11. 1 z=i liow many ,Vs? 12. AVhat is tlie sum of ?, and I ? in. Wliat is the sum of J ami ;., ? 1-1. Wliat is tlm sum of J and ,'o ? 15. What is tlio sum of .l, ,1 and -,\, ? If). H is what part of OV 17. I is what pari of HV What part of O? 18. J is what pari of I V Of H ? Of O? 111. How many H's = 0? 20. Hi)w many T's =^ O? 21. How many J's = O? 22. In 1 liow many J/s? ^V's? 23. I = how many J,'s? 24. J) = how many iV'^^^ 25. J = how many /h's'i^ 2f). .', = how many /«'s? 27. I = how many tb'*^'^ 28. What is the sum of J and ?, ? 29. What is the sum of J and -,^^^ ? 80. What is the sum of i and yV? 31. What is the sum of ^, \ and -^-^7 32. What is ^ of i ? 33. What is i of ^? 18C TDK RATIONAL ARITHMETIC. 1. What is the weight o£ 4 packages together, the first weighing -J- of a pound; the second, ^ of a ponnd; the third, I of a pound; and the fourth, 1| pounds? 2. A tailor uses 4^- yards of chitli for a coat; If; yards for a vest; and 3^^^ yards for a pair of trousei's. How many yards does he use for the suit? 8. A man sold 3 J pounds of butter to one customer, 2i pounds to another, and 4| to a third. How many pounds did he sell to all three? 4. A lady spends i of the year in the city, } of the year at the seashore, and the rest of the year in traveling? AVhat part of the year does she spend in traveling ? 5. From a piece of cloth 15 yards long, 8^- yards were sold at one time and 2 J yards at another time. How many yards Avere sold in all? Hoav many yards were left? G. A baker having 5 dozen biscuits, sold 14 dozen to one man, and 2J dozen to anotlier. How many dozen did he sell in all? How many had he left? 7. |- of John's kite string is whip-cord, the rest is cotton string in 2 pieces, the first piece is J as long as the whip-cord. AVliat part of the entire string is the first piece of cotton string ? Tlie second piece ? 8. A grocer having | of a dozen of pineapples, sold l of them. What part of a dozen did he sell? 0. One boy stays in the country ^ of each year, a second boy stays J as long as the first boy? What part of the year does the second boy stay? 10. How many boxes holding \ of a pound of candy each, can be filled from l- a ])ound? From | of a pound? From 1^ pounds? 11. A man bought 1\ pounds of nuts and divided them equally among his 4 children. What part of a pound did each receive ? PART SECOND. ISl 1. A boy bought at the grocery 1 pound of sugar, 1^ pounds of butter and -^ pound of tea. How many ounces did the three weigh together? 2. A man bought 8 J pounds of sugar and returned 12 ounces of it. How many ounces did he keep? 3. A grocer put 5 pounds of sugar into 2 equal packages. How many ounces in each package? 4. A woman bought at the grocery 1| pounds of butter at 24^ a pound ; a quarter of a pound of tea at 60^ a pound and 4 pounds of sugar at 5|^ a pound. How much is her bill? 5. A clerk sold one customer 7 yards of cloth at 80^/ a yard; 9 yards of ribbon at l&f a yard and | a yard of velvet at $1.50 a yard. AVhat was the amount of his sale? 6. A man bought a hatchet for 75^. a saw for $1.25, 6|- pounds of ] jails at 4^ a pound, and 2 dozen screws at 9^ a dozen. What was his bill? 7. A grocer bought 3 barrels of sugar containing 198 pounds each, at 4^ a pound; a box of tea containing 23 pounds at 45^ a pound, and 2 sacks of coffee containing 75 pounds each at 20^ a pound. What was his bill? 8. A merchant bought 3 dozen pairs of shoes at $2.25 per pair, one dozen at $2.50 a pair, and one-half dozen at $2.75 a ])air. How much was his bill? 9. A bookseller bought 50 books at S&f each, 2 dozen boxes of paper at 13^ each, 9 dozen pencils at 11^ a dozen. What was his bill ? 10. Eailroad fare is 3^ per mile. From Chicago to Aurora it is 37 miles; from Aurora to Galesburg, 120 miles; from Galesburg to Burlington, 43 miles. What is the fare from Chicago to Aurora? From Aurora to Galesburg? From Galesburg to Burlington? What is the fare from Chicago to Burlington? 182 THE RATIONAL ARITHMETIC. 1. A man oavijs a lot ou wliicli ho builds 2 houses. The first is 244^ feet wide and 68 feet knitj^; the second is 25 feet wide and ()2l feet long. AVliat is the area of tlie ground covered hy the two houses V 2. The lot is 125 feet long and ()0 feet wide. What is the area of the ijround not covered ])V tlie houses? 3. A street is i)()() feet Jong and (>() feet wide; there is a sidewalk 7 feet wide on each side. What is the area of the remainder of the street? 4. A railroad runs a train of 3 cars e\er)' 30 minutes from (J o'clock ill tli(! morning until <> in the evening. How many cars run over the track in the 12 hours? 5. A man mails 40 letters requiring 2^/ postage each, 375 circulars requiring 1^/- postage cjicIj, and 30 [)ackages Avhich require 4^/- each. What is the cost of the postage on the whole? 0. A man subscribed for the Youth's Com[)anion for one year at $1.75, for St. Nicholas for 6 months at $2.50 a year, for the Century for 3 months at $4 a year and for McClure's for 18 months at $1 a year. How much must he pay for all the subscriptions? 7. A boy bought 24 1-cent papers at j^ each, 16 2-cent papers at 1^^ each and 5 10-cent magazines at 7^ each. He sold his entire stock at regular prices. How much money did he make? 8. A boy gets $3.75 for a week's work; lie pays 10^ each day for lunches, buys a ball for 15^/ and a stamp album for 75^. How much money does he have left at the end of the week? 9. A man gets $17.50 a week for four weeks. In that time he pays $11 for rent, buys half a ton of coal at $7.50 a ton, pays $12.75 for groceries and $().03 for dry goods. How much money has he left from his salary? PART SECOND. 183 1. 48 men dig a celhir in IS days. In how many days could 12 men liave dui; itV 2. How many ^-pound [)ackages can be made from 18 chests of tea, each containing 60 pounds? 3. How many pounds of sugar at G^ a ])ound will 0(pial iji value 258 gallons of syrup at 4(K/ a gallon? 4. A merchant exchanged 70 barrels of sugar at .S22.')0 p(;r l)arrel for flour at §5 per barrel. How many ])arrels of flour did he receive? 5. If 250 desks which cost $0 each are sold for §12 each, what will be the gain? <). AVliat will 144 quarts of strawberries cost at 50^/ a peck? 7. What is the difference between 829 tons and -^.^ of 9b48 tons ? 8. Mr. Monroe s[)ends i^l39.15.25 more in Februarv than in Jfuiuarv, and $15.25 more in March than in February. How much does he spend in all ? 9. A gentleman paid for a ])urchase with a $5 bill, mikI received back in change one half-dollar, 8 qunrters, 2 dimes and 2 nickels. What was the amount of his change? What was the amount of his purchase? 10. Find the distance in inches around a room that is 18 feet long and 14| feet wide. 11. A woman received §10,000 for a farm. She gave $10(M) to a church, $500 to a school, and §2980 to a hospital. How much of the money had she left? 12. A carpenter bought 464 feet of lund^er at cme time and ^ as much at another time. How many feet did he bu}' in all? 13. There are 387 squares of marble in the floor of the dining- room and seven-ninths as many in the parlor floor. How many squares in the parlor floor? How many in both floors? 184 THE RATIONAL ARITHMETIC. 1. A man paid $24 for a suit of clothes, -J as much for a pair of shoes, J as much for a hat. What was the cost ol the entire outfit? 2. A man paid for his house $48(50; the h)t cost him J as much as the house; the grading, fencing and street cost J as much as the lot. WJiat did the three cost him? 3. A bookseller sold $128 worth of hooks in one day. They cost him L less tlnm he sold them for. How much was liis profit and what did the books cost iiim ? 4. A bookseller sold 64 books at 12^^/ each, 48 ])ooks at 15(/- a linea]' foot for making a street. What will ])e tlie cost of a, ([iiMi'ter of a mile of such a street? 7. A ))oy I'ode 7^ miles on his wheel. How many rods did he ride? 8. It is HS yai'ds west from the door of Jolm's house to the schooh If he went to tlie store 45 yards east and then to school, how many yards did he walk? How many feet? 1). How many yards of border will be required for a room 21 feet long and 18 feet wide? 10. The tire of a wheel measures Ct feet. How many revolu- tions will it make in going 24 rods? 11. A boy steps 2 feet. How many yards will lie stej) in 80 steps? How many steps will he take in Avalking a mile? In walking % a mile? In walking ^ of a mile? 12. If there are 8 blocks in a mile, how many feet ai'e thei'e in a block ? 18. A field is ^ a mile square. How many miles will a man travel in going around the field? PART THIRD. 18^^ A B C 1. This line is drawn to a scalo oC 1 iiicli to i\w, mile. A man ij^oes from C to A find returns to U. How njajiv miles lias he traveled? 