,SON, HINKT.E & CO. LAXTON, JREMSEH & HAFFELFINGER. WORK: CLARK & MAYNARO. LIBRARY OF THK UNIVERSITY OF CALIFORNIA. OK Received Accession No. 7 3 189*1. WHITE'S GRADED-SCHOOL SERIES. PRIMARY ARITHMETIC, UNITING ORAL AND WRITTEN EXERCISES IN A NATURAL SYSTEM OF INSTRUCTION, BY E. E. CINCINNATI : WILSON, H INKLE & CO, PHIL'A: CLAXTON, REMSEN & HAFFELFINGER. NEW YORK: CLARK & MAYNARD. WHITE'S GBADED-SCHOOL SERIES. COMPLETE IN THREE BOOKS. I. PRIMARY ARITHMETIC. II. INTERMEDIATE ARITHMETIC. III. COMPLETE ARITHMETIC. PLAN OF PRIMARY ARITHMETIC, Lessons I to XI develop the idea of numbers from one to ten and combine groups of objects. Lessons XI to XX teach the Addition and Subtraction of num- bersresults not exceeding ten. Lessons XX to XXIX teach the Addition and Subtraction of num- bers results not exceeding fifty. Lessons XXX to XLII teach the Addition of numbers to amounts not exceeding one hundred. Lessons XLIII to LII teach the Subtraction of numbers minu- end in Oral Exercises not exceeding one hundred. Lessons LII to LXXIII teach the Multiplication of numbers- product in Written Exercises not exceeding one thousand. Lessons LXXIII to XC teach the Division of numbers dividend in Written Exercises not exceeding one thousand. Lessons XC to XCII inclusive contain a General Review. Entered, according to Act of Congress, in the year 18GS, by WILSON, HINKLE & CO., In the Clerk's Office of the District Court of the United States, for the Southern District of Ohio. KI.ECTROTYPED AT THE FRANKLIN TYPE FOUNDRY, CINCINNATI. PREFACE. THE true method of imparting to a child a clear comprehension of the value of numbers, the foundation of arithmetical knowl-* edge, consists of three steps, viz. : 1. The perception of numbers represented by objects in sigiit. 2. The conception of numbers applied to objects not in sight. 3. The conception of numbers not applied to objects. A knowledge of the elementary combina- tions of numbers is best communicated in the same manner. A faithful observance of this natural ord?r constitutes one of the characteris:ic features of this first book in arithmetic. Ab- stract numbers and operations are reached, in practice as well as in theory, as the final step. The plan every-where observed is, first, Physical Objects (in sight or represented by pictures); sec- ondly, Concrete Numbers; and, thirdly, Abstract Numbers. In this and other evident features, the book is n practical embodi- ment of the simplest and most vital principles of the inductive method of instruction. But the distinguishing feature of the book, as well as of the Series of which it forms a part, is the complete UNION of Mental (Oral) and Written Arithmetic. This is secured, not by scattering a few miscellaneous slate exercises through the work, but by making every oral exercise preparatory to a written one, and by uniting both as the essential complements of each other. Slate and blackboard exercises are introduced at the very beginning of the course, and are continued, increasing in number and diffi- culty, to the end. Each lesson gives the pupil something to do, as well as something to study. Two other noticeable features of the book are the great variety of exercises the object being to make the pupil accurate and rapid in combining small numbers and their preeminently progressive character. Attention may also be called to the pre- sentation of converse operations, as Addition and Subtraction, Multiplication and Division, in connection with each other, as well as separately ; to the converse forms of the tables and their non memoriter character; and, also, to the superior typography, and the number, beauty, and utility of the illustrations. It is hoped that these and other features will commend the work to all intelligent and progressive teachers. Columbus, Ohio, May, 18G8. SUGGESTIONS TO TEACHERS. THE first thirty lessons of this book may be mastered in the earlier part of the primary course. To this end, the pupils should be advanced very slowly, and the exercises should be multiplied until great rapidity and accuracy are secured. The first step in every new combination is to combine groups of objects, and, both in the pupil's study and the teacher's instruc- tion, the pictorial illustrations should be supplemented by the use of visible objects, as counters, blocks, beans, etc. The teacher should also refer to other familiar objects in sight, as chairs, desks, slates, etc. Attention should be called to the difference between the pictures in the lessons, and the objects which they represent. Pupils should be required to give answers in complete sentences. Suppose the question to be, "How many tops are 5 tops and 4 tops?" The answer should be, "5 tops and 4 tops are 9 tops. 11 To secure rapidity, drills may occasionally be introduced in which onlv results are given, as "9 tops."* Nothing is gained by requiring pupils to give reasons for answers to simple exam- ples, and even problems which admit of a formal analysis should be solved briefly and concisely. See page 51. The written exercises are designed to go hand in hand with the oral, and should be taught with equal thoroughness. They are so easy and progressive that but little explanation will be found necessary. They should not only be copied and performed by the pupils on their slates, but they should also be used as blackboard exercises. Such exercises are exceedingly valuable both as a means of awakening interest and of imparting skill in numerical calculations. Blackboard exercises, affording a great variety of combinations, and requiring but little labor in copying, may be easily arranged. The following are given as illustrations : 0) (2) (3) 1 5 4 32 76 12 8 54 98 20 16 76 11 10 28 24 948 13 4 12 36 4 32 By pointing successively to the figures in the oblique rows and to the figure between 'them, the first diagram will afford an excellent drill in adding or in multiplying, the "4," or any other figure in its place, being the number added or multiplied, as the case may be. The second diagram will afford a good exercise in subtraction, anJ the third in division. PRIMARY ARITHMETIC, 3UBSSOH * Touch your head. How many heads have you? How many chins? Hold up one hand. Hold up two hands. How many fingers do I hold up? Hold rfj| up two fingers. Hold up one thumb. Hold ^ up two thumbs. How many eyes have you? How many cheeks? How many tongues ? How many lips ? How many feet? How many nuts do you see in this picture.? How many leaves? How many stems has each nut ? Bring me one block. Bring me two blocks. Take away one block. How many blocks are left? Hand me two books. Take one of them. How many books have I left? Make two marks on your slate. Make the figure one on your slate, thus : X Make the figure two on your slate, thus : J?. Make the figure 2 two times. PRIMARY ARITHMETIC. H. To TEACHERS. Drill the pupils until they can tell the number of objects in each group, and combine the groups, without counting. Hold up two fingers. Hold up two hands. r{S How many fingers do I hold up? Hold up )^( three fingers. Hold up two fingers. Here is a picture of a dog. How many fore feet has he ? How many hind feet? How many of his feet can you see? Bring me two blocks. Bring me one more. How many blocks have I now? Take one block. How many blocks have I left? Make three marks on your slate. How many acorns in each of these groups? How many in the third group more than in the first? How many groups of rabbits do you see? How many rabbits in the first group? How many rabbits in the second group? How many balls are and ? and are how many balls? Make the figure three on your slate, thus: j. Make the figures 1, 2, 3. PRIMARY ARITHMKTIC. USSSON HI. . How many fingers do I hold up on my right hand ? How many on my left hand? How many on both hands? Hold up four fingers. Here is a picture of a fine ox. How many horns has he? How many ears ? How many legs ? How many feet? Bring me four blocks. Take one of them. How many blocks have I now? Make three marks on your slate. Make four marks. How many groups of pears do you see? How many pears in the first group ? How many in the second group? How many in the third group? How many pears in the second group more than in the first? How many flowers in each of these groups ? How many more flowers in the second group than in the first? How many blocks are liSP ||p HP and HIP ? HP and |ijp pip are how many blocks? How many balls are and 4i? PRIMARY ARITHMETIC. Make the figure four, thus : ^. Make the figure 4 four times. Make 1, 2,- 3, 4. To TEACHERS. Multiply these exercises until the pupils can add the groups instantly, without counting. USSSOSI How many fingers do I hold iip on my right hand? How many on my left hand? How many on both hands? Hold up four fingers. Hold up five fingers. How many geese do you see in this picture ? How many goslings ? If two gos- lings should go away, how many would be' left? Place four blocks on the table. Add one block more. How many blocks are there now? Take away two blocks. How many blocks are left? How many groups of tops are here? How many tops in the first group? How many in the third? How many in the second? How many horses in each of these groups? How many in the first group more than in the second ? PRIMARY ARITHMETIC. 9 Place three blocks on the table. Add two blocks more. How many blocks are there? How many balls are and ^p? and are how many balls? Make the figure five, thus : & Make the 'figure 5 five times. Make 1, 2, 3 ; 4, 5. USSSOH V. How many fingers do I hold up on my right hand? How many on my left hand? How many on both hands? Hold up five fingers. Hold up six fingers. How many little chickens do you see in this picture? How many are near the old hen's beak? How many are near her right wing? How many in both groups? Place five blocks on the table. Add one block more. How many blocks on the table now? Take away three blocks. How many blocks are left? Here are how many groups of girls ? How many girls are in the first group? How many in the second? How many more girls in the second group than in the first? 10 PRIMARY ARITHMETIC. How many kittens in each group below? How many more in the first group than in the second? How many stars are -/- ;|c -)'- -/- -/ and -/-? '!' */r '!- '!' an( i '!- w are how many stars? How many stars are -*'- -)J- and -)'- -)(-? ]\Iake the figure six, thus : & Make 1, 2, 3, 4, 5, 6. How many figures have you made? 3L.BSSOH How many fingers do I hold up on my right hand? How many on my left hand? How many on both hands? Hold up six fingers. Hold up seven fingers. Here is a bird's nest. How many eggs are in it? If the bird should lay one egg more, how many eggs would there then be in the nest? Place six blocks on the table. Add one block more. Six blocks and one block are how many blocks ? Take away two blocks. How many blocks are left on the table? Here are two groups of beautiful acorns. How many acorns in the first group ? How many in the PRIMARY ARITHMETIC. 11 second group? How many more in the second group than in the first? How many pears in each of these groups? How many more in the first than in the second ? If two ipears should be taken from the first group, how many would be left? How many blocks are and ' and PJOiiP are how many blocks? Make the figure seven, thus : f. Make the figure 7 seven times. Make 1, 2, 3, 4, 5, 6, 7. USSSOH VH. How many fingers do I hold up on my right hand ? How many on my left hand? How many on both hands? Hold up eight fingers. Put down two fingers. How many fingers are now up? OJ ^ Here are two fine rab- bits. How many ears have both of them? How many legs has each rabbit? How many legs have they both? Place four blocks on the table. Add four blocks more. How many blocks are now on the table? 12 PRIMARY ARITHMETIC. Place eight blocks on the table. Take away one block. How many blocks are left ? Take away two blocks more. How many blocks are now left? How many boys are in the first group? How many in the second? How many in the third? How many boys in the third group more than in the first? How many tops are spinning in the first group? How many in the second? How many in the first more than in the second? If two tops were taken from the first group, how many would be left? and are how many balls? Make the figure eight, thus: (- ->(- -)'- and -> '- -X- ? JL .V- .V. and -V- -V- -V- -V- -V- -V- are how many stars? How many stars are -)'- -)'- -)'- -JJ- and -"- -) -)(- -/- ->'- ? Make the figure nine, thus : 0. Make the figure 9 nine times. Make 1, 2, 3, 4, 5, 6, 7, 8, 9. 14 PRIMARY ARITHMKTIC. How many fingers do I hold up? How many thumbs? How many fin- gers and thumbs counted together? Here is a nice fan, and a pair of gloves. How many fingers has each glove? How many fingers have both gloves? How many folds has the fan? Count them. How many nails are on your right liand? How many nails on your left hand? How many on both hands? How many keys in the first group? How many in the second? How many in the third? How many more keys in the third group than in the first? How many poplar trees in the first row? How many in the second row? How many more trees in the first row than in the second? ^ULJLJ _JOLJL^ Place ten blocks in a row. Take away five blocks. How many blocks are left? Take away five more. How many blocks are now left? Make the character naught, thus : ^ This stands for not any or nothing. Make ten, thus : /#. Make 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. PRIMARY ARITHMET JUBSSON 03' Count the balls in each row from left to right and from right to left. Count also the rows up and down. Naught. One. Two. Three. Four. Five. Six. Seven. Eight, Nine. Ten. 1 2 3 4 5 6 7 8 9 10 How many balls are in the lowest row? How many in the third row from the top? How many in the fifth row ? How many in the seventh ? How many horizontal rows are there ? How many verti- cal rows? To TEACHERS. Make this table on the blackboard, using circles, squares, triangles or other simple figures, and drill the pupils in rapid counting, thus (pointing to the figures): One; one, two; two, one; one, two, three; three, two, one, etc. each row being counted in two directions. Count first the horizontal rows and then the vertical. The drill should be continued until great rapidity and accuracy are secured. 16 PRIMARY ARITHMETIC. USSSON ORAL EXERCISES. To TEACHERS. The object of this and the next eight lessons is to teach the addition and subtraction of numbers not exceed- ing ten. The first step is to add and subtract groups of visible objects, or objects represented by pictures ; the second, to add and subtract groups of objects not in sight (concrete numbers) ; and the third, to add and subtract the corresponding abstract numbers. The exercises in each step should be multiplied until the results are given by the pupils instantly, without counting. The tables may be recited thus: and 1 are 1; 1 and 1 are 2; 2 and 1 are 3, etc.; and 1 from 1 leaves 0; 1 from 2 leaves 1, etc. 1. Here is a bird's nest and here is one. One nest and one nest are how many nests? Two nests and one nest are how many nests? 2. One bird and one bird are how many birds? Two birds and one bird are how many birds? How many are 1 and 1 ? 2 and 1 ? 3. John caught three fishes, and then he caught one more. How many did he catch in all? Four fishes and one fish are how many fishes? How many are 3 and 1? 4 and 1? 4. Charles has picked five fine clusters of cherries and John one. Five clusters and one cluster are PRIMARY ARITHMETIC. 17 how many clusters? Six clusters and one cluster? How many are 5 and 1? 6 and 1? 5. If Charles should give one of his clusters to Jane, how many would he have left? One cluster from five clusters leaves how many clusters? One from 5 leaves how many ? 1 from 6 ? 6. Seven acorns and one acorn are how many acorns? Eight acorns and one acorn? How many are 7 and 1 ? 8 and 1 ? 7. Eight boys and one boy are how many boys? Nine boys and one boy are how many boys? One boy from nine boys leaves how many? 8. How many tops are 5 tops and 1 top? 6 tops and 1 top? 3 tops and 1 top? 8 tops and 1 top? 7 tops and 1 top ? 9 tops and 1 top ? 9. One top from 3 tops leaves how many tops? 1 top from 5 tops? 1 top from 7 tops? 1 top from 8 tops? 1 top from 6 tops? 1 top from 10 tops? Hoiv many are TaJce and 1? 1 from 1. 1 and 1? 1 from 2. 2 and 1? 1 from 3. 3 and 1? 1 from 4. 4 and 1 ? 1 from 5. 5 and 1? 1 from 6. 6 and 1? 1 from 7. 7 and 1 ? 1 from 8. 8 and 1? 1 from 9. 9 and 1? 1 from 10. P. A. 2. 18 PRIMARY ARITHMETIC. 10. How many are 2 and 1? 4 and 1? 6 and 1? Sandl? 9andl? 3 and 1? 5 and 1? 7 and 1? 11. One from 3 leaves how many? 1 from 5? 1 from 6? 1 from 7? 1 from 9? 1 from 10? 1 from 8? 1 from 4? 3L.BSSOH 3CH, ORAL EXERCISES. 1. How many fingers are one finger and one fin- ger ? One finger and two fingers ? 2. How many clusters of grapes are one cluster and two clusters ? Two clusters and two clusters ? How many are 1 and 2? 2 and 2? 3. Jane has picked three violets and Kate two : how many violets have both picked? Four violets and two violets are how many violets? How many are 3 and 2? 4 and 2? 4. Two violets from five violets leave how many violets? Two violets from six violets? Two from 5 leaves how many ? 2 from 6 ? 5. Here are five lambs, and here are two more. How many lambs do you see? PRIMARY ARITHMETIC. 19 6. Two lambs from six lambs leave how many lambs? Two lambs from seven lambs? Two from 6 leaves how many? 2 from 7? 7. How many robins do you see? Six robins and two robins are how many robins? Seven robins and two robins? How many are 6 and 2 ? 7 and 2 ? 8. How many do two birds from eight birds leave? Two birds from nine birds? TW T O from 9 leaves how many? 2 from 8? 9. Here are eight shells in one group and two shells in another. How many are eight shells and two shells? How many are 8 and 2? 7 and 2? 10. Jane found ten shells and gave two of them to Willie: how many had she left? Two from 10 leaves how many? 2 from 9? How many are and 2? 1 and 2? 2 and 2? 3. and 2? 4 and 2? 5 and 2? 6 and 2? 7 and 2? 8 and 2? TaJce 2 from 2 from 2 from 2 from 2 from 2 from 2 from 2 from 9. 2 from 10, 20 PRIMARY ARITHMETIC. 11. How many are 2 and 2? 4 and 2? 3 and 2? 5 and 2? 6 and 2? 8 and 2? 7 and 2? 12. Two from 4 leaves how many? 2 from 3? 2 from 5? 2 from 7?' 2 from 6? 2 from 8? 2 from 10? 2 from 9? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (1) (2) ' (3) (4) (5) (6) 222222 122112 Add 246875 122222 122121 (1) (2) (3) (4) (5) (6) 122212 From 4 6 8 10 9 7 Add _1 _2 _1_ _4 Take 222222 To TEACHERS. These exercises should be copied by the pupils on their slates, added, and the results properly written below. They, or similar exercises, should also be written on the blackboard, and the class drilled on them until the results are given instantly. In adding the columns at the right, the results only should be named; as, (Ex. 3) 1, 3, 5, 7, 9. ORAL EXERCISES. 1. How many blocks are one block and two blocks? One block and three blocks? 2. How many horses do you see? Two horses and three horses are how many horses? Three horses and three horses? PRIMARY ARITHMETIC. 21 3. Two marbles and three marbles are how many marbles? Three marbles and three marbles? How many are 2 and 3? 3 and 3? 4. A man has five horses : if he sell three of them, how many will he have left? Three from 5 leaves how many? 3 from 6? 5. How many fawns are in these two groups? Five fawns and three fawns are how many fawns? 6. Four squirrels are running on a fence and three are on a tree. How many are four squirrels and three squirrels? Five squirrels and three squirrels? How many are 4 and 3 ? 5 and 3 ? 7. Six kittens and three kittens are how many kit- tens? 7 kittens and 3 kittens? 8. How many boys are six boys and three boys ? Seven boys and three boys? How many are 6 and 3? 7 and 3? 9. Three kittens from -nine kittens leave how many ? Three kittens from ten kittens ? Three from 9 leaves how many? 3 from 10? 10. How many pears are 7 pears and 3 pears?* 6 pears and 3 pears? 5 pears and 3 pears? 4 pears and 3 pears? 3 pears and 3 pears? 22 PRIMARY ARITHMETIC. 11. How many caps are 1 cap and 3 caps? 3 caps and 3 caps? 5 caps and 3 caps? 4 caps and 3 caps? 6 caps and 3 caps? 7 caps and 3 caps? 12. Three pears from 4 pears leave how many pears? 3 pears from 6 pears? 3 pears from 8 pears? 3 pears from 10 pears? 3 pears from 7 pears? Hoiv many arc and 3? 1 and 3? 2 and 3? 3 and 3? 4 and 3? 5 and 3? 6 and 3? 7 and 3? Take 3 from 3 from 3 from 3 from 3 from 3 from 3 from 3 from 10. 13. How many are 1 and 3? 3 and 3? 2 and 3? 5 and 3? 4 and 3? 7 and 3? 6 and 3? 14. How many are 3 and 2? 3 and 1? 3 and 4? 3 and 5? 3 and 6? 3 and 3? 3 and 7? 15. Three from 4 leaves how many? 3 from 6? 3 from 5? 3 from 8? 3 from 7? 3 from 10? 3 from 9? 16. Three from 5 leaves how many? 2 from 5? 3 from 9? 2 from 9? 3 from 8? 2 from 8? 3 from 10? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) 333333 Add _2 _ _5 _7 _6 _3 (1) (2) (3) (4) (5) (6) From 5 7 8 10 9 6 Add Take 333333 (1) (2) (3) (4) (5) (6) 1 3 3 1 1 3 3 2 2 2 1 3 3 2 1 PRIMARY ARITHMETIC. 23 3UBSSON ORAL EXERCISES. 1. How many fingers are one finger and three fin- gers? One finger and four fingers? 2. Here are two rabbits, and here are four more. How many are two rabbits and four rabbits? One and 4 are how many? 2 and 4? 3. If four of these six rabbits should run away, how many would be left? Four rabbits from six rabbits leave how many rabbits? Four from 5 leaves how many? 4 from 6? 4. Henry has bought three pine-apples, and Jane four : how many pine-apples have they both ? 