2. From B he s^oes to C and returns to B. How many miles has he traveled? 3. From B he goes to A and back to B. How many rods has he traveled? J:. Suppose the line to be drawn to a scale of I) rods to 1 inch. How many yards from A to B? From B tt^ C? From A to C ? 5. John lives at B, Ned at A and the school-house is at C. John goes to Ned\s house in the morning, then to school, and home in the evening. How many rods has he traveled? 6. The next day Ned goes to school and Jolin is not there. He i^oes back to John's home and they 2 25 37)^ 50 62^2 75 87 1/2 TOO 12i 121 121 121 121- 121- 2 191 121 X 6 = 12I X 7 - 121 X 8 ^ 25 - 121 = 50 - 121 = 75 - 12^ =: 100 - 12^ = Of 100?"" 4. 25 is what part of 50? Of 75? 50 is what part of 75? Of 100? 75 is what part of 100? 5. 121 jg ^yiiat part of 25 ? 121 is what part of 100? 6. How many timos 12?, is 371? 024 ? 871? 7. What part of 100 is 37^-? 62^? 87|^? 12* 121 12* 12* 12* 12* 12* 121 PART THIRD. 191 1. A woman sold 4 dozen eggs at 124^' a dozen. How much did she get for them ? 2. What is the cost of 5 pounds of butter at 12^^- a pound? 3. How many 12^^' in a dollar? In J of a dollar? In a half dollar? ''in 75^? 4. A hoy bought a dozen little chickens at 12t\^- each. The feed cost him 75^' and he sold the chickens when they were grown at 25^' each. How much did he make in the chicken business? 5. A farmer hired a boy to watch his corn-field and prom ised him 12-|^ for every 3 squirrels and 12^^- for every 5 crows that he killed. At the end of a week the boy turned in 6 squirrels and 10 crows. How much money should the farmer pay him ? 6. A woman bought 10 yards of ribbon at 12|Y' ^ yard and 8 yards of silk at 87^^/ a yard. What was the cost of the ribbon? Of the silk? Of both together? 7. A boy bought a ball for 12^^;, a bat for 25^- and a glove for 37iY'. How much did he pay for his base-ball outfit?" 8. A girl bought a doll for 25^', a tablet and pencil for 12^^' and a book for 37i^'. How mucli change should she receive if she gave the storekeeper 5^1? 9. A book-seller bought 5 books at 127^^- each, 8 boxes of paper at 12^(/; each and 7 dozen pencils at 12^^ a dozen. What was the cost of the whole? 10. A hall is 12i feet wide and C times as long. How long is it? 11. A board is 12^- inches wide and 7 times as long. How many inches long is it? 12. A boy bought 3 dozen eggs for | of a dollar, and sold them for J of a dollar. What part of a dolhir did he gain? How many cents a dozen did he gain? 192 THE RATIONAL ARITHMETIC. 1. A clerk sold 1 piece of silk cord 4J feet long, another 7^ feet long. How many yards did lie sell in all ? 2. A man wishes to put 2 rows of wire above a fence 12 rods long. How many feet of wire does he need ? 3. How many yards of carpet are needed to lay one width in a hall 224- feet long and on a fliofht of 16 stairs, each step requiring 1-| feet of carpet? 4. John rides 12 miles, his brother f as far. How many rods does his brother ride? 5. A field is 160 rods long and 80 rods wide; how many feet of wire will enclose it twice ? 6. A man left home and drove 5 miles east ; turned and drove 1,000 rods back. How far was he from home? 7. The hall of a hotel is 14 yards long and 16^ feet wide. How many feet of border will be required to go around the walls? 8. How many boards 12 feet long will make a fence 1 mile long, if there are 3 rows of boards? 9. One walk is 150 feet long, a second 80 feet long, and a third 240 feet. What is the length in yards of all together? 10. One rail of a track is 30 feet long. How many miles long is a track having on 1 side 352 rails, each 30 feet long? 11. A street-car company lays 7 miles of track, J of it running- east and west, the rest north and south. How manv rods of track are there in all ? How many running each direction? 12. A boy walked 2 miles, taking steps 2 feet long. How many steps did he take? 13. In building a fence around a field | of a mile long and \ of a mile wide, a farmer used old material for 2,250 yards, and purchased the rest. How many yards of fencing did he buy ? PART THIRD. 19 Q 1. A horse can go 1 mile in 6 minutes. How many rods can lie go in an hour? 2. A carriage wheel measures 12 feet around the outside. How many times will it turn around in going 3 miles? In going 5 miles? 3. A wheel is 10 feet around the outside. How many yards will it move in going around 120 times on the ground? 4. A lot is 23 yards wide. How many rods will a man walk in crossing the lot 8 times? 5. A boy's top-string is 2 yards long, he cuts from it a piece 18 inches long. AVhat is the length in feet of the remaining part? 6. A mile of gas pipe is laid at $5 a rod. AVhat is the cost of laying? 7. A ])lock is 18 rods wide and 24: rods long. How many steps of 2 feet in length will a boy take in going around it once? 8. A street car goes 10 miles in an hour. At the same rate, how many rods will it go in 15 minutes? 9. At 25^' a foot, what will be the cost of 4: rods and 1 foot of hose? 10. A boy starts from his home and takes 80 steps of 2 feet each in a minute. He walks at that rate as far as he can go and return in 10 minutes. How far Avas he from home when he turned to go back? 11. A man walked 4 miles an hour and a boy walked 2 miles an hour. They started in the same direction at the same time. How many rods apart were they in 15 minutes ? 12. AYhat Avill be the cost of a ditch half a mile long at $1.25 a rod? 13. What is the distance around a lot which is 50 yards and 2 feet long and 8 yards and 1 foot wide ? 194 THE RATIONAL ARITHMETIC. 1. Give the iiuml)or of 12's ill r 8. 24 30 42 144 18 132 96 ()0 48 36 12 X 4 = . 12 X 1) = . 12 X 7 = - 12 X 10 = . 12 X 8 = _ 12 X 2^, = _ 12 X 51 3- - 84 m 108 72 120 12 X 12 12 X 83. = 12 X 12 X f — 12 24 10 18 9 5 3 J • s m L_ ITf () 27 22 30 27 36 15 21 14 33 3 = 12 X 12 = 12 X 6 r- 12 X 11 = 12 X 101 ^ 12 X 12 X 31 '^\^ 12 X 121 ... 12 X ^ 4. h\ is wliat })aTt of 11? What })art of 5. T' 1 X 2 := 5J- X 4 := 51 X 7 = 51 X 8 =- 51 X 6 = - 51 X 9 - - 54^ X 3 = _ 51x10= - 6. \ of 320 ^ 1 of 320 = J^ of 320 = 7. 2 X 320 = . 5 X 320 = . 16^ X 3 16^- X (i l4 X 4 161 X 2 161 X i4x 164: X \\ X 161 92 77 00 132 m 88 3 X 11 - - 3 X 12 = . 3 X 5 := . 3 X 8 rr . 3 X \) ^ - S 111 110 99 33 121 44 3 X 8< = 51=. 1 — 3 X 3 X 9^ == 3 X 121 ^ _ l()i? Of 22? ll X 8 = _ 11 X 9 -= _ 11 X 12 -: - 11 X 4 = - 11 X 7 = - 11 X 10 = - 11 X 6 = - 11 X 11 = - 4 of 320 Vg of 320 -3V of 320 3 X 320 4 X 320 a. What part of 320 is 40? AVhat part is 80? 20? PART THIRD. 195 1. If 1 cord of wood cost ^5t\, how much will 4 cords cost? 2. How many 12 pound packages of sugar can be made from 72 pounds? 3. How many bins holding ^h bushels can be filled from IG^ bushels of grain ? 4. A man walked IGJ miles 1 day and bfy miles the next. How many miles did he walk in all? How many miles farther the first day than the second? 5. At |5| a ton, how many tons of coal can be bought for $22"? 0. 11 men received $132 for digging a ditch. They shared the money equally. What did each one receive? 7. A farmer bought 10 sheep at $3 each and sold them at the rate of 3 for $12. What was the entire cost? How much did he receive? AVhat was his gain? 8. A flag staff 48 feet high was broken into 2 pieces, 1 piece being 3 times as long as the other. What Avas the length of each piece? 9. What is the cost of a bale of cotton containing 400 pounds, at 5^^' a pound? At 7^/ a pound? 10. From a bin holding 77 bushels, 55 Inishels were taken out. How many bins holding 5| bushels each can be filled from the remainder? 11. $40 a month is paid by a man for his rent; his other monthly expenses are 7 times as much. What is the amount of his other expenses? Of total expenses? 12. A\^hat is the average rate of speed made by a train travel- ing 320 miles in 8 hours? 13. A grain dealer sold 320 bushels of corn in 40 bushel loads. How many loads did he sell? 14. A bushel of wheat weighs 4 pounds more than a bushel of corn. What is the difference in weight between 80 bushels of each? 196 THE RATIONAL ARITHMETIC^ 1. Draw diagrams on a scale of 3 feet to 1 inch for Tooms of the following dimensions: 12 feet long and 9 feet wide. 24 feet long and 18 feet wide. 30 feet long and 27 feet wide. 33 feet long and 21 feet wide. 15 feet long and 12 feet wide. 21 feet long and 12 feet wide. 27 feet long and 15 feet wide. 24 feet long and 15 feet wide. Give perimeters in feet. In yards. 