5. How many oranges are three oranges and four oranges? Four oranges and four oranges? Three and 4 are how many? 4 and 4? 6. How many acorns are five acorns and four acorns? Six acorns and four acorns? 7. How many are five marbles and four marbles? Six marbles and four marbles? Five and 4 are how many? 6 and 4? 24 PRIMARY ARITHMETIC. 8. Nine robins are standing on a limb : if four should fly away, how many would be left ? 9. Four robins from ten robins leave how many robins? Four robins from nine robins? Four from 9 leaves how many? 4 from 10? 10. Here are two rows of trees. How many trees in both rows ? How many are 3 trees and 4 trees ? 5 trees and 4 trees? 6 trees and 4 trees? 11. How many are 2 doves and 4 doves? 4 doves and 4 doves? 6 doves and 4 doves? 5 doves and 4 doves? 3 doves and 4 doves? 12. Four trees from 6 trees leave how many trees? 4 trees from 8 trees? 4 trees from 10 trees? 4 trees from 7 trees? 4 trees from 9 trees? How many are and 4? 1 and 4? 2 and 4? 3 and 4? 4 and 4? 5 and 4? 6 and 4? Talte 4 from 4 from 4 from 4 from 4 from 4 from 4 from 13. How many are 2 and 4? 4 and 4 ? 3 and 4? 5 and 4? 6 and 4? 14. How many are 4 and 1 ? 4 and 3? 4 and 5 ? 4 and 4? 4 and 2? 4 and 6? 15. Four from five leaves how many? 4 from 4? 4 from 6? 4 from 7? 4 from 9? PRIMARY ARITHMETIC. 25 16. Four from 6 leaves how many? 4 from 8? 3 from 8? 4 from 10? 3 from 10? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) 44444 Add _2 j4 _3_ _5 _6_ (1) (2) (3) (4) (5) From 6 8 7 9 10 Take 4 4 4 4 (1) (2) (3) (4) (5) (6) 4 4 2 2 1 2 2 1 2 1 4 4 1 2 2 1 2 1 1 (6) 1 4 2 2 3 5 Add 1 2 2 1 3 2 3UESSGM ORAL EXERCISES. 1. How many girls are one girl and five girls? Two girls and five girls? 2. Plow many are two palm trees and five palm trees ? One palm tree and five palm trees ? How many are 1 and 5? 2 and 5? 3. A hunter saw six "deer, and five of them ran away : how many deer were left ? 4. Five deer from six deer leave how many deer? Five deer from seven deer? Five from 6 leaves how many? 5 from 7? 5. Here are two groups of flies. How many flies are three flies and five flies? Four flies and five flies? 26 PRIMARY ARITHMETIC. 6. How many rabbits are three rabbits and five rabbits? Four rabbits and five rabbits? How many are 3 and 5? 4 and 5? 7. Mr. Smith owns eight sheep : if he sell five of them, how many sheep will he have left? Five from 8 leaves how many? 5 from 7? 8. Kate has five pears in one basket, and five in another : how many pears lias she in both ? 9. How many are four stars and five stars? Five stars and five stars? 10. Five pears from nine pears leave how many pears? Five pears from ten pears? Five from 9 leaves how many? 5 from 10? 11. How many quails are 2 quails and 5 quails? 1 quail and 5 quails? 3 quails and 5 quails? 5 quails and 5 quails? 4 quails and 5 quails? 12. Five birds from 6 birds leave how many birds? 5 birds from 8 birds'? 5 birds from 7 birds? 5 birds from 10 birds? 5 birds from 9 birds? JToiv DI a 11 1/ are and 5? 1 and 5? 2 and 5? 3 and 5? 4 and 5? 5 and 5? Taltc J5 from 5. 5 from . 6. 5 from . 7. 5 from 8. 5 from 9. 5 from 10. PRIMARY ARITHMETIC. 27 13. How many are 1 and 5? 3 and 5? 2 and 5? 4 and 5? 5 and 5? 14. How many are 5 and 2? 5 and 1? 5 and 3? 5 and 5? 5 and 4? 15. Five from 5 leaves how many? 5 from 7? 5 from 6? 5 from 8? 5 from 9? 5 from 10? 16. How many are 3 and 3? 4 and 4? 5 and 5? 2 and 2? 4 and 3? 5 and 3? 7 and 3? 17. Two from 8 leaves how many? 4 from 8? 5 from 8? 3 from 8? 3 from 9? 4 from 9? 5 from 9? 2 from .9? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) 555555 Add 254130 (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 2 From 7 10 9 6 8 5 Add _ Take 555555 1 2 USSSONf ORAL EXERCISES. 1. Jane picked one nice cluster of cherries, and Harry picked six clusters: how many clusters did they both pick? 2. How many clusters are one cluster and six clus- ters? Two clusters and six clusters? How many are 1 and 6? 2 and 6? 23 PRIMARY ARITHMETIC. 3. How many clusters of cherries will remain if you take six clusters from seven clusters? Six clus- ters from eight clusters? Six from 7 leaves how many? 6 from 8? 4. Charles found three shells on the sea-shore, and John six: how many shells did both find? 5. How many pebbles are two pebbles and six pebbles? Three pebbles and six pebbles? How many are 2 and 6? 3 and 6? 6. How many shells will remain if you take six shells from nine shells? Six shells from eight shells? Six from 9 leaves how many ? 6 from 8 ? 7. How many rabbits in each of these groups? How many are four rabbits and six rabbits? Three rabbits and six rabbits? How many are 4 and 6 ? 3 and 6 ? 8. A hunter saw ten rabbits, and caught six of them : how many rabbits got away ? 9. How many will remain if you take six marbles from ten marbles? Six marbles from nine marbles? Six from 10 leaves how many? 6 from 9? 10. How many blocks are 2 blocks and 6 blocks? 1 block and 6 'blocks? 3 blocks and 6 blocks? 4 blocks and 6 blocks? PRIMARY ARITHMETIC. 29 11. How many pears are 1 pear and 6 pears? 3 pears and 6 pears? 2 pears and 6 pears? 4 pears and 6 pears? 12. Six blocks from 7 blocks leave how many blocks? 6 blocks from 6 blocks? 6 blocks from 8 blocks? 6 blocks from 10 blocks? 6 blocks from 9 blocks? Hoiv many are and 6? 1 and 6? 2 and 6? 3 and 6? 4 and 6? Talce 6 from 6. 6 from 7. 6 from 8. 6 from 9. 6 from 10. 13. How many are 1 and 6? 3 and 6? 4 and 6? 2 and 6 ? 6 and 1 ? 6 and 2? 6 and 4? 14. Six from 7 leaves how many? 6 from 8? 6 from 10? 6 from 9? 6 from 6? 15. How many are 4 and 3? 5 and 4? 3 and 6? 6 and 2? 4 and 5? 6 and 3? 5 and 3? 16. How many are 2 and 4? 3 and 6? 5 and 3? 4 and 4? 6 and 4? 3 and 4? 4 and 5? 17. Two from 6 leaves how many? 3 from 9? 5 from 10? 4 from 7? 4 from 9? 2 from 8? 3 from 10? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) 66666 61112 Add 32410 11033 06432 (1) (2) (3) (4) (5) 2 1 3 2 1 From 9 8 10 7 6 A <*d JL_ Take 66666 30 PRIMARY ARITHMETIC. USSSOKI ORAL EXERCISES. 1. How many pine-apples are one pine-apple and seven pine-apples ? Two pine-apples and seven pine- apples ? 2. A fruit dealer bought eight pine-apples, and sold seven of them: how many had he left? 3. Seven pine-apples from eight pine-apples leave how many pine-apples? 4. How many are two apples and seven apples? Two peaches and seven peaches? Two pears and seven pears? Two plums and seven plums? How many are 1 and 7? 2 and 7? 5. Seven apples from eight apples leave how many apples? Seven apples from nine apples? Seven from 8 leaves how many? 7 from 9? 6. Here are two rows of tops, and all are spinning. How many tops are three tops and seven tops ? Two tops and seven tops? 7. If seven of these tops should stop spinning, how many would then be spinning? Seven tops from ten tops leave how many tops? Seven tops from nine tops? Seven from 10 leaves how many? 7 from 9? PRIMARY ARITHMKTIG. 31 8. How many nuts are two nuts and seven nuts? Three nuts and seven nuts? Three cakes and seven cakes? How many are 1 and 7? 2 and 7? 3 and 7? 9. How many crowns are 1 crown and 8 crowns? 2 crowns and 8 crowns ? 10. How many girls are one girl and eight girls? Two girls and eight girls? How many are 1 and 8? 2 and 8? 11. There are ten boys playing together: if eight of them go home, how many boys will be left? Eight boys from ten boys leave how many boys? Eight from 10 leaves how many? 8 from 9? 12. How many chairs are 1 chair and 7 chairs? 1 chair and 8 chairs ? 2 chairs and 7 chairs ? 2 chairs and 8 chairs? 13. How many crowns will remain if you take 7 crowns from 10 crowns? 8 crowns from 10 crowns? 7 crowns from 9 crowns? 8 crowns from 9 crowns? 8 crowns from 8 crowns? Sow many are and 7? 1 and 7? 2 and 7? 3 and 7? and 8? 1 and 8? 2 and 8? Take 7 from 7. 7 from 8. 7 from 9. 7 from 10. 8 from 8. 8 from 9. 8 from 10. 14. How many are 2 and 7? 2 and 8? 3 and 7? Iand8? land 7? 8 and 2? 7 and 3? 32 PRIMARY ARITHMETIC. 15. Seven from 10 leaves how many? 7 from 8? 7 from 9? 8 from 10? 8 from 8? 8 from 9? 16. How many are 4 and 5? 4 and 6? 5 and 4? 6 and 4? 3 and 6? 3 and 5? 6 and 3? 5 and 3? 2 and 6? 4 and 3? 4 and 6? 2 and 5? 17. How many remain when you take 3 from 7? 3 from 9? 4 from 10? 5 from 10? 6 from 10? 3 from 8? 5 from 8? 6 from 8? 4 from 8? 8 from 8? 7 from 9? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 777888 771801 Add 231120 101014 017103 (1) (2) (3) (4) (5) (6) 100081 From 9 10 8 9 10 8 Add _! J* _i _i _1 J. Take 777888 REVIEW. 1. John has 4 marbles in one hand, and three mar- bles in the other: how many marbles has he in both hands ? 2. Jane has found a nest with 7 eggs in it : if she take 4 eggs from the nest, how many will remain? 3. Frank had 5 cherries, and his mother gave him 4: how many cherries had he then? 4. Willie has 3 apples in his hand, and 6 in his basket : how many apples has he ? PRIMARY ARITHMETIC. 33 5. There are 8 pigeons sitting on a limb: if 5 fly away, how many pigeons will be left? 6. There are 9 men in a stage coach : if 4 get out of the coach, how many men will be left ? 7. How many are 2 and 2? 2 and 2 and 2? 2 and 2 and 2 and 2? 2 and 2 and 2 and 2 and 2? 2andl? 2 and 3 and 5? 8. How many are 3 and 3 and 3? 3 and 1 and 3? 3 and 4? 3 and 4 and 2? 4 and 2? 4 and 2 and 3? 4 and 4 and 2? 9. How many will remain if you take 5 from 7? 5 from 9? 5 from 8? 6 from 8? 6 from 10? 6 from 9? 4 from 7? 4 from 9? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 654312" 221120 Add 345678 120104 112203 (1) (2) (3) (4) (5) (6) 111422 From 9 8 7 10 6 5 Take 654635 A <*d 123120 3L.BSSOH EEVIEW. 1. John holds up 5 fingers, and Henry 3: how many fingers do both hold up? 2. Charles has placed 9 blocks on the table: if Mary take away seven of them, how many blocks will be left on the table ? P. A. 3. 34 PRIMARY ARITHMETIC. 3. Susan has made 8 figures on her slate: if she should rub out 5 of them, how many figures would be left? 4. There are 3 bottles in one row, and, 5 bottles in another : how many bottles in both rows ? 5. A farmer has 5 cows in one lot, and 4 cows in another lot : how many cows has he in both lots ? 6. Charles had 10 cents, and spent 7 cents for an orange : how many cents had he left ? 7. Jane picked 9 peaches, and gave 6 of them to her little brothers: how many peaches had she left? 8. How many are 4 and 4? 4 and 4 and 2? 4 and 3? 4 and 3 and 3? 5 and 3? 5 and 3 and 2? 2 and 3? 2 and 3 and 4? 9. How T many will remain If you take 5 from 8? 5 from 9? 6 "from 10? 6 from 8? 4 from 7? 4 from 9? 4 from 8? 3 from 10? 3 from 8? 10. Take 3 from 6. 3 from 9. 3 from 7. 4 from 8. 4 from 10. 4 from 7. 7 from 9. 7 from 10. 8 from 10. 6 from 10. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) 243565 111016 Add 756432 130111 323420 (1) (2) (3) (4) (5) (6) 221121 From 6 7 8 9 7 10 J J 1 2 2 1 Take 3 4 5 6 4 7 Add 2 JL_ J^ J, _^ J^ PRIMARY ARITHMETIC. 35 3UBSSGH ORAL EXERCISES, To TEACHERS. The object of this and the next lesson is to develop the idea of each number from eleven to twenty inclusive, to teach its name, and the mode of representing it by figures. Make ten marks on the blackboard, and make beneath these, successively, one mark, two marks, three marks, etc. Add the lower group to the upper, and give the appropriate name to the result, as to four and ten, fourteen. Blocks, beans, etc., may also be used in a similar manner. Before answering the three questions below the illustrations, the pupil should, in each case, add and subtract the groups of objects represented; thus: "Ten trees and one tree are eleven trees; one tree from eleven trees leaves ten trees." 1. How many boys are 10 boys and 1 boy? How many are 10 and 1 ? Write eleven, thus : //. One from 11 leaves how many? 2. How many stars are 10 stars and 2 stars? How many are 10 and 2? Write twelve, thus: Two from 12 leaves how many? 3. How many balls are 10 balls and 3 balls? How many are 10 and 3 ? Write thirteen, thus : Three from 13 leaves how many? 4. How many are 10 birds and 4 birds? 10 boys and 4 boys? 36 PRIMARY ARITHMETIC. How many are 10 and 4 ? Write fourteen, thus : Four from fourteen leaves how many ? 5. How many pens are 10 pens and 5 pens? How many are 10 and 5? Write fifteen, thus: Five from 15 leaves how many? Write and read 10, 11, 12, 13, 14, 15. 6. How many stars are 10 stars and 6 stars? How many are 10 and 6 ? Write sixteen, thus : Six from 16 leaves how many? 7. How many arrows are 10 arrows and 7 arrows? How many are 10 and 7 ? Write seventeen, thus : Seven from 17 leaves how many? 8. How many soldiers are 10 soldiers and 8 sol- diers? How many are 10 and 8 ? Write eighteen, thus : Eight from 18 leaves how many? 9. Ten knives and 9 knives are how many knives ? PRIMARY ARITHMETIC. 37 How many are 10 and 9 ? "Write nineteen, thus : /tf. Nine from 19 leaves how many? 10. Ten pens and 10 pens are how many pens? How many are 10 and 10 ? Write twenty , thus : Ten from 20 leaves how many? Copy and read 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. Count from 10 to 20 forward and backward. ORAL EXERCISES. 1. How many are 10 and 1? 10 and 2? 10 and 3? 10 and 4? 10 and 5? 10 and 6? 10 and 7? 10 and 8? 10 and 9? 10 and 10? 2. How many are 10 and 2? 10 and 5? 10 and 6? 10 and 4? 10 and 1? 10 and 7? 10 and 8? 10 and 10? 3. Ten from 12 leaves how many? 10 from 13? 10 from 14? 10 from 16? 10 from 15? 10 from 17? 10 from 18? 10 from 19? 4. How many will be left if you take 10 from 14? 10 from 16? 10 from 18? 10 from 20? 5. How many are 10 and 2? 10 and 5? 10 and 6? 10 and 7?' 10 and 10? 6. How many are 10 and 3? 10 and 5? 10 and 7? 10 and 9? 10 and 8? 10 and 6? 38 PRIMARY ARITHMETIC. In the following table the first twenty numbers are expressed by words, figures, and letters. By Words. By Figures. Ry letters. ROMAN. SCRIPT. One. &*& ROMAN. SCRIPT. 1 / KOMAN. ITALIC. I 7 Two. 5*. o <9 II 77 Three. 52^. 3 3 III 777 Four. ^jfcut. 4 ^A IV 7F Five. ^ve. 5 j V F Six. ^k 6 /" VI F7 Seven. ?&&$. 7 / VII F77 Eight. %>*a/it. 8

n&cn. 17 // XVII JTF77 Eighteen . &n . Nineteen, o//^^^. 18 /< -x- 10 .. -;<. .. .. .. .. .. .jj. -jj. -;;- 20 .. .. .. .. .. .. .. .. .. .. 30 .. -;;. -v- .;;. .;;. ,;;. .;;. -v. .. .. 40 .. .. .. .. -;;- .. -;;- .. .. .. 50 jk/_ _x/_ J^/_ _x/_ _\/_ j>/_ J/_ _\/_ *i^ Jk/_ ^A >- .;;. .. .. .. .. .. .. .jj. .. 70 - -::- so t\ t\ t\ t\ /\ 'I"" /\ *\ #\ *\ ^1^ \f \t \t \t \f *t \t \t \t 100 WRITTEN EXERCISES. 1. Copy and read the following numbers: 20 30 40 50 60 70 80 90 21 31 41 51 61 71 81 91 22 32 42 52 62 72 82 92 23 33 43 53 63 73 83 93 24 34 44 54 64 74 84 94 25 35 45 55 65 75 85 95 26 36 46 56 66 76 86 96 27 37 47 57 67 77 87 97 28 38 48 58 68 78 88 98 29 39 49 59 69 79 89 99 2. Copy and read 21, 26, 33, 36, 38, 40, 44, 45, 48. 3. Copy and read 27, 36, 26, 37, 46, 48, 43, 55, 59. 4. Copy and read 61, 63, 66, 64, 75, 73, 77, 78, 80. PRIMARY ARITHMKTIG. 55 5. Copy and read 84, 83, 85, 87, 90, 94, 96, 97, 100. 6. Copy and read 18, 27, 36, 48, 54, 67, 75, 86, 94. 7. Begin with 5 and count to 100 by fives. 8. Begin with 10 and count to 100 by tens. ADDITION. 3UBSSOH ORAL EXERCISES. To TEACHERS. The object of this and the next eleven les- sons is to teach the addition of any number less than 10 to any number less than 100. The exercises are so arranged as to lead the pupil to add first the units. In finding the sum of 19 and 2, 29 and 2, or 39 and 2, for example, the 9 and 2 are first added. This gives the unit figure, and by adding 1 to the left hand figure the sum is obtained. The WRITTEN EXERCISES should be used both as slate and blackboard exercises. The columns of figures should be added both up and down. 1. Charles has 9 cents in one hand, and 2 cents in the other : how many cents has he in both hands ? 2. Mary has written 8 words : if she write 2 words more, how many words will she have written? 3. A farmer has put 10 sacks of flour in his wagon : if he put in 2 sacks more, how many sacks will there be in the wagon? 4. How many are 5 boys and 2 boys? 15 boys and 2 boys ? 35 boys and 2 boys ? 25 boys and 2 boys ? 45 boys and 2 boys? 56 PRIMARY ARITHMKTIG. 5. How many trees are 7 trees and 2 trees? 17 trees and 2 trees? 27 trees and 2 trees? 37 trees and 2 trees? 47 trees and 2 trees? 6. How many are 8 and 2? 18 and 2? 28 and 2? 38 and 2? 58 and 2? 48 and 2? 7. How many are 9 and 2? 19 and 2? 39 and 2? 29 and 2? 49 and 2? 59 and 2? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) 22122 12222 Add 89976 12221 12211 (1) (2) (3) (4) (5) 12222 22212 12222 Add 15 17 16 19 18 12222 12211 (1) (2) (3) (4) (5) 12221 22222 12221 Add 18 29 27 38 26 12212 12212 (1) (2) (3) (4) (5) 12222 22122 12211 Add 19 28 39 37 48 Add 1 2 1 2 2 &.BSSOH ORAL EXERCISES.' 1. Charles has 8 marbhs in one hand, and 3 marbles in the other: how many marbles has he in both? 2. Frank has 18 cherries : if his mother give him 3, how many cherries will he then have? 3. Mary has picked 17 plums: if she pick 3 more, how many plums will she then have? TH3 PRIMARY ARITHMKTIC, Tt ^ T y3J| ^ 4. There are 9 birds on one tree, and 3 birds on Another: how many birds on both trees? 5. Harry had 19 cents, and his father gave him 3 cents : how many had he then ? 6. How many are 12 eggs and 3 eggs? 14 eggs and 3 eggs? 18 eggs and 3 eggs? 15 eggs and 3 eggs? 19 eggs and 3 eggs? 17 eggs and 3 eggs? 7. How many are 5 and 3? 15 and 3? 35 and 3? 55 and 3? 25 and 3? 45 and 3 ? 8. How many are 7 and 3? 17 and 3? 37 and 3? 57 and 3? 27 and 3? 47 and 3? 67 and 3? 9. How many are 8 and 3? 28 and 3? 18 and 3? 38 and 3? 48 and 3? 68 and 3? 10. How many are 9 and 3? 29 and 3? 19 and 3? 49 and 3? 39 and 3? 59 and 3? WRITTEN EXERCISES. (1) 3 Add 18 (2) 3 27 (3) 3 29 (4) 3 28 (1) (2) (3) (4) (5) (6) 333333 (1) (2) (3) (4) O O O O Add 17 36 29 38 (1) (2) (3) O O Q Add 19 25 37 (1) 3 Add 16 (2) 2 49 (3) 1 39 (4) 3 47 (4) 2 28 3 3 1 3 3 1 3 3 3 3 2 2 3 3 3 3 2 2 3 3 1 3 3 a 3 3 3 3 2 3 3 3 3 3 3 2 3 3 1 3 2 1 3 3 3 3 2 3 3 3 1 3 3 2 3 3 1 3 3 1 3 3 3 3 2 3 3 3 1 3 3 2 Add 3 1 3 2 2 3 58 PRIMARY ARITHMKTIC. 3UESSOH ORAL EXERCISES. 1. There are 8 horses in one field, and 4 horses in another: how many horses in both fields? 2. Thomas received 15 cents for picking ten quarts of cherries, and 4 cents for selling them : how many cents did he receive in all? 3. There are 18 cows in one field, and 4 cows in another: how many 5u cows in both fields? 4. There are 19 boys and 4 girls in a class : how many pupils in all? 5. How many are 6 pears and 4 pears? 16 pears and 4 pears? 36 pears and 4 pears? 26 pears and 4 pears? 46 pears and 4 pears? 6. How many are 5 and 4? 15 and 4? 35 and 4? 45 and 4? 25 and 4? 55 and 4? 7. How many are 7 and 4? 17 and 4? 37 and 4 ? 57 and 4? 47 and 4? 27 and 4? 67 and 4? 8. How many are 9 and 4 ? 19 and 4 ? 29 and 4 ? 49 and 4? 69 and 4? 59 and 4? 39 and 4? 9. How many are 8 and 4? 18 and 4 ? 48 and 4? 38 and 4? 28 and 4? 58 and 4? 10. How many are 9 and 2? 19 and 2? 39 and 2? 29 and 2? 59 and 2? 49 and 2? 69 and 2? 11. How many are 8 and 3? 18 and 3? 38 and 3? 48 and 3? 28 and 3? 58 and 3? 47 and 3? 67 and 3? 57 and 3? 37 and 3? 27 and 3? PRIMARY ARITHMETIC. 59 WRITTEN EXERCISES. (1) (2) (3) (4) (1) (2) (3) (4) (5) (6) 4444 441444 Add 16 24 28 36 441422 441422 (l) (2) (3) (4) 444422 4444 444444 Add 27 35 39 37 444442 441421 (1) (2) (3) (4) 444424 4444 441422 Add 17 38 26 47 444442 441441 (1) (2) (3) (4) 441421 3 2 3 3 444422 Add 19 28 38 47 Add 414221 ORAL EXERCISES. 1. A garden contains 8 peach trees, and 5 pear trees : how many trees of both kinds in the garden ? 2. Harry sold three oranges for 18 cents, and two lemons for 5 cents : how many cents did he receive ? 3. A drover bought 19 hogs of one farmer, and 5 hogs of another : how many hogs did he buy? 4. A man paid 17 dollars for a cow, and 5 dollars for her calf: how much did he pay for both? 5. How many are 8 stars and 5 stars? 18 stars and 5 stars? 16 stars and 5 stars? 19 stars and 5 stars? 17 stars and 5 stars? 6. How many are 6 and 5 ? 16 and 5? 36 and 5? 56 and 5? 26 and 5? 46 and 5? 60 PRIMARY ARITHMETIC. 7. How many are 7 and 5 ? 17 and 5 ? 37 and 5 ? 27 and 5 ? 47 and 5 ? 57 and 5 ? 8. How many are 8 and 5 ? 18 and 5 ? 38 and 5 ? 48 and 5 ? 28 and 5 ? 58 and 5 ? 9. How many are 9 and 5 ? 19 and 5 ? 49 and 5 ? 29 and 5? 59 and 5 ? 39 and 5? 10. How many are 5 and 5? 15 and 5? 35 and 5? 55 and 5? 25 and 5? 45 and 5? WRITTEN EXERCISES. (1) (2) (3) (4) (1) (2) (3) (4) (5) (6) 5 5 5 5 5 5 1 5 5 5 Add 26 27 25 28 5 5 5 5 2 5 ~~~ ~~~ 5 5 5 5 2 5 (1) (2) (3) (4) 5 5 5 5 5 5 15 15 15 15 5 5 1 5 5 5 Add 16 26 20 28 5 5 5 5 5 2 5 5 1 5 2 2 (l) (-) (3) (4) 5 5 1 5 5 2 25 25 25 25 5 5 5 5 2 1 Add 37 45 39 43 5 5 5 5 2 2 5 5 1 5 5 2 (1) (2) (3) (4) 5 5 1 5 2 2 14 37 23 23 Add 5 1 5 2 2 1 Add 26 14 28 39 1 ORAL EXERCISES. 1. How many are 5 and 6 ? 5 and 16 ? 5 and 36 ? 5 and 26? 5 and 46? 2. How many are 4 and 6 ? 4 and 16 ? 4 and 36 ? 4 and 46 ? 4 and 26? 4 and 56? 3. How many are 2 and 2 and 3 and 1 and 4 and 3 and 5? PRIMARY ARITHMETIC. 61 4. How many are 5 and 4 and 3 and 2 and 1 and 2 and 3 and 4 and 5? 5. Begin with 2 and count to 50 by adding 2 suc- cessively, thus: 2, 4, 6, 8, 10, 12, etc. 6. Begin with 1 and count to 51 by adding 2 suc- cessively. 7. Begin with 3 and count to 42 by adding 3 suc- cessively, thus: 3, 6, 9, 12, 15, 18, etc. 8. Begin with 2 and count to 41 by adding 3 suc- cessively. WRITTEN EXERCISES. (1) (2) (3) (1) (2) (3) (4) (5) (G) (7) (8) 5 4 3 55544454 Add 16 27 28 53243255 55144355 (l) (2) (3) 53243454 25 15 35 55544254 Add 26 25 27 53343354 55544255 (1) (2) (3) 53543155 35 25 45 55344254 Add 18 19 20 53243354 55144455 (1) (2) (3) 53243354 14 13 25 55344255 Add 26 37 35 Add 33533144 - V- >-'>^-- - - ORAL EXERCISES. 