2. Draw diagrams on a scale of 3 yards to 1 inch, for lots of the following dimensions: 15 yards long and 12 yards wide. 18 yards long and 15 yards wide. 12 yards long and G yards wide. 15 yards long and 9 yards wide. 24 yards long and 12 yards wide. 33 yai'ds long and 15 yards wide. 21 yards long and 12 yards wide. 27 yards long and 12 yards wide. Give perimeters in yards. In feet. 3. Draw diagrams on a scale of J mih^ to |- inch, for fields of the following dimensions: I mile long and \- mile wide. 1 mile long and |- mile wide. 2 miles lono^ and l.V miles wide, li miles lonof and .V mile wide. 1\ miles long and 1 mile wide. 1^ mile long and -\ mile wide. li miles long and | mile wide. 1\ miles long and l mile wide. Give perimeters in miles. In rods. PART THIRD. 197 1. Review page 176. 2. When dividing by numbers larger than 12, the changes may more easily be written below the numl)er, as shown in 8. This way of dividing is called Long Division, but the plan is the same as in Short Division. 3. Divide 559 by 13. Change 55 tens and 9 to 52 tens and 39; write ^3 the 52 tens below the 55, draw a line, and 13 j 559 beneath it write the 39, placing tho 3 tens in '^'^ tens' column. 39 Now divide : 52 tens -^ 13 == 4 tens ; 39 -J- 13 = 3, 39 making the answer 43. Write this above the 559, placing each figure in its proper column, the 4 tens above the 5 tens, the 3 above the 9. 4. Divide 4874 by 21. Change 48 hundreds and 7 tens to 42 232-^1- hutidreds aud 07 tens; write the 42 hun- 21)4874 dreds below the 48, draw a line, and be- 42 neath it write the 67 tens, placing the 6 67 hundreds in hundreds' column. 63 Now divide: 42 hundreds -^ 21 = 2 hun- 44 dreds. Place this part of the answer above 42 the 4,874, in hundreds' column. Change 67 2-rem. tens and 4 to 63 tens and 44, writing them in the same way as before. Now divide: 63 tens -4- 21 = 3 tens. Write this part of the answer in its proper column, beside the 4 hundreds. Change the 44 to 42 and 2. 42 -^ 21 = 2. Write this in the ones' column of the answer. The division of the remainder, 2, may be expressed by writing ^ after the rest of the answer, making 232/y. 198 THE RATIONAL ARITHMETIC. 1. Divide: 264 by 11, by 21, 31, 41, 51. 528 by 12, by 22, 32, 42, 52. 377 by 13, by 23, 33, 43, 53. 434 by 14, by 24, 34, 44, 54. 675 by 15, by 25, 35, 45, 55. 352 by 16, by 26, 36, 46, 56. 2. Divide each of the followiug iiuinbers by each of the above series. 118 154 172 120 156 188 213 237 248 253 269 293 3123 3234 3345 3456 3567 3785 4678 5788 6879 7890 8901 8493 9012 8123 7243 6542 5987 9648 3. A mail })aid ^31.46 for egg^ at 13e the area of each triangle in feet? 15. Find the area of the following right-angled triangles: Base three feet, altitude six feet. Base four feet, altitude three feet. Base six feet, altitude eight feet. Base eight feet, altitude ten feet. Base tAvelve feet, altitude eight feet. Base fifteen feet, altitude twelve feet. Base ten inches, altitude five inches. 210 THE RATIONAL ARITHMETIC, PART THIRD. 211 Note.— The plan on the opposite page represents a garden, which has been cut into various parts by the walks running through it. The plan is drawn to the scale of 10 feet to an inch. 1. Measure the line around the entire plan and find the length of the path around the gai'den. 2. From these measurements, what is the area of A? 3. What is the area of B? 4. What is the area of C? 5. Wliat is the area of I)? (>. What is the area of E? 7. Wiiat is the area of F? 8. How many square feet are there in the entire garden? 9. A is what part of B? C? D? E? F? 10. F is what part of the entire garden ? 11. How did you find the area of C? 12. How did you find the area of D? 13. In what other ways beside finding the areas of tlie tri- angles could you find the area of tlie entire garden ? NoTK. — Suppose the plan on the opposite page, representing a piece of land, is drawn to a scale of one inch to 8 rods. 14. What will be the value of A at 25^^- a sq. vd. ? 15. What will be the value of B at 30^/ a sq. rd. ? 1(). What will be the value of C at 28^' a sq. rd. ? IT. What will be the value of D at 27^/ a sq. rd. ? 18. What will be tlie value of E at 21^- a sq. id. ? 19. What w^ill be the value of F nt 29^- a sq. yd. ? 20. How many sq. rds. in the entire field? 21. How many acres? 22. How many sq. yds. in A? 23. How many sq. ft. in B? 24. How many sq. yds. in C? 25. How many sq. ft. in 1)? 2*). How many sq. yds. in E? 27. How many sq. ft. in F? 212 THE RATIONAL Altl ITIMETIU. 1. A woman who raises cliickens puts 13 eggs under each of 6 hens. The first hatched out all but 1, the second all but 2, tlie third all but 3, tlio fourth all but 4, and the others aJl but 5 eacli. How many chickens were liatched ? 2. How many pigeons will it take to pick up a bushel of corn (5G lbs.) if each one picks up 1 oz. ? 3. A man buys 12 tons of hay for $80 and sells it for 60'/- per cwt. How much does he make? 4. An expressman receives $3.25 per day for 30 days. It costs him 30^' per day to feed his horse. He pays $4.20 for repairs to his wagon. How much has he left? 5. An express company carries 400 packages at 15^/ each, 28 trunks at 50^/ each, and 12 bicycles at 40^' each. What does it get for them all ? 6. There are 40 street cars on one line and each can carry 00 people. How many people will they all carry in 12 round trips if I carry their full number each way and the remainder carry 30 persons each way? 7. A baker has 400 loaves of bread. He sells f at 5y^ per loaf, 60 loaves at 4r(/-, and gives the rest away. How much does he get for the bread ? 8. How many sheej) luust there be to produce a ton of wool if the wool from each sheep weighs 4 11 )S.? If each sheep produces 5 lbs. ? 1). How many balls of kite string will it take to reach 1| miles if each ball contains 200 yards? 300 yds.? 10. A farmer raised 840 bu. of potatoes on 5 acres of land. Wliat was the value of the average produce of 1 acre at 40^' per bushel? 11. A man set out 12,000 cabbag(^ plants, but J of them died and -jQ of the remainder were stolen. What did he re- ceive for the rest at $3 per hundred? PART THIRD. 213 1. An orchard of 600 trees produced 3 bbls. of apples to the tree. The owner sold them at $1. 40 per bbl., but the barrels cost him 25^ each. What did he get for the apples after paying for the barrels ? 2. A peach orchard produced 210 ])u. of peaches. If 1 bu. fills 5 baskets, what is the value of the crop at 20^' a basket ? 3. A farmer pays some boys 1M,ck(Ml in a case 6 feet long, 4 feet wide and 4 feet high ? 4. How many cubic feet of ;iir will a glass jar 24 inches long, 18 inches wide and 12 iuclx's liiijli hold? 5. From a vessel liolding 2 cubic feet of water 864 cubic inches were tfdvon. How many cubic inches remain? How many (;ubic feet? 6. In 1 jar there are 81)4 cubic inches of liquid; in another 2592 cubic indies. How many cubic feet in a third jar, holding as much as the first and second together? 7. A ]nan put 12 inches of sand into a box 9 feet long and 5 feet wide. How many cubic feet of sand in the box ? 8. A wagon box 3 feet Avide and 9 feet long is 1^ feet deep. How many cubic feet will it hold? 9. A ditch 45 feet long and 2 feet wide contains (530 culnc feet. How deep is the ditch? 10. A freight car is 32 feet long and () feet wide inside and is filled with sand 3£ feet deep. How many cubic feet of sand are in the car? 11. A wall is 44 feet long 5^ feet high and 18 inches thick. How many cubic feet in the wall? 12. A sidewalk is 6 inches thick and 6 feet wide. How many cubic feet in 124 feet of the sidewalk? 13. In a building there are 18 pillars 2 feet by 18 inches and 14 feet high. How many cubic feet in these pillars ? 216 THE RATIONAL ARITHMETIC. Cu. in. = cubic inch 1 cu. ft. 1 cu. yd. 1728 cu. in. 27 cu. ft. 1. Add: cu. ft. : 1 cord 128 cu. - cubic foot Igal. ft. 2.31 cu. in. cu. yd. = Ibu. 21501 cu. : cubic yard in. (nearly) cu. yds. 7 cu. ft. 6 cu. in. 27 cu. yds. 6 cu. ft. 14 cu. in. 55 2 10 250 2 2 17 4 2 41 3 3 40 8 3 3 1 2 160 8 4 120 8 4 50 cu. yds. 20 cu. ft. 10 cu. in. 75 cu. yds. 4 cu. ft. 7 cu. in. 800 7 5 ' 50 7 6 600 5 1 64 3 4 20 3 8 125 2 2 8 2 3 800 9 7 300 2. Subtract: cu. yds. 10 cu. ft. 25 cu. in. 1200 cu. yds. 9 cu. ft. 18 cu. in. 350 6 16 900 • 5 9 275 cu. yds. 14 cu. ft. 20 cu. in. 800 cu. yds. 11 cu. ft. 15 cu. in. 920 7 13 246 6 cu. yds. 12 7 cu. ft. 6 256 3. Multiply: cu. yds. cu. ft. 6 7 cu. in. 576 cu. in. 432 3 4 cu. yds. 4 cu. ft. 13 cu. in. 864 cu. yds. 4 cu. ft. 2 cu. in. 192 2 9 PART THIRD. 21? 1. A boy carried enough wood to make a pile 4 ft. long, 2 ft. wide and 2 ft. high. What part of a cord did he carry? 2. What must be the cubic contents of a jar to hold f of a gallon ? 2i gals. ? 44 gals. ? 3. How many cubic inches are there in a bin holding 2 bu. ? ^ bu. ? ^ bu. ? 4| bu. V 6i bu. ? 