1. Frank has 7 sour apples, and 6 sweet ones: how many apples has he? , 2. Jane's father gave her 8 cents, and her mother gave her 6 cents : how many cents did she receive ? 62 PRIMARY ARITHMETIC. 3. Jane read 9 verses, and Mary 6 verses more than Jane : how many did Mary read? 4. In a certain orchard there are 19 apple trees, and 6 peach trees : how many trees in the orchard ? 5. How many are 5 raisins and 6 raisins? 15 rai- sins and 6 raisins? 14 raisins and 6 raisins? 17 raisins and 6 raisins? 19 raisins and 6 raisins? 6. How many are 5 and 6 ? 15 and 6 ? 35 and 6 ? 55 and 6 ? 45 and 6 ? 25 and 6 ? 65 and 6 ? 7. How many are 7 and 6 ? 17 and 6 ? 37 and 6 ? 57 and 6? 47 and 6? 27 and 6? 8. How many are 9 and 6 ? 1 9 and 6 ? 39 and 6 ? 59 and 6? 29 and 6? 9. How many are 8 and 6 ? 18 and 6 ? 48 and 6 ? 58 and 6? 68 and 6? 38 and 6? 28 and 6? WRITTEN EXERCISES. (l) (2) (3) 6 6 6 Add 7 9 8 (1) (2) (3) 6 16 26 Add 16 38 25 (l) (2) (3) 16 36 26 Add 15 24 48 (1) (2) (3) 24 35 47 (1) (2) (3) (4) (5) (6) (7) (8) 6 6 6 3 3 6 4 6 6 6 6 3 2 4 6 5 6 6 2 6 3 6 4 6 6 6 1 3 6 4 6 5 6 6 6 6 2 4 1 6 6 6 1 3 6 6 2 5 6 6 6 6 3 4 3 6 6 6 6 6 6 4 4 5 6 6 6 6 2 6 6 5 6 6 6 6 3 6 6 6 6 6 6 6 1 6 4 6 6 6 6 6 2 6 3 6 6 6 6 6 3 6 2 6 Add 65 46 26 Add 6123641 PRIMARY ARITHMETIC. 63 *JSSSOItt ORAL EXERCISES. 1. Five and 6 are how many? 6 and 15? 35 and 6? 6 and 45? 6 and 25? 2. Nine and 6 are how many? 6 and 19? 6 and 39? 14 and 8? 8 and 24? 3. How many are 7 and 4? 17 and 4? 18 and 5? 28 and 5? 36 and 6? 6 and 36? 4. How many are 8 and 4? 18 and 6 ? 35 and 7 ? 42 and 4? 41 and 5? 23 and 9? 5. How many are 3 and 4 and 5 and 6 and 2 and 3? 6. How many are 4 and 3 and 6 and 5 and 2 and 5 and 6 and 2? 7. Begin with 1 and count to 49 by adding 4 suc- cessively. 8. Begin with 2 and count to 52 by adding 5 suc- cessively. WRITTEN EXERCISES. (1) (2) (3) (4) (1) (2) (3) (4) (5) (6) (7) 16 15 27 46 2254453 Add 46 37 45 17 3113464 2224415 (1) (2) (3) (4) 3334426 24 23 44 35 1445534 Add 18 27 48 27 2455543 2454552 U) (2) (3) (4) 3453561 36 46 26 44 2452516 Add 14 35 25 47 3341625 2342633 (l) (2) (3) (4) 3343644 36 26 45 55 2344656 Add 43 62 37 36 Add 1345665 PRIMARY ARITHMETIC. USSSCHS ORAL EXERCISES. I. John has 8 marbles, and Charles 7: if Charles should give all of his marbles to John, how many marbles would John then have? 2. There are 6 chickens in one brood, and 7 chickens in another : how many chickens are there in both broods? 3. There are 9 forks in the basket, and 7 on the table: how many in both places? 4. A boy gave 18 cents for a slate, and 7 cents for a pencil : how many did he give for both? 5. How many are 8 pins and 7 pins? 18 pins and 7 pins? 16 pins and 7 pins? 14 pins and 7 pins? 17 pins and 7 pins? 19 pins and 7 pins? 6. How many are 4 and 7 ? 14 and 7 ? 34 and 7 ? 54 and 7 ? 44 and 7 ? 24 and 7 ? 7. How many are 6 and 7 ? 16 and 7 ? 46 and 7 ? 36 and 7 ? 56 and 7 ? 26 and 7 ? 8. How many are 8 and 7 ? 18 and 7 ? 38 and 7 ? 28 and 7? 48 and 7? 58 and 7? 78 and 7? 9. How many are 7 and 7 ? 17 and 7 ? 37 and 7 ? 27 and 7? 47 and 7? 57 and 7? 10. How many are 6 and 7? 16 and 7? 7 and 16 ? 36 and 7 ? 7 and 36 ? 7 and 25 ? II. How many are 28 and 3? 28 and 5? 28 and 8? 28 and 4? 28 and 6? 28 and 8? PRIMARY ARITHMETIC. 65 WRITTEN EXERCISES. (1) (2) (3) (4) (1) (2) (3) (4) (5) (6) 7 17 27 37 772734 Add 14 26 38 46 727377 771734 (l) (2) (3) (4) 722777 17 27 37 47 777734 Add 17 23 45 39 771774 772337 (i) (2) (3) (4) 772774 33 -24 25 13 777734 21 32 44 55 772777 Add 17 27 37 27 Add 722334 UBSSOH ORAL EXERCISES. 1. How many are 6 and 7? 7 and 15? 7 and 35? 6 and 35? 5 and 35? 8 and 35? 2. How many are 7 and 16? 6 and 16? 5 and 16? 7 and 33? 6 and 33? 5 and 38? 3. How many are 13 and 7? 7 and 13? 33 and 7 ? 7 and 43 ? 53 and 7 ? 63 and 7 ? 4. How many are 4 and 5 and 6 and 7 and 3 and 4 and 2 and 7? 5. How many are 1 and 3 and 5 and 7 and 6 and 4 and 6 and 3 and 5 and 6? 6. Begin with 2 and count to 52 by adding 5 suc- cessively. 7. Begin with 3 and count to 51 by adding 6 suc- cessively. 8. Begin with and count to 49 by adding 7 suc- cessively. P. A. 5. 66 PRIMARY ARITHMETIC. 9. Begin with 3 and count to 51 by adding 4 suc- cessively. (i) WRITTEN EXERCISES. (2) (3) (4) 23 54 46 35 Add 46 29 17 28 (1) (2) (3) (4) 36 44 66 25 Add 25 55 14 37 (l) (2) (3) (4) 36 45 23 14 41 33 43 54 (1) (2) (3) (4) (5) (6) 7 3 4 7 4 3 5 4 7 6 7 4 7 5 4 7 5 5 5 7 5 6 6 6 5 5 7 7 7 7 7 7 4 6 2 6 7 5 3 7 3 5 7 7 7 7 4 4 - 7 5 3 7 5 3 7 7 4 7 6 2 Add 12 16 18 27 Add 555671 ORAL EXERCISES. 1. William walked 12 miles before dinner, and 8 miles after dinner: how many miles did he walk? 2. A school-house has 9 windows in the sides, and 8 windows in the ends: how many windows has it? 3. Mary wrote 7 lines in her copy-book, and 8 lines on a piece of paper : how many lines did she w r rite ? 4. Albert gave 15 cents for a top, and 8 cents for a pen- cil: how many cents did he pay for both? 5. How many are 8 boys and 8 boys? 18 boys and 8 boys? 16 boys and 8 boys? 14 boys and 8 boys? 15 boys and 8 boys? PRIMARY ARITHMETIC. 67 6. How many are 4 and 8 ? 14 and 8 ? 34 and 8 ? 24 and 8? 44 and 8? 64 and 8? 7. How many are 6 and 8 ? 16 and 8 ? 36 and 8 ? 56 and 8? 46 and 8? 26 and 8? 8. How many are 5 and 8 ? 15 and 8 ? 45 and 8 ? 65 and 8 ? 55 and 8 ? 35 and 8 ? 9. How many are 7 and 8 ? 17 and 8 ? 37 and 8 ? 57 and 8? 47 and 8? 27 and 8? 10. How many are 9 and 8? 19 and 8? 8 and 19 ? 8 and 29 ? 49 and 8 ? 8 and 49 ? WRITTEN EXERCISES. (1) (2) (3) (4) (i) (2) (3) (4) (5) (6) 28 38 18 48 8 2 2 8 8 4 Add 14 26 38 42 8 8 8 3 3 5 8 2 2 2 4 6 (1) (2) (3) (4) 8 8 8 1 2 7 18 28 58 38 8 2 2 8 8 8 Add 25 17 23 19 8 8 1 2 3 7 8 8 2 3 4 6 (l) (2) (3) (4) 8 8 8 8 8 5 44 43 35 18 8 8 8 8 8 4 25 34 27 46 8 8 8 8 8 3 Add 18 18 28 28 8 8 8 8 8 2 Add 812341 JUESSOH ORAL EXERCISES. - 1. How many are 3 and 5 and 7 and 4 and 6 and 8 and 2 and 8? 2. How many are 8 and 7 and 5 and 3 and 2 and 4 and 6 and 7? 68 PRIMARY ARITHMETIC. 3. How many are 9 and 5 ? 48 and 4 ? 53 and 7 ? 45 and 8 ? 27 and 8 ? 44 and 6 ? 4. How many are 15 and 6? 44 and 7? 36 and 8? 26 and 5? 18 and 3? 47 and 6? 5. How many are 16 and 5? 26 and 5? 46 and 5? 17 and 8?' 37 and 8? 57 and 8? 6. How many are 15 and 7? 25 and 7? 55 and 7? 14 and 6?* 34 and 6? 44 and 6? 18 and 3? 28 and 3? 48 and 3? 7. A boy bought a slate for 25 cents, a piece of rubber for 8 cents, and a lead pencil for 5 cents : how many cents did he pay for all? 8. Begin with 3 and count to 51 by adding 6 suc- cessively. 9. Begin with 5 and count to 54 by adding 7 suc- cessively. 10. Begin with and count to 48 by adding 8 suc- cessively. 11. Begin with 4 and count to 52 by adding 8 suc- cessively. WRITTEN EXERCISES. (1) (2) (3) (4) (1) (2) (3) (4) (5) (6) 35 44 27 36 8 3 6 6 2 8 Add 44 46 38 47 5 8 8 1 3 6 8 4 6 8 4 4 (l) (2) (3) (4) 5 8 8 2 5 1 41 34 50 44 8 1 6 8 8. 2 Add 13 26 27 29 8 8 8 3 6 3 8 2 6 8 7 4 (1) (2) (3) (4) 8 8 8 4 8 5 17 25 33 17 8 3 6 8 8 6 53 29 36 18 8 4 8 5 8 7 Add 26 43 28 45 Add 5 5 6 6 7 8 PRIMARY ARITHMETIC. 69 ORAL EXERCISES. 1. There are 7 cows in one pasture, and 9 cows in another : how many cows in both pastures ? 2. John saw 9 pigeons on a tree, and 6 pigeons on the ground : how many pigeons did he see ? 3. Wallace caught 8 fishes, and Willis caught 9: how many fishes did both catch? 4. A farmer gave 6 dollars for a yoke, and 9 dollars for a chain : how many dollars did he give for both? 5. How many are 5 plums and 15 plums and 9 plums? 17 plums and 13 plums and 9 plums? 16 plums and 14 plums and 9 plums? 6. How many are 3 and 9 ? 13 and 9 ? 43 and 9 ? 53 and 9 ? 23 and 9 ? 33 and 9 ? 7. How many are 5 and 9 ? 15 and 9 ? 45 and 9 ? 25 and 9 ? 35 and 9 ? 8. How many are 7 and 9 ? 17 and 9 ? 37 and 9 ? 57 and 9? 27 and 9? 47 and 9? 9. How many are 9 and 9 ? 29 and 9 ? 19 and 9 ? 49 and 9? 59 and 9? 10. How many are 8 and 9? 9 and 18? 35 and 9? 9 and 35? 24 and 9? 9 and 24? 11. How many are 6 and 9? 26 and 9? 9 and 26? 46 and 9? 9 and 46? 37 and 9? 9 and 37? 43 and 9? 9 and 43? 9 plums? 9 plums? 9 plums? 70 PRIMARY ARITHMETIC. Addition is the process of finding the sum of two or more numbers. The number obtained by adding two or more num- bers is called the Sum or Amount. WRITTEN EXERCISES. (1) (2) (3) (4) (l) (2) (3) (4) (5) (6) 19 29 39 49 9 2 3 9 3 4 Add 44 36 28 12 9 2 2 3 9 9 ~~~ 9 9 3 9 4 5 (l) (2) (3) (4) 9 2 9 4 5 9 14 5 13 14 9 9 3 9 9 6 15 14 22 15 9 9 9 9 9 9 24 13 19 16 9 9 9 9 9 9 23 25 16 18 9 9 9 9 9 9 Add 19 39 29 29 Add 9 2 3 4 5 6 WRITTEN EXERCISES IN ADDITION. Copy and add the following examples : (1) (2) (3) (4) (5) (6) (7) (S) (9) (10) 2 3 3 2 3 7 8 6 3 8 3 2 4 3 6 5 3 3 6 1 3 2 5 5 4 8 9 4 4 2 2 3 4 3 6 4 3 9 2 3 3 2 5 4 3 5 4 8 1 2 1 4 3 2 7 8 9 2 3 3 2 3 2 1 6 7 8 1 5 2 3 4 5 6 5 3 7 3 7 3 2 3 1 5 4 6 2 9 9 1 1 1 5 3 3 2 3 4 2 (11) (12) (13) (14) (15) (16) (17) (18) 22 13 24 25 28 16 25 17 32 34 25 27 15 29 26 38 24 22 16 18 24 28 19 15 21 27 34 * 29 27 27 27 26 PRIMARY ARITHMKTIG. 71 Copy and read the following numbers : (1) (2) (3) (4) (5) (6) 100 110 120 100 122 135 101 111 121 110 133 134 102 112 122 120 144 136 103 113 123 130 155 164 104 114 124 140 166 167 105 115 125 150 177 177 106 116 126 160 188 186 107 117 127 170 199 185 108 118 128 180 200 144 109 119 129 190 125 163 Copy and add the following examples: (1) (2) (3) (4) (5) (6) 46 43 63 125 146 149 54 55 42 248 186 127 37 36 57 105 137 136 82 44 69 123 123 144 63 61 43 149 145 133 45 38 46 208 233 245 (7) (8) (9) (10) (11) (12) 207 218 158 248 145 222 247 243 236 339 127 333 283 239 317 216 308 246 195 216 245 138 299 184 Copy and read the following numbers : (1) (2) (3) (4) (5) (6) 200 210 204 214 324 420 300 320 305 325 446 325 400 420 405 425 666 840 500 530 501 531 533 945 600 630 601 631 440 630 700 740 702 742 567 738 800 840 807 847 836 545 900 940 906 947 924 456 72 PRIMARY ARITHMETIC. SUBTRACTION. XJSSSOH XJUEH. ORAL EXERCISES. 1. Here is a beautiful picture. What are the men doing? How many are making the fence? 2. How many are 5 men less 2 men? 7 men less 2 men? 9 men less 2 men? 11 men less 2 men? 3. How many horses are 6 horses less 2 horses? 8 horses less 2 horses? 10 horses less 2 horses? 4. How many is 6 less 2 ? 8 less 2 ? 10 less 2 ? 5. How many fence-posts do you see? How many are 5 posts less 3 posts? 7 posts less 3 posts? PRIMARY ARITHMETIC. 73 6. The farmer has 10 sheep, but only 3 of them are in sight. How many are 10 sheep less 3 sheep? 11 sheep less 3 sheep? 12 sheep less 3 sheep? 7. How many is 10 less 3? 11 less 3? 12 less 3? 8. How many are 11 men less 2 men? 21 men less 2 men ? 41 men less 2 men ? 61 men less 2 men ? 9. How many are 12 sheep less 3 sheep ? 22 sheep less 3 sheep? 32 sheep less 3 sheep? 52 sheep less 3 sheep? 10. Two from 11 leaves how many? 2 from 21? 2 from 41? 2 from 31 ? 2 from 51 ? 11. Three from 12 leaves how many? 3 from 22? 3 from 42 ? 3 from 32 ? 3 from 52 ? 3 from 62 ? 12. How many is 10 less 2 ? 