4. A cord of wood is usually piled 8 ft. long and 4 ft. wide. How high is it? 5. A bin holds 16 bu. How many cubic inches does it con- tain? 6. A water trough contains 12 gals, of- water. It is 14 in. wide and 9 in. deep. How long is it? 7. How many cu. yds. of earth will be excavated for a cellar that is 24 ft. long, 21 ft. wide and 12 ft. high? 8. From a cellar 36 ft. long and 18 ft. wide 6804 cu. ft. of earth was taken. How deep was the cellar? 9. How many cu. yds. of rock was blasted from a tunnel that is 9 J ft. high, 80 ft. long and 12| ft. wide? 10. A cubic foot of water weighs 1000 ounces. What will water enough to fill a trough 6 ft. long, 2 ft. wide, and li ft. deep weigh in pounds ? 11. If oil weighs -J as much as water, what is the weight of a cubic foot of oil in pounds? 12. A street sprinkler holds 168 cu. ft. of water. How much does it hold in pounds ? 13. If such a street sprinkler is emptied every 24 minutes during 9 hours, how many buckets of water are used if a bucket holds ^ of a cu. ft. ? 14. A rectangular tank 6 ft. wide, 10 ft. long, and 3 ft. deep is full of water. What is the weight of the water? 15. 35 cu. ft. of coal will weigh about 2000 pounds. How many tons will a wagon box 7 ft. long, 5 ft. wide, and J ft. high weigh if loaded full ? 218 THE RATIONAL ARITHMETIC. / [5 1 2 3 4 5 6 15 30 45 60 75 90 1. Add 15 15 15 2. 15 X 2 = 15 X 4 = 15 X 5 = 15 30 15 15 45 15 15 fiO 15 15 80 45 15 X 3 15 X () 15)45 30 30 30 15)G0 15)90 3. 15 is what part of 30? 60? 45? 90? 75? 30 is how many 15's ? What pai-t of 45 ? 00 ? 75 ? 90 ? 45 is how many 15's? How many 30's? What part of 00? Of 75? 90? OOis how many 15's? How many 30^s? 45's? AVJiat part of 75? ' Of 90? 75 is how many 15's? How many 30's? 45'sf OO's? What part of 90? OOis how many 15's? How many 30's? 45's? OO's? 75's? 4. A boy bought 3 dozen oranges at the rate of 15^/ a (hizen. AVliat did they cost him ? 5. A girl bought 12 liandkerchiefs at the rate of 2 for 15r/. WJiat did they cost her? 6. Railroad fare for a picnic excursion was 15^ for the round trip. How much was collected on a train of 9 cars with 65 persons in each car? PART THIRD. 219 1. At a school entertainment there were 186 grown people who paid 15^/ eacli and 824 children at lOf/- each. The expenses were $15.25. How much was left for the school ? 3. A class of 25 pupils have a spelling lesson of 15 words. 15 of them write the lesson once, 6 of them write it twice, and 4 write it three times. How many words do they all write ? 3. The pupils of a school put $14.06 into the Penny Savings Bank on Monday and take out $2.40; they put in $7.24 on Wednesday and take out $1.56, and they put in $1).28 and take out $4.10 on Friday. How iiiuch more do they put in than they take out for the week? 4. A peddler buys 15 bu. of nppkis at 90^/ per busJjel and sells them at 15^/ ])er half peck. How much does he make if he sells them all? 5. A banana ])eddler buys 100 dozen bananas for $7.50. He sells ^ of them nt 15<'/ per dozen, 4 of them at KK/ per dozen, 20 dozen at 5'/ ])er dozen, and the rest spoiled. How much does he make? 6. A junk dealer buys 1000 pounds of old iron for $1.20 and 400 pounds of lead for $6. He sells the iron for ^^/' per pound and the lead for 3|^- per pound. How much does he make? 7. A milk dealer sells every day 6 cans of milk each holding 8 gallons. How many customers has he if each one takes 2 qts. ? If each takes 3 pts. ? 8. If he pays 90^- per can for the milk, and sells it for 5^* per quart, how much does he gain ? 9. A sugar plantation in Cuba produces 480 lilids. of sugar, averaging 540 lbs. in weight. What is the value of the sugar at 2|-^' a pound? At 2^' a pound, what is the value of the sugar from 15 such plantations? 220 THE RATIONAL ARITHMETIC. gi. = gill, pt. = pint. qt. = quart, gal. = gallon. bbl. = hhd. = barrel. = hogshead. 1 pt. 1 qt. A gi. 2 pts. 1 gal. 1 bbl. 4 qts. 31^gais. (commonly) 1 hhd. 2 bbls. 1. Review pages 74 and 130. 2. Add: gals. qts. pts. 4 2 1 gals, qts. pts. 7 3 bbls. 2 gals. qts. 14 1 3 11 2 2 3 6 3 bbls. gals. qts. 1 20 1 • gals. qts. pts. 15 1 hhcl 1 . bbls. gals. qts. 16 1 11 1 2 3 1 15 1 3. Subtract: gals. qts. pts. 7 4 2 gals. qts. pts. 4 2 2 gals. 14 qts. pts. 6 3 3 3 1 2 11 4 4 2 bbls. gals. qts. 3 30 2 bbls. gals. qts. 4 15 3 hhcl, 2 , bbls. 1 gals. (|ls. 31 2 1 21 2 1 1 8 1 1. Multiply: gals. qts. pts. 2 3 1 gale. qts. pts. 7 12 « bbls. 2 gals. <(ts. 10 2 2 4 3 5. A milkman starts witli 42 gals. ; sells -| of the milk to pri- vate customers, the rest to a hotel. How many quarts does he sell to the hotel? 6. A druggist put 1 qt. of liquid into bottles holding | gi. each. How many bottles did he use? 7. How many jelly glasses holding | of a pt. each can be filled from 1 gal. of jelly ? PAirr THIRD. 2'Zl 1. How many pint bottles will hold 2 gals. 1 pt. of vinegar? What is it worth at 13^* a quart? 2. If a gallon of wine cost $4, what will 5 pts. cost? 3. From a milk can holding 8 gals., ^^g of the milk was spilled. How many quarts were left? How many gallons? 4. How much ice cream will a man make if he uses a gallon and a half freezer and has it full twice, and half full the third time? 5. How many gals, in 412 gills? (). What part of 12 gals, is 4| gals. ? 7. A man sold 12 cans of mineral water, each holding 6 gals. at 15^ per gal. How much did he receive? 8. How many oil barrels, each holding 45 gals., can be filled from a tank holding 10,800 gals, of oil? 9. A hotel uses 25 gals. 3 pts. of milk each day. How much does it use in 3 w^eeks? 10. There are 231 cu. in. in 1 gal. How many cubic inches in a bottle holding 2 qts. ? 11. How many cubic inches in a cistern holding 10 bbls. ? 12 bbls. ? 16 bbls. ? 12. En a jar that holds 2 gals., 3 qts. of water are placed. How many cubic inches of the jar are unfilled? 13. From a barrel of vinegar a grocer fills 2 four-gallon jugs and puts 3 gals, and 1 qt. in another jug. How many gals, had he left? 14. A man sells 3 gals, and 2 qts. of molasses to one cus- tomer; 2 gals, and 1 qt. to another customer, and 1 qt. and 1 pt. to a third. How many quarts did he sell in all? How many gallons? 15. From a barrel full of rain water, 80 qts. were taken out at different times. The water remaining in the barrel measured 40 qts., the rest having evaporated. How many quarts had evaporated? '•JO'-) THE RATIONAL ARITHMETIC. Add 16 16 16 1 2 3 4 5 6 16 32 16 16 32 16 32 32 16 32 48 64 80 06 16 32 48 48 48 2. 16 X 3 := _. 16 X 5 = 16 X 2 == 16 X 6 =: 16 X 4 = 3. 16 is what part of 32? 48? 64? 80? 96? 4. 32 is how many 16's? What part of 48? Of 64? 80? 96? 5. 48 is how many 16's? How many 32's? Wlmt part of 64? Of 80? 96? 6. 64 is how many 16's? How many 32's? 48'sV What part of 80? Of 96? ' 7. 80 is how many 16's? How many 32"s? 48's? 64's? What part of 96 ? 8. 96 is how many 16's? How many 32's? 48's? 64's? 9. A farm of 96 acres was divided into 16 equal parts. How many acres in eacii? 10. In a square mile of land there are 16 farms equal in size. How many acres in each? If one of these farms is di- vided into 3 fields, two of which contain K) acres each, what is the area of the third field? 11. From a bin containing 80 lbs. of meal, 2 eight-lb. pack- ages were taken. How many sixteen-lb. packages can be made from the remainder? PART THIRD. 223 1. A brick mason contracts to build a chimney for $72. If it takes 10 clays to do the work and he pays each of his 2 helpers $1.50 per day, what is his rate of pay per day? 2. A man agreed to haul away 1560 cu. yds. of clay for $264. He paid 4 teamsters $3.90 each per day for 13 days. How much did he have left ? What did each teamster receive ? 3. If each teamster was paid at the rate of 13^* per cu. yd., how many yds. did he haul to earn what he received? 4. A man hauls sand for \)(J- per cu. yd. If his wagon holds 1|- cu. yds. and he hauls 18 loads per day, what is his daily pay? 5. A newsboy buys his papers at the rate of 10 for 6^' and sells them for 1^' each. How much will he gain if he sells 75 papers? 120 papers? 6. He sells 45 on Monday, 54 on Tuesday, 81 on AVednes- day, and 70 on Thursday. AVliat does he gain in the 4 days ? 7. On Friday he buys 100 papers and sells all but 5 that are spoiled by the rain. What does he receive for his work on Friday? 8. A newspaper prints 1| million copies in 6 days. At the end of the week 13,526 copies had been given away and 29,674 copies were left on hand. What was the average daily circulation? 9. If \ of these papers are sold by newsboys, how many newsboys must there be, if each one sells 100 papers every day? 10. A man divides 80 acres of land into streets and building lots. The streets take up ^g of the land, and the remainder is divided into blocks each containing 3 A. How many blocks? 224 THE RATIONAL ARITHMETIC. 1 qt. = 2 pt. pk. = peck. bu. = bushel. 1 pk. = 8 qt. 1 bu. := 4 pk. 1. Review pages 76 and 131. 