20 less 2 ? 40 less 2 ? 30 less 2 ? 60 less 2 ? 50 less 2 ? 13. How many is 11 less 3 ? 21 less 3 ? 41 less 3? 51 less 3 ? 31 less 3 ? 61 less 3 ? 81 less 3 ? To TEACHERS. The object of this and the next seven lessons is to teach the subtraction of any number less than 10, from any number not exceeding 100. The pupil should first be taught to take the smaller number from the larger number as a whole. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) From 11 21 41 52 31 61 82 72 92 Take 222233333 (1) (2) (3) (4) - .(5) (6) (7) (8) (9) From 13 23 41 51 66 74 72 49 29 Take 3 3 3 3 2 2 2 3 2 (1) (2) (3) (4) (5) (6) (7) (8) (0) From 10 20 30 40 50 60 70 80 90 Take 1 1 2 2 2 3 3 3 3 74 PRIMARY ARITHMETIC. USSSOKT ORAL EXERCISES. 1. Mary has 12 raisins: if she eat 4 of them, how many will she have left? 2. Susan has picked 11 peaches and 4 pears: how many more peaches has she than pears? 3. Mr. Smith has 13 hogs: if he sell 4 of them to a drover, how many will he have left? 4. Four pears from 11 pears leave how many? 4 pears from 21 pears? 4 pears from 41 pears ? 4 pears from 31 pears ? 5. Four from 12 leaves how many? 4 from 22? 4 from 42? 4 from 32? 4 from 52? 6. Four from 7 leaves how many? 4 from 17? 4 from 37? 4 from 57? 4 from 47? 4 from 27?. 4 from 67? 4 from 77? 7. How many is 13 less 4? 23 less 4? 43 less 4? 33 less 4? * 63 less 4? 53 less 4? 8. How many is 11 less 4? 21 less 4? 41 less 4? 61 less 4? 31 less 4? 51 less 4? 9. Begin with 36 and count back to by subtract- ing 4 successively, thus : 36, 32, 28, 24, etc. 10. Begin with 43 and count back to 3 by sub- tracting 4 successively. 11. Begin with 33 and count back to by sub- tracting 3 successively. 12. Begin with 35 and count back to 1 by sub- tracting 2 successively. PRIMARY ARITHMETIC. 75 WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) From 17 27 47 36 56 88 35 49 44 Take _4'_4_4_4_4_4_4_4_4 (1) (2) (3) (4) (5) (6) (7) (8) (9) From 12 22 42 52 13 23 43 63 53 Take 4 j4 4 _4 _4 Jl _4 _4 _4 (1) (2) (3) (4) (5) (6) (7) (8) (9) From 11 21 41 61 14 13 23 43 33 Take J_i_ljl_!jl_J_4_f (1) (2) (3) (4) (5) (6) (7) (8) (9) From 46 27 48 66 37 78 88 96 66 Take 14 14 24 44 24 24 55 74 44 L.BSSOH ORAL EXERCISES. 1. In a spelling exercise, Martha wrote 12 words on her slate, and misspelled 5 of them: how many words did she spell correctly? 2. A farmer has 13 chickens: if he sell 5 of them, how many will he have left? 3. Alice made 14 figures on her slate, and then erased 5 of them : how many figures were left? 4. Five stars from 11 stars leave how many? 5 stars from 21 stars? 5 stars from 31 stars? 5 stars from 51 stars? 5. Five from 12 leaves how many? 5 from 22? 5 from 42? 5 from 62? 5 from 32? 76 PRIMARY ARITHMETIC. 6. How many is 14 less 5? 24 less 5? 44 less 5? 34 less 5? 54 less 5? 64 less 5? 7. How many is 27 less 5? 38 less 5? 42 less 5? 61 less 5? 59 less 5? 8. Five from 13 leaves how many? 5 from 23? 5 from 43? 5 from 63? 5 from 53? 5 from 33? 5 from 63? 5 from 83? 9. How many is 19 less 5? 29 less 5? 49 less 5? 39 less 5? 53 less 5? 63 less 5? 73 less 5? 43 less 5? 33 less 5? 10. Begin with 43 and count back to 3 by sub- tracting 5 successively. 11. Begin with 52 and count back to 2 by sub- tracting 5 successively. (i) From 14 Take 5 (2) 24 5 WRITTEN EXERCISES. (3) 44 5 (4) 12 5 (5) 22 5 (6) 42 5 (7) 23 5 (8) (9) 43 63 5 5 (1) (2) From 45 67 Take 23 45 (3) 54 53 39 25 (5) 77 55 (6) 65 45 (7) 57 45 (8) 0) 64 89 33 47 (1) (2) From 21 31 Take 15 15 (3) 33 15 (4) 32 15 (5) 50 25 (6) 44 25 (7) 48 25 (8) 53 35 (9) 54 35 (1) From 32 Take 13 42 14 (3) 52 23 33 24 (5) 43 24 (6) 53 35 (7) 22 13 (8) 32 24 (9) 52 35 To TEACHERS. Teach the pupil how to proceed when the lower unit figure is greater than the upper. Let him first learu the how and afterward the why. PRIMARY ARITHMETIC. 77 ORAL EXERCISES. I. Harry bought 15 slate pencils, and gave 6 of them to his sister : how many had he left ? 2. A farmer has 13 oxen in one field, and 6 in another: how many oxen in the first field more than in the second? 3. Jane is 14 years old, and her brother is 6 years younger : how old is her brother ? 4. Six raisins from 12 raisins leave how many rai- sins? 6 raisins from 22 raisins? 6 raisins from 42 raisins? 6 raisins from 11 raisins? 5. Six from 13 leaves how many? 6 from 23? 6 from 43? 6 from 33? 6 from 63? 6. Six from 18 leaves how many? 6 from 28? 6 from 48? 6 from 58? 6 from 78? 6 from 68? 7. How many is 15 less 6? 25 less 6? 45 less 6? 65 less 6? 35 less 6? 55 less 6? 8. How many is 14 less 6? 34 less 6? 54 less 6? 24 less 6? 44 less 6? 64 less 6? 1 9. How many is 14 less 6? 23 less 6? 35 less 6? 21 less 6? 42 less 6? 53 less 6? i 10. Begin with 36 and count back to by sub- tracting 6 successively. II. Begin with 33 and count back to 3 by sub- tracting 6 successively. 12. Begin with 42 and count back to by sub- tracting 6 successively. 78 PRIMARY ARITHMETIC. WRITTEN EXERCISES. (1) From 15 Take _6 (1) From 25 Take 16 (l) From 22 Take 14 (1) From 137 Take 24 (2) 25 (2) 35 26 (2) 44 35 (3) (4) 35 14 6 6 (3) 45 26 (3) 31 16 34 16 43 26 (2) (3) 257 146 45 36 (5) (6) 34 54 6 6 (5) 54 26 (5) 25 16 (6) 64 36 (6) 54 45 (7) 13 _6 (7) 33 26 (7) 62 13 (4) (5) (6) 188 296 267 45 56 44 (8) (9) 43 63 6 6 (8) 43 36 (8) 63 34 (7) 168 55 (9) 63 56 (9) 31 14 (8) 149 38 3UESSOH ORAL EXERCISES. . Alice is 14 years old, and her brother is 7 years younger than she : how old is her brother? 2. There are 16 knives in a basket: if .7 of them be placed on the table, how many knives will re- main in the basket? 3. A hen has 11 chickens, but a hawk carried off 7 of them: how many chickens were left? 4. Seven apples from 12 apples leave how many ? 7 apples from 22 apples ? 7 apples from 42 apples ? 7 apples from 52 apples? 7 apples from 32 apples? 5. Seven from 15 leaves how many? 7 from 25? PRIMARY ARITHMETIC. 79 7 from 55? 7 from 85? 7 from 65? 7 from 45? 7 from 35? 7 from 75? 6. How many is 16 less 7? 36 less 7? 26 less 7? 46 less 7? 66 less 7? 56 less 7? 7. How many is 14 less 7? 44 less 7? 54 less 7? 64 less 7? 84 less 7? 34 less 7? 74 less 7? 24 less 7? 84 less 7? 8. How many is 19 less 7? 29 less 7? 59 less 7? 68 less 7? 38 less 7? 32 less 7? 44 less 7? 33 less 7? 35 less 7? 9. Begin with 35 and count back to by sub- tracting 7 successively. 10. Begin with 40 and count back to 5 by sub- tracting 7 successively. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) From 16 36 46 21 41 61 25 55 75 Take j;_717_71727J71747 (1) (2) (3) (4) (5) (6) (7) (8) (9) From 73 45 84 87 55 66 63 50 44 Take 472757673747273727 (1) (2) (3) (4) (5) (6) (7) (8) From 145 247 365 473 586 693 287 364 Take 36 143 246 344 277 475 176 246 (1) (2) (3) (4) (5) (6) (7) (8) From 234 344 454 364 474 284 204 354 Take 143 153 284 246 187 167 185 245 (1) (2) (3) (4) (5) (6) (7) (8) From 205 333 415 616 427 384 532 516 Take 127 227 345 508 276 279 348 347 80 PRIMARY ARITHMETIC. ORAL EXERCISES. 1. Charles found 13 quinces on a quince-tree, and picked 8 of them : how many were left ? 2. John found 15 nuts, and ate 8 of them : how many had he left ? 3. Kate had 22 problems to solve, and she has solved 8 of them : how many has she to solve ? 4. John bought 25 oranges, and sold 8 of them before dinner: how many had he left? 5. How many are 14 nuts less 8 nuts? 24 nuts less 8 nuts? 44 nuts less 8 nuts? 34 nuts less 8 nuts? 54 nuts less 8 nuts? 6. How many is 12 less 8? 32 less 8? 52 less 8? 62 less 8? 42 less 8? 22 less 8? 7. How many is 16 less 8? 26 less 8? 46 less 8? 36 less 8? 56 less 8? 76 less 8? 66 less 8? 8. Eight from 15 leaves how many? 8 from 35? 8 from 40? 8 from 30? 8 from 59? 9. Begin with 40 and count back to by sub- tracting 8 successively. 10. Begin with 45 and count back to. 5 by sub- tracting 8 successively. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) From 13 33 53 12 42 62 17 27 57 Take 8 18 28 8 18 38 8 18 38 PRIMARY ARITHMETIC. 81 (1) (2) (3) (4) (5) (6) (7) (8) (9) From 25 55 65 24 44 63 83 51 71 Take 18 28 38 18 28 38 58 36 25 (l) (2) (3) W (5) (6) (7) (8) From 148 256 198 273 366 354 275 486 Take 65 76 76 65 84 55 _87 92 (1) (2) (3) (4) (5) (6) (7) (8) From 422 433 344 555 866 477 688 399 Take 364 225 256 367 276 248 586 157 ORAL EXERCISES. 1. Clara had 17 words to write, and she IK:S written 9: how many words has she yet to write? 2. John has 15 marbles, and Samuel has 9 less than John : how many marbles has Samuel ? 3. A grocer has 25 sacks of flour : when he has sold 9 sacks^ how many will he have left? 4. Sixteen birds lit on a tree, and 9 of them soon flew to the g round: how mau y were left on the tree? 5. How many will remain pins? 9 pins from 23 pins? 9 pins from 43 pins? 9 pins from 63 pins? G. How many is 15 less 9? 35 less 9? 55 less 9? 45 less 9? 65 less 9? 7. How many is 18 less 9? 38 less 9? 48 less 9? 58 less 9? 78 less 9? 68 less 9? P. A. 6. 82 PRIMARY ARITHMETIC. 8. Begin with 45 and count back to by sub- tracting 9 successively. 9. Begin with 40 and count back to 4 by sub- tracting 9 successively. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) From 17 37 47 26 56 86 35 45 55 Take 9 19 29 19 29 49 19 29 39 (1) (2) (3) (4) (5) (6) (7) (8) (9) From 24 44 64 53 63 83 42 52 72 Take J 19 29 39 29 59 29 49 59 (l) (2) (3) (4) (5) (6) (7) . (8) From 236 135 344 453 363 172 284 464 Take 67 118 226 225 244 154 155 336 (l) (2) (3) (4) (5) (6) (7) (3) From 344 456 265 237 473 686 468 557 Take 283 367 187 178 358 496 279 328 USSSOM JL REVIEW. 1. Three from 31 leaves how many? 5 from 31? 7 from 31? 9 from 31? 6 from 31? 2. Four from 43 leaves how many? 6 from 43? 8 from 43? 7 from 43? 9 from 43? 3. Five from 44 leaves how many? 7 from 44? 9 from 44? 6 from 44? 8 from 44? 4. How many is 52 less 4? 52 less 6? 52 less 8? 52 less 3? 52 less 5? 52 less 7? 52 less 9? PRIMARY ARITHMETIC. 83 5. How many is 55 less 6? 55 less 8? 55 less 5? 55 less 7? 55 less 9? 55 less 10? 6. How many is 60 less 3? 60 less 7? 60 less 9? 60 less 4? 60 less 6? 60 less 8? 60 less 5? Subtraction is the process of finding the differ- ence between two numbers. The number obtained by subtracting one number from another is called the Difference or Remainder. WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) From 68979786978 9 Take3 >>45 3 4 2 '? > > 8 (13) (14) (15) (16) (17) (IS) (19) (20) From 13 15 14 10 15 17 16 19 Take _5 7 6 7 8 _9 7 8 (21) (22) (23) (24) (25) (26) (27) (28) From 22 23 44 55 46 34 35 42 Take 16 VL 28 29 28 1? 1! 25 (29) (30) (31) (32) (33) (34) (35) (36) From 122 233 148 255 249 234 159 249 Take 46 57 68 79 J7 46 67 85 (37) (38) (39) (40) (4i) (42) (43) (44) From 232 344 356 438 242 459 387 346 Take 145 276 218 347 126 339 258 185 (45) (46) (47) (48) (49) (50) (51) (52) From 433 545 573 999 796 307 606 704 Take 227 366 383 666 669 249 546 665 (53) (54) (55) (56) (57) (58) (59) (60) From 581 494 301 409 603 350 270 600 Take 309 305 129 227 542 169 165 321 8i PRIMARY ARITHMETIC. PROMISCUOUS ORAL EXERCISES. 1. Harry is 12 years old, and Charles is 9: what is the sum of their ages ? 2. Mary is 15 years old, and Kate is 8 : what is the difference between their ages? 3. Mr. Jones has 20 pears in his basket: if he give a little boy 4 of them, how many pears will remain in the basket? 4. Frank sold four oranges for 16 cents, and a pint of nuts for 4 cents: how many cents did he receive? 5. If you add 9 urns and 6 urns and 5 urns, what will the sum be? 6. If you take 6 tops from 15 tops, what will the difference be ? 7. A farmer has 16 cows in one pasture, and 7 in another: how many cows in both pastures? 8. There are 25 eggs in a basket, and 8 in a nest : how many more eggs in the basket than in the nest? 9. Mr. Gray has 15 peach trees in his orchard, and 6 in his garden: how many more peach trees in the orchard than in the garden ? 10. Clara has 16 pearl beads, and Jane has 9: if Jane should give hers to Clara, how many beads would Clara then have? 11. What is the number obtained by adding two or more numbers together called? PRIMARY ARITHMETIC. 85 12. What is the sum of 27 and 8? 27 .and 4? 25 and 4? 25 and 8? 25 and 6? 13. What is the amount obtained by adding 32 and 8? 36 and 7? 44 and 6? 14. What is the number obtained by subtracting one number from another called? 15. What is the difference between 9 and 15? 8 and 24? 6 and 21? 16. What will be the remainder if you take 7 from 33? 6 from 42? 17. When we take one number from another what is the process called ? 18. Subtract 7 from 15. 7 from 35. 8 from 36. 19. What is the sum of 8 and 45? What is their difference ? 20. Willis has 15 plums: how many more must he pick to have 25 plums? 21. How many blocks must you add to 16 blocks to make 23 blocks? 22. A coat cost 25 dollars, and a vest 16 dollars; how much did the coat cost more than the vest? 23. How many are 5 and 4 and 6 and 8 less 9? 24. How many are 8 and 9 less 6 less 5? 25. How many are 8 and 5 and 6 less 3 less 4 less 6? 26. How many are 5 and 6 and 7 less 4 less 5 less 3? 27. How many are 23 and 5 and 8 and 4 less 5 less 6 less 7? 86 PRIMARY ARITHMKTIC MULTIPLICATION, JuJSSSOH ORAL EXERCISES. 1. What season of the year does this picture repre- sent? What are the boys doing in the orchard? 2. How many boys are twice 1 boy? 3 times 1 boy? 3. How many barrels are empty? How many are 4 times 1 barrel? How many are twice 1 ? 3 times 1 ? 4 times 1 ? 4. How many apple trees in sight? How many are 5 times 1 tree? 6 times 1 tree? How many are 5 times 1 ? 6 times 1 ? PRIMARY ARITHMETIC. 87 5. How many are 7 times 1 apple ? 8 times 1 apple ? 9 times 1 apple? 10 times 1 apple? How many are 7 times 1 ? times 1 ? 10 times 1 ? To TEACHERS. Develop the idea of multiplication, using visible objects, as books, blocks, pencils, etc. Division may be taught orally in connection with multiplication. Hoiu many are 1 time 1 ? . . . . . . 1 2 times 1 ? . . . . . 1 1 3 times 1? . . ..111 4 times 1 ? 1111 5 times 1 ? . . 11111 6 times 1 ? . . . . 1 11111 7 times 1 ? . ..11 11111 8 times 1 ? . . .111 11111 9 times 1 ? . . 1111 11111 10 times 1 ? . 1 1111 11111 3UESSOH 3UHI. ORAL EXERCISES. 1. How many boys are in the field? How many are twice 2 boys? 2. How many barrels are filled with apples? How many are 3 times 2 barrels? How many are twice 2 ? 3 times 2 ? 3. How many are 4 times 2 barrels? 5 times 2 bar- rels? 6 times 2 barrels? 4. How many are 4 times 2 ? 5 times 2 ? 6 times 2 ? 5. How many are 7 times 2 apples ? 8 times 2 apples ? 6. How many are 7 times 2 ? 8 times 2 ? 7. How many are 9 times 2 trees? 10 times 2 trees? 88 PRIMARY ARITHMKTIG. 8. How many are 9 times 2 men? 9 times 2 deer? 10 times 2 men? 10 times 2 deer? How many are 9 timejs 2? 10 times 2? 9. How many are 3 times 2 tops? 4 times 2 tops? 2 times 2 tops? 5 times 2 tops? 7 times 2 tops? 6 times 2 tops? 8 times 2 tops? 10 times 2 tops? 9 times 2 tops ? To TEACHERS. Show the pupil, that 3 times 2 is the sum of three 2's; that 4 times 2 is the sum of four 2's, etc.; and when the table is studied or recited, require the corresponding number of 2's at the right to be added. The subsequent tables should be studied in the same manner. How many are 1 iim 9? 9 2 times 2? ... 9 9 3 times 2? ... 222 4 times 2? ... 2222 5 times 2? ... 9 2 2 2 6 times 2? . . . o 22222 7 times 2? ... 8 times 2? ... 9 times 2? . . 2 . 2 2 222 222 22222 22222 22222 10 times 2? . 2 2 2 2 2 22222 10. How many are 2 times 2? 4 times 2? 3 times 2? 5 times 2? 7 times 2? 6 times 2? 9 times 2? 10 times 2? 8 times 2? 11. How many are 5 times 1? 5 times 2? 7 limes 1? 7 times 2? 9 times 1? 9 times 2? 6 times 1? 6 times 2? 12. How many are 4 times 1? 4 times 2? 8 times 1? 8 times 2? 7 times 1? 7 times 2? 13. How many times 2 are 4? 6? 8? 10? 12? 14? 16? 18? 20? PRIMARY ARITHMETIC. 89 WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) Multiply 2 2 2 2 ' 2 2 2 2 By . . . 5 4 6 9 8 7 (1) (2) (3) (4) (5) (6) (7) (8) Multiply 1 1 2 1 2 2 1 1 By . . . 6 9 7 _8 4 6 7 5 (1) (2) (3) (4) .( 5 ) (0) Multiply 22 21 12 22 11 21 By ... 4 3 J 3 8 4 (1) (2) (8) (4) (5) (6) Multiply 11 22 11 12 20 10 By ... 6 4 9 3 4 9 UBSSON ORAL EXERCISES. 1. A cart has 2 wheels: how many wheels have 4 carts? SOLUTION. 4 times 2 wheels are 8 wheels: 4 carte Aave 8 wheels. 2. A drayman earns 2 dol- lars a day : how many dollars will he earn in 6 days? 3. John bought 5 lemons at 2 cents apiece: how many cents did they cost? 4. If one bag hold .2 bush- els of oats, how many bushels will 8 bags hold ? 5. What will 6 bushels of apples cost at 1 dollar a bushel ? At 2 dollars a bushel ? 90 PRIMARY ARITHMETIC. 6. If 2 boys can sit at one desk, how many can sit at 8 desks? How many at 10 desks? 7. If 1 step is 2 feet, how many feet are there in 7 steps? In 5 steps? In 6 steps? 8. If 2 horses make a span, how many horses will make 4 span? 8 span? 9. Albert saw 5 yoke of oxen: how many oxen did he see ? WRITTEN EXERCISES. Copy and complete these tables : Model. (1) (2) (3) (4) (5) 1X1 = 1 2X1 2X2 2X2 5X1 5X2 1X2-2 2X2 2X4 4X2 - 1X7 4X2 1X3-3 2X3 2X6 6X2 7X2 6X2 1X4-4 2X4 2X8 8X2 2X6 8X2 1X5-5 2X5 2X3 3X2 1X5 7X2 1X6 = 6 2X6 2X5 5X2 8X1 9X1 1X7-7 2X7 2X7 7X2 2X5 9X2 1X8-8 2X8 2X1 9X2 4X2 8X1 1X9-9 2X9 2X9 9X1 3X2 4X1 To TEACH;EBS. Teach the pupil that the sign of multiplica- tion (X) when placed between two numbers, shows that the number before it is to be multiplied by the number after it. 3X2 is to be read 3 multiplied by 2, which is the same as 2 times 3. 3 X 2 6 may be read, for convenience, 3 times 2 equal 6. 3-.3SSSOH ORAL EXERCISES. 1. How many leaves are 2 times 3 leaves? 3 times 3 leaves? 4 times 3 leaves? PRIMARY ARITHMETIC. 91 3 times 2. Two times 3 figs are how many figs ? 3 figs? 4 times 3 figs? How many are 2 times 3? 3 times 3? 4 times 3? 3. James has found 5 times 3 shells: how many shells has he found? 4. How many are 5 times 3 pebbles? 6 times 3 pebbles? 5 times 3 marbles? 6 times 3 marbles? How many are 5 times 3? 6 times 3? 5. Alice has picked 7 oak twigs, and each twig has 3 leaves : how many leaves has she picked ? 6. How many times 3 books do you see here? 8 times 3 books are how many books? 9 times 3 books? 10 times 3 books? How many are 8 times 3 ? 9 times 3 ? 10 times 3 ? 7. How many are 3 times 3 pens? 5 times 3 pens? 7 times 3 pens? 9 times 3 pens? 10 times 3 pens ? 8 times 3 pens ? 6 times 3 pens ? How many are 1 time 3? 3 9 times 3? 3 3 3 times S? 3 3 3 4 times 3? 3 3 3 3 6 times 3? 3 3 3 3 3 6 times 3^ 3 3 3 3 3 3 7 times 3? 3 3 3 3 3 3 3 8 times 3? ... 3 3 3 3 3 3 3 3 9 times 3? ..33 3 3 3 3 3 3 3 10 times 3? .333 3 3 3 3 3 3 3 92 . PRIMARY ARITHMETIC. 8. How many are 2 times 3? 3 times 3? 4 times 3? 5 times 3? 8 times 3? 10 times 3? 9. How many are 5 times 3? . 3 times 5? 7 times 3? 3 times 7 ? 9 times 3? 3 times 9 ? 10. How many are 3 times 2 ? 3 times 3 ? 5 times 1? 5 times 2? 5 times 3? 8 times 1? 8 times 2? 8 times 3? 6 times 3? 11. How many times 3 are 6? 9? 15? 12? 18? 24? 21? 27? 30? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) Multiply 3 3 3 3 3 3 3 3 3 By ... 2 4 6 8 _9 3 _JL 7 5 (1) (2) (3) (4) (5) (6) (7) (&) (9) Multiply 3 2 1 2 3 2 3 1 2 By ... 6 9 8 7 5 4 6 5 6 (l) (2) (3) (4) (5) (6) Multiply 33 32 31 . 30 13 23 By ... 3 4 8 7 .3 2 (1) (2) (3) (4) (5) (6) Multiply 33 33 33 22 22 22 By ... 4 5 6 7 8 9 To TEACHERS. Teach the pupil how to proceed when th< product of the two unit figures exceeds 9. HbBSSOM ORAL EXERCISES. 1. Each finger has 3 joints: how many joints have 2 fingers? 3 fingers? 2. If each stool has 3 legs, how many legs have 3 stools? 4 stools? 5 stools? PRIMARY ARITHMETIC. 93 3. At 3 cents apiece, what will 8 lemons cost ? 4. If a barrel will hold 3 bushels of apples, how many bushels will 7 barrels hold ? 5. A drover bought 9 sheep at 3 dollars a head : how many dollars did he pay for them? 6. Harry caught 3 fishes in his net, and John caught 6 times as many as Harry : how many did John catch? 7. A hunter killed 3 squirrels, and saw 5 times as many : how many squirrels did he see ? 8. What will 8 quarts of chestnuts cost, at 3 cents a quark? 9. What will 7 spools of thread cost, at 3 cents a spool ? 10. There are 3 feet in a yard: how many feet are there in 6 yards? WRITTEN EXERCISES. Copy and complete these tables : (1) (2) (3) (4) (5) 3X1 3X3 3X3 2X4 6 + 2 3X2 3X5 5X3 3X4 7 + 3 3X3 3X7 7X3 1X4 8+1 3X4 3X9 9X3 2X5 9 + 2 3X5 3X8 8X3 2X3 9+3 3X6 3X6 6X3 3X5 8 + 3 3X7 3X4 4X3 2X4 9 + 1 3X8 3X2 2X3 1X6 7 + 2 3X9 3X5 3X3 2X7 5 + 3 To TEACHERS. Explain the sign of addition ( + ) used in the 5th table, and teach the pupil to read it plus, as 6 plus 2; 7 plus 3, etc. 94 PRIMARY ARITHMETIC. 3L.BSSOM ORAL EXERCISES. 1. How many rabbits are 2 times 4 rabbits? times 4 rabbits? 4 times 4 rabbits? 2. Once 4 sheep are how many sheep? Twice 4 sheep ? 3 times 4 sheep ? 4 times 4 sheep ? How many are 2 times 3? 3 times 3? 4 times 3? %M> A A 3. Here are how many groups of arrows ? Five times 4 arrows are how many arrows? 6 times 4 arrows? 3 times 4 arrows? 4. How many girls are 5 times 4 girls? 6 times 4 girls? 4 times 4 girls? How many are 5 times 4? 6 times 4? 4 times 4? 5. How many hoofs has each of these horses? How many hoofs have 7 horses? 8 horses? 6. Seven times 4 shoes are how many shoes? 8 times 4 shoes? 6 times 4 shoes? How many are 7 times 4? 8 times 4? 6 times 4? 7. How many are 9 times 4 fingers? 10 times 4 fingers? 9 times 4 arrows? ,10 times 4 arrows? How many are 9 times 4 ? 10 times 4 ? 4 times 10 ? PRIMARY ARITHMETIC. 95 8. How many are 2 times 4 hats? 4 times 4 hats? 5 times 4 hats? 3 times 4 hats? 7 times 4 hats? 9 times 4 hats? 8 times 4 hats? 6 times 4 hats? How ', 1 many time arc 4? 4 2 times 4? 4 4 3 times 4? 4 4 4 4 times 4? 4 4 4 4 5 times 4? 4 4 4 4 4 6 times 4? 4 4 4 4 4 4 ^ times 4? 