2. Add: 3 bu., 1 pk., 6 qt. 1 bu., 2 pk., 3 qt. 2 bu., 3 pk., 4 qt. 1 bu., 2 pk., 1 qt. 2 bu., 1 pk., 5 qt. 3 bu., 4 qt. 4 bu., 2 pk., 5 qt. 5 bu., 2 qt. 3 bu., 3 pk., 7 qt. 1 bu., 2 pk., 3 pk., 6 qt. 1 qt. 3. Subtract : 5 bu., 3 pk., 6 qt. 3 bu., 2 pk., 7 qt. 6 bu., 1 pk., 5 qt. 1 bu., 2 pk., 4 qt. 2 bu., 5 qt. 1 bu., 1 pk., 1 qt. 4 bu., 2 pk., 4 qt. 8 bu., 3 pk., 5 qt. 12 bu., 2 pk., 6 qt. 1 pk., 4 qt. 2 bu., 2 pk., 2 qt. 7 bu., 4 qt. 4. Multiply. 2 bu., 2 pk., 3 qt. 3 bu., 1 pk., 3 qt. 4 bu., 1 pk., 1 qt. 2__ 3_ 4 5. How many bushels in 128 pks. ? In 150 pks. ? (3. How many quart boxes will 1 bu. 3 pks. 2 qts. fill ? 7. Find cost of 3 pks., 6 qts., 1 pt. of nuts, at 12i^ a pint? 8. In 96 qts. how many pecks? How many bushels? 9. What part of 7 bu. are 7 pks. ? 7 qts. ? 10. How many quarts of cherries can be bought for $2, if 1 bushel of cherries is worth $3.20? 11. I bought 7 bu. 3 pks. of potatoes on Monday; 8 bu. on Tuesday and 10 bu. 1 pk. 6 qts. on Wednesday. How many potatoes did I buy in all? 12. A teamster feeds his horses 36 qts. of oats a day. How long will 120 bu. of oats last him? What does it cost him each day when oats are worth 27^ a bu. ? PART THIRD. 225 1. From a sack of peanuts holding 3 bu., 25 qts. were taken. How many bushels remained? 2. A bushel of plums is divided equally among 12 people. How many quarts did each receive? 3. How many pecks of beans will a man sell who sells 3 qts. to each of 8 customers? 4. A woman measuring out 2J qts. of flour uses a measure holding J pt. How many times does she fill the meas- ure? 5. A barrel of apples was sold in 3 lots. The first sale was 1 bu. and 2 pks. ; the second 2 pecks; the third IJ bu. How many bushels were there in the barrel? 6. From 3 bushels of peas, a man sells ^ peck to one cus- tomer; 4 qts. to another, 1 pk to another. How many has he left? 7. If one-half a peck of peaches when canned make 3 qts., how many bushels must be bought to make 36 qts. of canned peaches? 8. A man bought at a feed store 5 bu. of corn, 2 bu. and 3 pks. of oats and IJ bu. of mixed feed. He had at home in the bins, 3 pks. of corn, ^ bu. of oats and 1 pk. of ground feed. How many bushels of feed did he have in the bins after he received what he bought? 9. In one year a farmer's family used 50^ bu. of potatoes. He saved 9 bu. 3 pks. for planting and sold 117 bu. and S^ pks. How many busliels did he raise that year ? 10. 240 boxes of peaches, holding 1 pk. each, were shipped to market. The fruit was picked in one-half bu. baskets. How many baskets of fruit were there? 11. A fruit dealer bought 2 crates of strawberries, each hold- ing 24 qts. ; and 6 crates, each holding 32 qts. The berries were put into pint boxes and sold for 10^ a box. What did the dealer receive for the berries ? 226 THE RATIONAL ARITHMETIC. 1 6% 1 2 3 4 5 6 1. Add: 16 1 16f 16^ J.Ug 50 331 33i 333^ 50 833^3 lOO 16| 83| 16| 2. 16| X 3 = 16| X 2 = 16| X 4 := 161 X 6 16-1 X 6 = 66|? 66f? 331? 831? 831? 33i's? 33i's? 331 's? 33i's? 100? What part of ()6|? 50's? 50^s? 66|'s? 50's? 66f's? 83i's? 3. 16f is what part of 50? 4. 331 is what part of 50 ? 5. 50 is how many 16f's? 831? 100? 6. 66f are how many 16|'s? 7. 83| are how many 16|'s? 8. 100 is how many 16|'s? 9. A man paid 16| of a dollar each for 15 books. What did they cost him? 10. A boy 33| miles from home, rode |- the distance on his wheel. How many miles did he ride? 11. A piece of cloth 3 yds. long sold for 50^*. What was tlie price per yd. ? 12. A girl picked 66f qts. of berries in 4 days. What was the average amount per day? 13. A hundredweight of grain was divided into 6 equal amounts. How many pounds in each? 14. From a tank of water, 16| gals, were drawn out, which were J, of the amount remaining. How many gallons were left in the tank? PART THIRD. 227 1. A schooner brought 48,972 spruce trees from iiortlieru Michigan to Chicago at Christmas time. What are they worth at 90^' a dozen? 2. A blacksmith shoes 42 horses at $2 each in 1 week. The shoes and nails cost him §8, shop rent $12, and he pays each o£ his two helpers $15 per week. What was his share of the money received? 3. A teamster has his two horses shod all around, twice each month, during December, January and February, and once a month the remainder of the year. What does it cost a year at $2 per shoeing for each horse? 4. A cooper made 1000 butter tubs at 12^' each and 600 bar- rels at 30^/ each. If he paid J of the price for lumber and I of it to his workmen, how much did he have left? 5. If each tub holds 24 pounds, what will 1000 tubs of but- ter be worth at 21^; per pound? 6. If each bbl. holds 3 bu. of apples, what will 600 bbls. bring if sold at 30^- per peck? 7. There are 630 sq. yds. of lathing needed in a new house and it can be done in 6 days. Will a man earn more by doing it by the day at $3 per day or by the square yard at 3^' per sq. yd. ? 8. If 54 laths will cover 4 sq. yds. how many will be needed for 600 sq. yds.? How many bundles of 50 laths each? 9. If each lath uses 6 nails, and 54 laths cover 4 sq. yds., how many nails will 600 sq. yds. use? How many pounds allowing 400 nails to the pound? 10. A carpenter works 5| days in a week at $3 per day, but breaks a saw worth $1.40 and loses a hammer worth 90^-. What is the week's work worth to him? 11. A painter has 3 helpers at $3.50 per day and 2 at $3. What must he charge for a week's work so as to have $25 for himself ? 228 THE RATIONAL ARITHMETIC. 1. Review pages 162 and 163. 2. What is the name of the first period? 3. AVhat is the name of the second period ? 4. How many places are there in units' period? 5. Each period has three places. Thousands. [Tnits. en ^ / •o '3 01 CD u U Tl , • , • a VI r/j '/• 13 1— < '^ rj !:3 W H O y^ H O 2 4 () ,12 3 0, Read the figures of each period as though they stood alone and then add the name of the period. 246 thousands. 123 units, or ones. 7. If we multiply the number 246,123 by 10 we will have the beginning of a new period, 2,461,230. 8. This will be read: 2 millions (this is the name of the new period). 461 thousands 230 9. The use of figures to represent numbers, as we have been doing, is called the Arabic Notation or method of writing numbers. 10. There is another method of writing numbers, in which letters are used. This is the Roman Notation. 11. Fill out the following blanks with figures: XI = L = , C =: XL = XC =^ I - VI - II - VII - III - VIII = IV - IX - V - X ^- 12. What is the equivalent in figures of I? V? X? L? C? D? M? PART THIRD. 229 1. If a letter is followed by one or more letters of equal or less value, the sum of all is the value of the iiumbei represented. Thus: VI = 6; XI = 11; XX = 20; CLX = 160; DC = 600. 2. If a letter is followed by another of greater value, the difference of the two is the value of the number represented. Thus: IV = 4; IX = 9; XIX = 19; XL = 40; CD = 400. 3. Read the following numbers written in the Roman Nota- tion: IV XIX XXXIV XLIX XCIX CCCXXVI VIII XVI XLIV LIV CIX MCLXXIV II XIV XXVII LXIX CLXIX DIX IX XXXIX XI LXXVIII LC MLV 4. Write the following numbers in the Roman Notation: 9 = 4 -: 7 = 6 = 14 = 29 = 13 = 78 =: 44 = 83 = 59 = 94 = 96 = 104 = 199 = 335 = 549 == 2000 = D. (Write answers to the following in Roman numerals.) Columbus discovered America in MCDXCII; 20 years later Florida was explored. In what year was Florida explored ? 6. The first battle of the Revolution was fought in MDCCLXXV; the last battle was fought 6 years later. What was the year of the last battle? 7. Washington was elected President in MDCCLXXXIX; Lincoln was elected 71 years afterward. In what year was Lincoln elected? o 30 THE RATIONAL ARITHMETIC. Add the following: (1) 7843 (2) 32765 (3) 25987 (4) 96875 (5) 81818 (6) 247 8789 89247 6586 40984 92193 91838 9576 76348 78379 50839 87689 9705 2589 20873 96468 9787 76434 87278 8956 94608 980 67898 68979 3849 3210 13495 20876 76580 37590 89878 7029 68950 67099 54777 89763 79929 47992 3 3 4 In each column the number to be carried may be indicated by placing the figure immediately underneath the column, as in problem 1. To prove your work, add the columns from the top, downward. (') 68 (8) 238 (9) 3271 (10) 17284 (11) 24567 (12) 237 97 472 4089 35873 89012 48984 89 836 3765 89656 4567 3789 43 980 2188 25784 89876 54976 30 722 3900 92375 54378 500 78 405 146 4895 71084 98989 3897 83 348 6589 25874 24864 57878 29 765 8077 39058 3099 36498 48 897 9384 87643 87655 9889 67 305 6589 97979 98788 65847 98 969 9283 86786 4890 678 88 413 878 5670 78978 86767 88796 39 438 8023 27605 67987 3480 64 765 9387 43991 4389 27938 89 735 4738 37642 97689 988 95 897 8777 49877 9480 77658 47 407 642 4738 79988 84976 7865 1225 1225 1 1 1 Another method of proof is to divide the columns into shorter col- umns, add separately, as indicated in number?, and add these separate sums. PART THIRD. 231 6384 1945 The larger number is called the Minuend. 4889 6834 The smaller number is called the Snhirahend. The result is the Difference or Remainder. The addition of the difference and the subtra- hend should give the minuend and is the Proof. 2. Subtract the following: (1) (2) (3) (4) (5) (6) 8346 24890 36745 48234 57855 72180 5838 17901 17829 29018 29666 23092 (7) (8) (9) (10) (llj (12) 62387 83475 90281 38297 27666 87726 34299 56077 37345 19088 18785 68640 (13) (14) (15) (16) (17) (18) 418967 687240 723485 868240 927200 70724 L 229875 478119 438907 372906 418117 354438 (10) (20) (21) (22) (23) (24) 381487 592173 600840 821380 727248 917288 191598 394205 236450 291653 570649 129399 3. A man began business with $5,275.75; in five years he had §22,794.50. How much liad he gained? 4. One country road is 20 mi. 160 rds. long; another is 14 mi. 80 rds. long; how much longer is the first? 5. A cotton dealer bought 328,900 lbs. of cotton one year, and 715,600 lbs. the next. How many more lbs, did he buy the second year? 6. One vessel is valued at $1,250,000; another at ^975,800. What is the difference in value? 7. A box containing 43,200 cu. in. was divided into two parts; one holding 25,920 cu. in. How many cu. in. in the second part? 232 THE RATIONAL ARITHMETIC. 1. Reviow pages 95 and 173. 2. Multiply 892 by 235. r 892 X 5 892 X 235 = ] 892 X 3 tens ' 892 X 2 hundreds 892 The number multiplied is the Multiplicand. 235 The number multiplied by is the Multiplier. 4460 892 X 5 2676 892 X 3 tens 1784 892 X 2 hundreds 209620 The result of multiplying is the Product. It will be noticed that the first right hand figure of each partial pro- duct is placed directly beneath the figure by which we are multiplying. Thus, when multiplying by 3, the first figure of the partial product, G, is placed beneath and in a line with the 3; and when multiplying by 2, the 4 of the partial product is placed directly beneath the 2. 3. Multiply 729 by 460. 729 X 460 = ] ^^ ^ f^ ^ ^ ( 729 X 4 hundreds 729 460 43740 729 X 60 2916 729 X 4 hundreds 335340 4. Multiply 476 by 308. 476 X 308 = 476 308 476 X 8 476 X 3 hundreds 3808 1428 146608 476 X 8 476 X 3 hundreds PART THIRD. 233 1. Find the following products: 573 X 248 384 X 537 735 X 376 487 X 789 858 X 305 275 X 937 972 X 219 976 X 253 835 X 583 508 X 607 506 X 429 4005 x 129 968 X ()75 651 X 234 309 x 150 2060 X 456 809 X 584 943 X 923 847 X 907 3070 X 250 548 X 394 475 X 406 653 X 295 1022 X 284 2. An elevator in a tall building goes up 165 ft. and down the same distance each trip. How many feet does it go in 152 trips? 3. If it cost 56^- per word for a cablegram from Japan to Chicago, what is the cost of a message of 1213 words? 4. If a steamer burns 378 pounds of coal in going 1 knot, how many pounds will she burn in going 15,288 knots? 5. There are 40 street lamps on 1 mile of street, each burn- ing 18 cu. ft. of gas every night. How much gas will they burn in the month of April? (). A library has in one case 27(^ books, which contain, on an average, 304 pages each. How many pages of reading matter in the bookcase? 7. There are 897 hills of corn in a single row and 364 such rows in a field. How many Mils of corn in the entire field? 8. There are 43,560 square ft. in an acre. If 189 pounds of water fall on one square ft. in a j-ear, how many pounds will fall on an acre? 9. There are 12 elevators in a builditig. They each make 94 round trips in a day and carry, on an average, 4 passengers each way. How many passengers make single trips on all of them in a day? 10. In a single layer in a wall there are 964 bricks. The wall is 197 bricks high. How many bricks does it contain ? 234 THE RATIONAL ARITHMETIC. 1. Divide 20, 30, 40, 60, 90, 70, 80, each by 10. In each case what do you do when dividing by 10? Divide 250, 520, 750, 640, 980, 370, each by 10. 2. Divide 400, 900, 800, 500, 300, each by 100. In eacli case what do you do when dividing ])y 100? Divide 7500, 8900, 2400, 6400, 3700, each by 100. 3. Divido 7000, 9000, 2000, 8000, each by 1000. In each case what do you do when dividing by 1000? Divide 75000, 26000, 867000, 845000, each by 1000. 4. Divide 860 by 20. The nunil)er to be divided (860) is called the Dividend. The number to be divided by (20) is called the Divisor. The result of the division (43 below) is the Quotient. ( 1 0)860 ) 20 =^ 10 X 2. Then 860 -^ 20 = < '2)m \ =20)860 ( —43) 43" When the dividend and divisor both end in a cipher, the cipher may be canceled as above and the division made as indicated without the ciphers. 5. Divide 9200 by 400. 40 0)9200 23 When the dividend and the divisor end in two or more ciphers, an equal number of ciphers may be canceled from each as above, and the division made as indicated without the ciphers. 6. Divide : 480 ^ 30 3600 -- 1200 16000 ~ 2000 720 -^ 40 2700 ^ 900 21000 -- 7000 540 -- 60 6300 - 700 60000 -^ 12000 270 -^ 90 13200 -^ 1100 25000 -^ 5000 650 - 50 8400 -- 400 24000 - 3000 490 -- 70 5000 -- 1000 54000 ^ 9000 720 -- 80 9300 -- 300 36000 -- 4000 780 -- 20 6400 ^ 800 96000 ^ 8000 PART THIRD. 231 1. Divide 21,816 by 72. 303 72)21816 216 216 216 • 2. Divide 15,250 by 61. 3. Divide 5130 by 342 250 61)15250 15 342)5130 122 342 305 1710 305 1710 4. Divide 25,215 by 105. 240AV Proof: 105 divisor. 105)25215 240 quotient. 210 4200 ■421 210 420 25200 15 rem. 15 rem. 25,215 dividend. To prove the correctness of division, multiply the divisor by the quotient, and add the remainder if there be one. The result should equal the dividend. 5. Divide : 3767 -^ 38 99,684 -- 234 7873 -- 41 91,464 -- 111 7692 -^ 32 94,770 -^ 135 67,654 -- 53 95,928 ^ 806 26,754 -=- 64 90,750 ^ 125 95,637 ^ 75 76,894 86 68,331 -^ 911 33,633 -- 111 236 THE RATIONAL ARITHMETIC. 1. A lumber vessel carried 887,392 barrel staves. Allowing 16 staves to the barrel, how many barrels can be made from them? 2. A ship traveled about 15,238 nautical miles in 66 days, stopping 12 days on the way for coal and other sup- plies. What was her average speed per hour? 3. The Danube Eiver is 1,725 miles long, the Ehine 600 miles and the Rhone 580 miles. How many times as long as the Thames, 220 miles, is their united length? 4. There are 102 counties in Illinois and the area of th(^ state is 56,650 square miles. What is the average sizu of each county? 5. Chicago's area is 119,689 acres. How many square miles of land in Chicago? 6. A field oE corn has in it 229,599 hills. There are 291 equal rows. Hoav many hills in each row? 7. A rectangular farm contains 552,866 square yards. One end of it is 563 yards long. How long is one side? 8. A field contains 926,156 square feet. One end of it is 679 feet long. How long is one side? 9. At a brick yard 3,276,221 bricks were made during the season. They were hauled away in 824 equal loads. How many bricks were hauled at a load? 10. ^48,077.29 was divided equally among 709 men. How much did each receive? 11. A merchant sold 999 bicycles for $41,793.72. What was the average selling price of each bicycle? 12. In 312 days of the year a merchant sold $91,040 worth of goods. What did his daily sales average? 13. In four years a factory uses 1,434,160 pounds of coal. What was the average amount used per week? 14. The Atlantic Ocean in the deepest part is 27,366 feet deep. What is its depth in miles? PART THIRD. 237 20 1 2 3 4 5 1. 2. 3. 4. o. 6. 7. 8. 9. 10. 11. 12. 13. How many 20's in 40? 40 is how many 20's? 60 is how many 20's? 80 is how many 20's? 100 is how many 20's? 20 40 60 80 100 In 80? 60? 100? What part of 60? Of 80? 100? 40's ? What part of 80 ? 100 ? 40's? 60's? What part of 100? 40's? 60's? 80's? A boy bought 80 papers for 44^-. The next day he bought 20 papers at the same rate. What did they cost him ? A train goes 40 miles in 55 minutes. At the same rate how long will it take to go 80 miles? A boy rode 9 miles in 1 hour. How far will he ride at the same rate in 40 minutes? 60 qts. of syrup cost ^7.20. At the same rate what will 5 gal. cost? A man puts 20 pounds of meal in one sack. How many sacks will he need for 1 hundredweight? ^ of a bu. of wheat weighs 20 pounds. How many bu. weigh 60 pounds? 80 pounds? 100 pounds? A toy bank holds $2 in dimes. How many weeks will it take to fill it if 20^* are put in each week ? Allowing 4 weeks to the month, how many terms of 20 weeks are there in 10 months of school? How many terms does a boy spend in school who attends 25 school months ? 14. It takes a man 20 minutes to reach his office. What part of an hour does it take him each day to go and return ? How many hours does it take him in 6 days ? 15. A man bought 40 horses for $2880. At the same rate what will be the cost of 100 horses ? 238 THE RATIONAL ARITHMETIC. oz. = ounce. lb. = pound. cwt. = hundredweight. T. = ton. lib. 1 cwt. IT. 16 oz. 100 lbs. 20 cwt. 1. How many ounces in 8 lbs. ? In 14 lbs. ? In 20 lbs. ? In 25 lbs. ? 2. How many pounds in 3|- cwt. ? In 7^ cwt. ? In 9^ cwt. ? 3. How many pounds in 1 T. ? In 4 T. ? In 3i T. ? 4. How many ounces in ^ cwt.? In 2| cwt.? In 3| cwt.? 5. How many ounces in | T. ? In 3^ T. ? In 2^ T. ? 6. How many hundredweights in ^ T. and in ^ T. together? 7. 1 T. equals 10 cwt. and how many pounds? 8. Add: 2 T. 17 cwt. 25 lbs. 1 T. 8 cwt. 60 lbs. 1 2 75 4 1 40 10 cwt. 25 lbs. 8 oz. 9 cwt. 20 lbs. 4 oz 5 30 6 4 9 9 4 44 2 6 18 2 9. Subtract: 3 T. 15 cwt. 14 lbs. 2 T. 12 cwt. 9 lbs. 2 7 8 18 6 i 15 cwt. 75 lbs. 8 oz. 16 cwt. 43 lbs. 12 oz. 8 35 5 14 23 8 10. Multiply: 3 T. 5 cwt. 15 lbs. 2 T. 3 cwt. 20 lbs. 4 5 2 cwt. 9 lbs. 2 oz. 4 cwt. 3 lbs. 4 oz. 8 4 11. Divide: 2)4 T. 18 cwt. 50 lbs. 3)6 T. 15 cwt. 48 lbs. PART THIRD. 239 1. At 10^ an oz. how much will 3^ lbs. of cinnamon cost? 4 J lbs ? 2. What will a ton of hay cost at ^^' a pound? 3. A bushel of wheat weighs 60 lbs. How many bushels in a load of wheat weighing 1 T., 6 cwt. and 40 lbs. ? 4. A family uses 75 lbs. of ice every day for 20 days. What does it cost them at 35^' per cwt. ? 5. From 10 cwt. of sugar a grocer sold 8 cwt., 40 lbs., 12 oz. How much was left? 6. 60 lbs., 10 oz. of tea were divided equally among 5 per- sons. How much did each receive? 7. A man bought 3 lbs., 8 oz. of meat at 16^- a lb. and 2 lbs.. 12 oz. of butter at 20^ a lb. What was the total cost^ 8. A bushel of oats weighs 32 lbs. How many bushels in 80 cwt. ? 9. From a keg of nails weighing 1 cwt., 15 lbs. and 8 oz. were taken at one time, 9 lbs. and 12 oz. at another. What was the weight of the remainder? 10. How many bales of cotton, each weighing 450 lbs. may be shipped on a vessel which can carry 2250 tons ? On a vessel that can carry 3000 tons? 11. What will it cost to have 8 tons of coal hauled at 75^ a load of 3500 lbs. ? 12. 500 bbls. of flour are shipped in 7 equal loads. How many tons will each load weigh if 1 bbl. weighs 196 lbs.? 13. A man hauled 8 loads of wheat, 35 bu. at a load. A bushel of wheat weighs 60 lbs. What was the weight of the 8 loads? How many hundredweight in each load? 14. A farmer owning 700 bu. of oats sold 9 loads of 2240 lbs. each. One bushel weighs 32 lbs. How many bushels had he left ? 240 THE' RATIONAL ARITHMETIC. sec. = second. hr. = hour. wk. = week. min. = minute. d. = day. mo. = month. yr. = year. 1 min. 1 hr. 1 d. Iwk. lyr. 60 sec. 60 min. 24 hr. 7d. 12 mo. 52 wks. 1 d 365 d. 1. Review page 157. 2. How many months in |- a yr. ? In 3^ yrs. ? In 5 J yrs. ? 3. How many minutes in 3 lirs. ? In 2^ hrs. ? In 1^- hrs. ? In 1^ of an hr. ? In one day ? 4. In 4 yrs. how many days? In 2-J- yrs. ? In |^ of a yr. ? 5. How many seconds in 5 min. ? In one hr. ? In |- an lir. ? In J a day? ^ 6. Add: 8 hrs., 30 min., 15 sec. 3 mo., 1 wk.. 7 d. 3 29 45 8 3 12 1 yr., 8 mo., 15 d. 2 yrs., 6 mo., 10 d. 3 2 5 2 4 15 7. Subtract: 24 hrs., 50 min., 30 sec. 4 yrs., 8 mo., 15 d. 8 30 15 12 6 6 yrs., 4 mo., 20 d. 5 yrs., 9 mo., 6 d. 3 3 12 4 8 5 §. Multiply: 4 lirs., 15 min., 30 sec. 3 hrs., 15 min., 20 sec. 2 3 4 yrs., 2 mo., 4 d. 5 yrs. 2 mo., 3 d. 5 6 PART THIRD. 241 1. Divide: 3)6 hrs., 45 min., 15 sec. 6)24 hrs., 30 min., 18 sec. 2)4 yrs., 8 mo., 12 cl. 5)5 yrs., 10 mo., 15 d. 2. Find the time between June 6, 1885, to Aug. 12, 1889. The difference between dates is found by subtraction, using the num- bers of the months named. yr. mo. d. Aug. 12, 1889 = 1889 8 12 June 6, 1885 = 1885 6 6^ 4 2 6 3. Find the time from: Jan. 2, 1865, to June 5, 1887. Mar. 12, 1885, to May 21, 1889. July 21, 1872, to Sept. 26, 1890. Feb. 15, 1860, to Oct. 29, 1878. Nov. 2, 1889, to Dec. 28, 1892. Apr. 10, 1879, to Aug. 25, 1897. 4. If a boy works -J of each day for 6 days at 20^- an hr., what is his week's salary ? If he Avorks 9 hrs. overtime, half of that time at 15^/ a half hour and the rest at 20^/ a half hour, Avhat is his pay for the extra work? 5. A man leaves his office for home at 5.45 p. m. , and arrives 45 min. later. AVliat time does he reach home ? If he takes the same time going and returning every day, how many hours does he thus spend in ten days? 6. A fast mail train runs from Chicago to Burlington in 5 hrs. 20 min. 45 sec. and a freight train runs the same distance in 9 hrs. 40 min. How much longer does it take the freight train? 7. James was born September 18, 1887, and Willie was born December 21, 1892. How much older is James? 24.2 THE. RATIONAL ARITH^IETIC. 1. There are 319 pages in a book, how many pages are there in 369 such books? 2. There are 18 windows on each side of a car. How many windows are there in 397 cars? 3. In a 7 story buikling, there are on each of the sides, 27 windows on each story; there are on each of the ends 16 windows on each story. How many windows in all? 4. A street paved with stone blocks contains 65 stones in width and 786 in length. One man must buy half of these. If they cost him 7^ each, how much must he pay for them? 5. How many grains will 1,648 silver dollars weigh, if one dollar weighs 41 2 A grains? 6. A man deposits -$372 in the bank each week day for 26 weeks. How much does he deposit in that time? 7. A man rides 116 miles a day on his bicycle. How far from the ciify can he go and return in 12 days? 8. It is 195 feet between the telegraph poles. How much wire is needed to put up 6 wires on 257 poles? 9. A merchant bought 97 rolls of carpet, 27 of them con- taining 56 yards to the roll, 34 containing 59 yards to the roll, and the remainder 63 yards to the roll. How many yards did ho buy? 10. A manufacturer sold 65 cases of shoes, each case contain- ing 6 dozen pairs, at $2.75 a pair. What was the amount of his sale? 11. A farmer had 2,365 bushels of wheat. He sold 1,240 bushels at 65^ a bushel, 643 bushels at 85^ a bushel, and the remainder at 96^ a bushel. How much did he get for the entire crop of wheat? 12. A merchant's sales were $127 each day for 23 days, $156 each day for 19 days, and $113 each day for 32 days. How much were his sales for the entire time? PART THIRD. 243 1. It is 85 miles from Chicago to Milwaukee. A man went from Chicago to Milwaukee and returned each day for 26 days. How many miles did he travel? 2. A man lived 27 miles from Chicago. He came into the city and returned 6 days each week for 14 w^eeks. How many miles did he travel? 3. A manufacturer sold 687 bicycles at $47 each. How much did he get for them ? 4. An agent sold 163 reapers at $145 each. What was the amount of his sale? 5. The cost of one car is $965. A railroad company buys 235 such cars. AVhat is the cost of the cars? 6. A square building is 115 feet high and 122 feet wide. What is the area of one of its sides in square feet? 7. The same building is covered with a flat roof. How many square feet in the roof? 8. 53 cars stand in a solid blockade on the street. 26 of them are 32 feet long and the remainder 37 feet long. How far is it from one end of the blockade to the other ? 9. A street car company sold 540 horses at $62.25 each. How much did it get for the horses? 10. A man works 8J hours a day, 6 days in the week, for 26 Aveeks. How many minutes does he work ? 11. For every 25 papers a boy delivered he received 13^. If he delivered at this rate 175 papers a day each week day for 2 weeks, how much money did he get? 12. The school year contained 40 weeks. Each week I burned a quart of oil, which cost me 13^ a gallon. What did my oil cost me for the school year? 13. An elevator boy received $13 a month as wages. At the end of the year he had spent $19 for clothing, $32 for car fare, $4.50 for books and had given his mother $48. How much money did he have left? 244 THE RATIONAL ARITHMETIC. 1. Review page 80. 2. A man had in his pocket one five-dollar bill, two two- dollar bills, three one-dollar bills, two half dollars, three quarters, four dimes, six nickels and three pen- nies. How can he make even change for any one of the following purchases: 8. A hat at $2.65 and a necktie at 50^'? 4. A vest at $3.50 and a dozen collars at 95^? 5. One book at $1.25 and another at 38^? 0. A box of paper at 50^', and inkstand at 65^/ and a fountain pen at $1.95? 7. A pair of shoes at $2.95? 8. Railroad fare at 14.42? 9. Hotel bill for 2 J days at $2.50 a day? 10. A magazine, 35^' ; a newspaper, 2^/, and a sheet of paper, envelope and stamp, 5^/? 11. A bicycle suit at Id 70? 12. Repairing bicycle, $4.70? 13. A boy went to the bank to get change, at various times, for the following amounts. How many of each piece of money might be given him? 14. A twenty-dollar bill so as to get five-dollar bills, one- dollar bills and half dollars? 15. A ten-dollar bill, so as to get two-dollar bills, one-dollar bills, half dollars and quarters? IG. A five-dollar bill, so as to get dollars, half dollars, quar- ters and dimes? 17. A two-dollar bill, so as to get half dollars and dimes? 18. A one-dollar bill, so as to get quarters, dimes, nickels and pennies ? 19. A half dollar, so as to get dimes, nickels and pennies? 20. A quarter, so as to get pennies, nickels and any other coin that he could get? PART THIRD. 245 24 sheets — one quire. 20 quires = one ream. 1. How many sheets in ^ a quire? In f of a quire? 2. How many sheets in J of a ream ? In 2 reams ? 3. How many quires in 72 sheets? In 96 sheets? In 240 sheets ? 4. "What is the cost of a quire of paper at 2^* a sheet? 5. What is the cost of a ream of paper when bought at V> sheets for 1^? 6. A man bought 1 box of paper containing 2 quires ajid another containing 5 quires. How many sheets of paper did he get? 7. If 12 sheets of paper cost 5^*, what is the cost of a ream at the same rate? 8. I paid $1.20 for a ream of paper. What was the cost of ^ a quire? 9. How many boxes will hold a ream of paper if each box contains IJ quires? IJ quires? 10. A man bought paper at $1.50 a ream and sold it at 12 sheets for 5^/. How much did he gain ? 11. A man bought paper at $2.75 a ream and sold it at 20^- a quire. What was his gain ? If he had paid §3 a ream and sold it at 25^* a quire, how much more would he have gained? 12. A ream of paper is divided into 40 equal parts. What part of a quire is each? 13. Prom 3 reams of paper 1 J reams were sold at one time and 3 quires at another time. How many sheets remained? How many quires? What part of a ream? 14 After collecting damaged lots of paper, a man found he had 18 quires and 10 sheets of one kind, 11 quires and 5 sheets of another kind, and 10 quires and 5 sheets of a third kind. He sold it at $1.25 a ream. What did he get for all? 246 THE RATIONAL ARITHMETIC. 1. A man leaves his home each week day at 8.11 in the morning and reaches his office at 8.27. He returns in the evening, leaving his office at 5.45 and reaching his home at 6.01. How many hours does he spend on the way in a Aveek? In the month of January, i£ there are 4 Sundays in a month? 2. A teacher leaves her home each morning at 8.20 and reaches the school-house at 8.47. She returns, leaving the school-house in the evening at 3. 48 and reaching her home at 4.05. How many hours does she spend on the way in 4 weeks? How many hours in the school year if there are 38 weeks of school in a year? 3. How far does she travel in 4 weeks if the school-house is 1^ of a mile from her home? How far does she travel in a school year of 40 weeks? 4. A train leaves St. Louis at 11.31 in the evening and reaches Chicago at 8 o'clock in the morning. It stops 11 minutes at stations on the way. AVhat is the actual running time from St. Louis to Chicago? 5. A train leaves Chicago at 9 o'clock in tlie evening and arrives in St. Louis at 7.28 the next morning. Another train leaves Chicago at 11.30 in the evening, reaching St. Louis at 8.04 next morning. In how much less time does one train run than the other, and which is the faster train? 0. A train leaves Chicago at 6.30 in the evening and reaches Omaha at 8.15 next morning. If 23 minutes are spent in stopping at stations, what is the actual running time from Chicago to Omaha? 7. A second train leaves Chicago at 10.30 in the evening and reaches Omaha at 4 o'clock the next afternoon. How much longer is this train on the way than the one which left Chicago at 6.30? PART THIRD. 247 1. If a block containing 3 A. is 20 rods wide, how long is it? If it contains 10 lots, how many square rods in each? 2. A lot cost ^200, the house cost 124^ times as much as the lot, and the fence ^ as much as the lot. What did the house and the fence together cost? 3. The battle of Lexington was fought April 19tli, 1775. How many Aprils have there been from then to the present day? 4. The buildings for the Columbian Exposition were dedi- cated October 12th, 1892. How many years, months and days since then? 5. Nathaniel Hawthorne was born July 4th, 1809, and Texas was admitted to the Union July 4th, 1845. What was Hawthorne's age in months, when Texas became a state? 6. Daniel Webster was born January 18tli, 1782, and James A. Garfield was born November 19th, 1831. How old was Webster when Garfield was born? 7. Memorial Day was first celebrated by order of John A. Logan, May 30th, 1868, and he was then 42 years, 3 months and 21 days old. When was he born? 8. Gen. Grant was born April 27th, 1822, and was 41 years, 2 months and 7 days old when Yicksburg, Miss,, was captured. When did he capture Yicksburg? 9. Gen. AYm. T. Sherman was born Feb. 8th, 1820, and fin- ished his great march through Georgia December 13th, 1864. How old was he on that day? 10. Gen. Sheridan Avas born March 6th, 1831, and made his famous ride from Winchester to the battlefield at Cedar Creek, October 19th, 1864. What was his age then? 11. Tlie area of Illinois is 56,650 square miles and the area of the Philippine Islands is 114,326 square miles. How much more than twice as large as Illinois are the Philippines ? 248 THE RATIONAL ARITHMETIC. 1. A grain dealer bought 25,000 bu. of wheat at 97^' per bushel, and after 3 months sold it for $1.12 per bu. He paid storage charges at the rate of -J^- per bu. each month. What was his gain ? 2. A grain elevator holds 800,000 bu. If it is kept full for 6 months, what will storage charges amount to at ^^• per bu. each month? 3. Six vessels carry 800,000 bu. of grain from Chicago to Buffalo. If 2 of them carry 160,000 bu. each, what is the average load of the other four? 4. Wheat weighs 60 lbs. to the bushel. What is the weight in T. of 160,000 bu. ? In cwt. ? 5. At 6^/ per cwt. what does it cost to ship 120,000 bu, of wheat from Chicago to Buffalo? 6. An elevator containing 645,000 bu. of grain caught fire and the grain was damaged. The grain was worth 87^ ]:>er bu. and was insured for $250,000. What was the loss ? 7. The owner of the grain, after receiving the insurance money, sold the damaged grain for feed at 13^' per bushel. What was his actual loss? 8. Corn weighs 56 pounds to the bushel. How many car loads of 15 tons each will fill a vessel that can carry 90,000 bu. ? 9. At 10^/' per hundredweight, what will it cost to ship 90,000 bu. of corn from Chicago to New York City? 10. A vessel owner agrees to carry 125,000 bu. of corn for $3750. How much does he receive per hundred- weight ? 11. A builder received $127.25 for making some repairs to a house. He pays his 2 helpers $2.50 each per day for the 12 days needed to do the work. AVhat is his own share of the money ? PART THIRD. 249 1. How many caps worth 33^^ each, can be bought for §15? For $24? -. If the price of bread is raised from 5^* to 6^ per loaf, how much more will 700,000 loaves cost? H. If a barrel of flour will make 196 loaves of bread, how many barrels are required to make 700,000 loaves? 4. A rapid-fire gun shoots 100 shells per minute, how many shells will 7 such guns shoot at the same rate in ^- a minute? In 1^ minutes? 5. If each shell weighs 1 lb., how many guns will it take to fire a ton of shells in 1 minute? G. If each shell uses up 6 ounces of powder, how much pow- der will be used by 15 guns in 1 minute? 7. A man earning §1.20 per day works 11 days in January, 17 days in February, 28 days in March, and 25 days in each of the next three months. How much does he earn in the six months? 8. A man working for $12 per week puts in J of a day over- time each day, for which he receives double pay. How much does he earn in 4 weeks if he works every work- ing day? 9. What will the bricks for a wall 39 ft, high cost at §5.25 per thousand, if one thousand bricks will carry up the wall 6 in. ? 10. A brick mason earning 50^' per hour, works 7 hours on Monday, 5 hours on Tuesday, and full time — 8 hours a day — for the rest of the week. What is his pay for the week? 11. A gang of 20 men digging for a foundation are stopped by rain from half past 9 to a quarter past 10 o'clock. If they are working for 20^' per hour each, how much pay does each one lose? How much would they all lose at 25^' per hour? 350 THE RATIONAL ARITHMETIC. %'■ '/, L- F B G w c D — „ — II :■' ..." ! ./W'V //•,/'/'■/ , ^%>^< E " J * UNIVERSITY OF CALIFORNIA UBRARY Jl'i'l'iiiiJiiii'ii liBii' lilHIi ii 11 iiiitlr lilliiiiiiiiiiiiiii liii iiiliiiiiti sMi-iii'iji. jffHilll!!! 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