4 4 4 4 4 4 4 8 times 4? ... 4 4 4 4 4 4 4 4 9 times 4? ..44 4 4 4 4 4 4 4 10 times 4? .444 4 4 4 4 4 4 4 9. How many are 2 times 4? 3 times 4? 5 times 4? 6 times 4? 4 times 4? 8 times 4? 7 times 4? 9 times 4? 3 times 4? 10 times 4? 10. Five times 4 are how many? mes 7? 6 times 4? 4 times 6? mes 8? 9 times 4? 4 times 9? 7^ times 4? 4 8 'times 4? 4 WRITTEN EXERCISES. (1) (2) (3) (4) (5) (G) (7) (8) Multiply 4 4 4 4 4 4 4 4 By ... 3 5 7 9 8 6 4 2 (1) (2) (3) (4) (5) (6) (7) $ Multiply 3 2 3 3 2 3 3 2 By ... 4 4 7 9 8 6 5 4 (1) (2) (3) (4) (5) (6) Multiply 44 43 42 41 40 41 By ... 2 3 4 8 9 5 (l) (2) (3) (4) (5) (6) Multiply 24 43 34 44 23 34 By ... 5 4 3 6 7 8 96 PRIMARY ARITHMETIC. ORAL EXERCISES. 1. There are 4 fingers on one hand: how many fingers are there on 2 hands? 3 hands? 5 hands/ 2. There are 4 quarts in a gallon: how mar.y quarts are there in 6 gallons? 7 gallons? 3. An elk has 4 legs : how many legs have 4 elks? G elks? 5 elks? 4. Four girls have 4 roses each : how many roses have hs r "^iSP^HBSfiS^WB^ 5. A wagon has 4 wheels : how many wheels have 7 wagons? 5 w r agons? 6. What will 8 loads of wood cost, at 4 dollars a load? At 3 dollars a load? 7. What will 7 pairs of shoes cost, at 4 dollars a- pair? At 3 dollars a pair? 8. What will 10 oranges cost, at 4 cents apiece? 9. If a sheet of paper make 4 pages, how many pages will 9 sheets make ? 10. If a man walk 4 miles in an hour, how far will he walk in 8 hours? 11. How many are 3 times 2? 3 times 3? 3 times 4? 5 times 3? 5 times 4? 7 times 2? 7 times 3? 7 times 4? 12. How many times 4 are 8? 12? 20? 1G? 24? 32? 28? 3G? PRIMARY ARITHMETIC. 97 WRITTEN EXERCISES. Copy and complete these tables : (i) (2) (3) (4) (5) 4X1 = 4X3 3X4 4X4 4 + 4 4X2- 4X1 1X4 6X3 6 + 3 4X3-' 4X5 5X4 6X2 6 + 4 4X4- 4X7 7X4 5X4 5 + 4 4X5- 4X2 2X4 5X3 5 + 2 4X6 - 4X4 4X4 5X2 7 + 4 4X7- 4X6 6X4 7X4 8 + 3 4X8- 4X9 9X4 8X3 9 + 4 4X9 4X8 8X4 9X2 9 + 3 LHSSOH auiIX. ORAL EXERCISES. 1. How many bunches of grapes in each of these groups? In 2 groups? In 3 groups? 2. How many are 2 times 5 doves? 3 times 5 doves? 4 times 5 doves? How many are 2 times 5 ? 3 times 5 ? 4 times 5 ? 3. The leaves of a flower are called petals. How many petals has each of these pretty violets ? 4. Jane has picked 5 violets, and Mary 5 times as many as Jane : how many violets has Mary picked ? 5. How many petals are 4 times 5 petals ? 5 times 5 petals? 6 times 5 petals? How many are 4 times 5? 5 times 5? 6 times 5? P. A. 7. 98 PRIMARY ARITHMETIC. 6. Edward has 5 marbles, and Albert 7 times as many as Edward : how many marbles has Albert ? ~>JD J& *>J& J2 Jd *> J *>~^ -> JO 7. Seven times 5 marbles are how many marbles? 8 times 5 marbles? How many are 7 times 5? 8 -times 5? 5 times 8? i ff i M i ff i 8. Mary kept the account in a spelling match be- tween two classes. The first class misspelled 9 times 5 words; the second 10 times 5 words: how many words did each class misspell? How many are 9 times 5 ? 10 times 5 ? 5 times 10? 9. How many are 3 times 5 cents? 5 times 5 cents? 4 times 5 cents? 7 times 5 cents? 6 times 5 cents? 9 times 5 cents? 10 times 5 cents? 8 times 5 cents ? Hoio 1 many time are >*i< >o 5 2 times 5? . . 5 5 3 times 5? . . 5 5 5 4 times 5? . . ^ 5 5 5 times 5? . . 5 5 5 5 5 6 times 5? g 5 5 5 5 5 7 times 5? . . 5 5 5 5 5 5 5 8 9 10 times times times 5? . . 5? % . . 5? . 5 . 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10. How many are 3 times 5? 6 times 5? 9 times 5? 10 times 5? 8 times 5? 7 times 5? 5 times 5? 4 times 5? 2 times 5? PRIMARY ARITHMETIC. 99 11. Four times 5 are how many? 5 times 4? 8 times 5? 5 times 5? 7 times 5? 3 times 5? 5 times 3? 9 times 5? 12. How many are 7 times 3? 8 times 3? 9 times 3? 7 times 4? 8 times 4? 9 times 4? 7 times 5? 8 times 5? 9 times 5? 13. How many fimes 5 are 10? 15? 20? 30? 40? 50? 25? 35? 45? WRITTEN EXERCISES. (l) (2) (3) (4) (5) (6) (7) (8) Multiply 5 5 5 5 5 5 5 5 By ... 5 4 7 6 9 8 2 J (l) (2) (3) (4) (5) (6) (7) (8) Multiply 3 4 7 G 8 2 5 By ... 5 5 5 5 5 5 5 5 0) (2) (3) (4) (5) (6) Multiply 54 53 52 51 50 51 By ... 2 3 . 4- 6 8 7 (1) (2) (3) (4) (5) (6) Multiply 25 35 45 15 55 52 By ... 4 6 8 2 9 5 ORAL EXERCISES. 1. An orchard has 6 rows of trees, and each row has 5 trees: how many trees in the orchard? 2. A recitation room contains 4 seats, and there are 5 pupils sitting on each seat: how many pupils in the room ? 100 PRIMARY ARITHMETIC. 3. Lucy gave 5 plums to her brother, and 6 times as many to her mother : how many plums did she give to her mother? 4. If a horse travel 5 miles an hour, how many miles will he travel in 7 hours ? 5. If a boat sail 5 miles an hour, how far will it sail in 10 hours? 6. Willie is 5 years old, and his father is 8 times as old as he : how old is Willie's father? How many are 8 times 5? 7. If a ladder have 5 rounds, how many rounds will 3 ladders have? 8. What will 7 lead-pencils cost, at 5 cents apiece? 9. What will 8 oranges cost, at 5 cents apiece? 10. What will 9 hats cost, at 5 dollars apiece? 11. What will 6 tables cost, at 5 dollars apiece? WRITTEN EXERCISES. Copy and complete these tables : (1) (2) (3) (4) (o) 5X1 = 5X3 3X5 5X4 5 + 5 5X2 = 5X5 5X5 5X6 6 + 5 5X3 = 5X7 7X5 3X7 8 + 5 5X4 = 5X2 2X5 4X8 9 + 4 5X5 = 5X4 4X5 5X8 7 + 5 5X6 = 5X3 3X5 4X9 7+4 5X7 = 5X6 6X5 3X9 4 + 5 5X8 = 5X8 8X5 5X6 8 + 4 5X9 = 5X9 9X5 5X9 6 + 4 PRIMARY ARITHMETIC, 101 3UBSSOH 3L.3O* ORAL EXERCISES. 1. How many girls are once 6 girls? 2 times 6 girls? 3 times 6 girls? 4 times 6 girls? How many are 2 times 6 ? 3 times 6 ? 4 times 6 ? 2. How many books in each of these rows ? Twice 6 books are how many books? 3 times 6 books? 4 times 6 books? 5 times 6 books? 3. William's little book-case has 5 shelves, and on each shelf are 6 books : how many books are there in the case? 4. How many pencils are 3 times 6 pencils? 4 times 6 pencils? 5 times 6 pencils? How many are 4 times 6 ? 5 times 6 ? 3 times 6 ? 5. Willie arranged his mother's spools of thread in 6 piles, by placing 6 spools in each pile : how many spools were there? 6. How many are 6 times 6 spools? 7 times 6 spools? 8 times 6 spools? 7. Six times 6 hats are how many hats? 7 times 6 hats? 8 times 6 hats? How many are 6 times 6 ? 7 times 6 ? 8 times 6 ? 8. How many legs has a bird ? How many has a mouse? How many has a fly? 102 PRIMARY ARITHMETIC. 9. If a fly lias 6 legs, how many legs do 9 flies have? 10 flies? 10. How many stars are 9 times 6 stars? 10 times 6 stars? How many are 9 times 6 ? 10 times 6 ? 8 times 6 ? 11. How many are 2 times 6 slates? 3 times 6 slates ? 5 times 6 slates ? 7 times 6 slates ? 6 times 6 slates? 9 times 6 slates? 8 times 6 slates? 10 times 6 slates? Hoiv 1 many time are 6? . . 6 2 times 6 ? . . 6 fi 3 times 6? . . 6 f> r> 4 times 6? . . 6 n fi 6 5 times 6? . . fi 6 6 6 6 6 times 6? . . 6 6 fi r> 6 6 7 8 9 10 times times times times 6? . . 6? . . 6? . . 6? . 6 . . 6 . 6 6 666 666 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 12. How many are 2 times 6? 5 times 6? 7 times 6? 4 times 6? 3 times 6? 8 times 6? 9 times 6? 10 times 6? 13. How many are 4 times 6? 6 times 4? 7 times 6? 6 times 3? 5 times 6? 6 times 5? 8 times 6? 6 times 6? 14. Seven times 5 are how many? 6 times 4? 5 times 3? 8 times 5? 7 times 6? 9 times 3? 8 times 6? 8 times 4? PRIMARY ARITHMETIC. 103 15. How many 6's in 12? 24? 18? 30? 42? 36? 54? 48? ^ Multiply 6 By . . . _4 (l) Multiply 4 By . . . _j> (1) Multiply 64 Bv . 3 (1) Multiply 63 By . /. 6 WRITTEN EXERCISES. (2) (3) (4) (5) 6 6 6 6 6 5 . 7 2 (2) (3) (4) (5) 5 7 6 3 6 6 6 6 (2) (3) (4) 63 65 62 4 6 5 (2) (3) (4) 64 55 65 5 8 4 (6) 6 (6) (7) (8) 6 6 3 9 (7) (8) 2 9 6 6 (5) 61 (6) 60 9 (5) (6) 62 41 7 9 how 3. tain ORAL EXERCISES. 1. Charles found 3 bird's nests, and each nest had 6 eggs in it: how many eggs did he find? 2. Mary's spelling lesson consists of 3 columns, and each column contains 6 words: many words in her lesson? How many letters in 6 words, if each word con- 6 letters? 104 PRIMARY ARITHMKTIG. 4. A drover bought 10 sheep, at 6 dollars a head : how many dollars did he pay for them ? 5. A house has 8 windows, and each window con- tains 6 panes of glass : how many panes of glass in all the windows? 6. If a boat sail 6 miles an hour, how far will it sail in 9 hours? In 10 hours? 7. What will 5 sheep cost, at 6 dollars apiece? 8. What will 7 lead-pencils cost, at 6 cents apiece? WRITTEN EXERCISES. Copy and complete these tables : (1) (-) (3) (*) (5) 6X1 = 6X3 3 X 6 4 + 5 9 3 6X2 = 6X2 2 <6 6 + 5 8 5 6X3 = 6X4 4X6 7- r 5 9 6 6X4 = 6X6 6X6 3 + 4 7 4 6X5== 6X5 5X6 8 + 4 6 3 6X6 = 6X8 8X6 7 + 4 7 6 6X7 = 6X7 7X6 2 + 6 8 4 6X8 = 6X9 9X6 5 + 6 6 6 6X9 = 6X1 1X6 4 + 6 9 5 ORAL EXERCISES. 1. How many pretty nests do you see? How many eggs in each nest ? How many eggs in two nests ? PRIMARY ARITHMETIC. 105 2. How many are 2 times 7 eggs? 3 times 7 eggs? 4 times 7 eggs ? 5 times 7 eggs ? 3. Three times 7 birds are how many birds? 4 times 7 birds ? 5 times 7 birds ? How many are 2 times 7 ? 3 times 7 ? 4 times 7 ? 4. How many bunches of cherries are here ? How many cherries in each bunch? How many cherries are there in 4 bunches? How many cherries in all the bunches? 5. How many cherries are 5 times 7 cherries? 7 times 7 cherries? 6 times 7 cherries? 6. Six times 7 peanuts are how many ? 7 times 7 peanuts arc how many ? How many are 5 times 7? 6 times 7? 7 times 7? 7. This beautiful leaf will fold up like a fan. How many blades has it? 8. If a leaf has 7 blades, how many blades do 8 leaves have ? 9 leaves ? 10 leaves ? 9. How many are 8 times 7 trees? 9 times 7 trees? 10 times 7 trees? How many are 8 times 7 ? 9 times 7 ? 10 times 7 ? 10. How many are 3 times 7 men? 4 times 7 men ? 6 times 7 men ? 8 times 7 men ? 5 times 7 men ? 7 times 7 men ? 9 times 7 men ? 10 times 7 men? 106 PRIMARY ARITHMETIC. How 1 many time are 7? ... 7 2 times 7? ... 7 7 3 times 7? ... 7 7 7 4 times 7? ... 7 / 7 7 5 times 7? ... 7 7 7 7 7 6 times 7? . . *. 7 7 7 7 7 7 7 times 7? ... 7 7 7 7 7 7 7 8 9 10 times times times 7? ... 7? . . 7 7? . 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 11. times How 7? 8 many times are 7? 5 9 times times 7? 7? 3 10 times times 7? 7? 2 6 times 7? 4 times 7? 12. times How 6? 6 many times are 5? 3 7 times times 7? 6? 7 6 times times 3? 7? 5 4 times 6? 6 times 4? 13. times Four times 5 are 6? 9 times 4? how many? 9 times 5? 4 9 times times 4? 7? 4 5 times 5? 5 times 7? 5 times 6? 14. 56? How many 63? 70? 7's in 14? 21? 35? 42? 28? WRITTEN EXERCISES. Multiply By ... a) 7 4 (2) 7 6 (3) 7 3 (4) 7 J> (o) 7 J (6) 7 2 (7) 7 9 (8) 7 7 Multiply By ... (l) 73 4 (2) 75 3 (3) 72 5 (4) 76 6 (5) 74 8 (6) 71 7 (7) 77 7 (8) 70 7 Multiply By ... (1) 33 8 (2) 44 7 (3) 55 6 (4) 66 4 (5) 22 9 (6) 77 3 (7) 77 5 (8) 37 6 - PRIMARY ARITHMETIC. 107 3UESSOK JL3ZKV* ORAL EXERCISES. 1. There are 7 days in a week : how many days are there in 4 weeks? 2. Kate found 3 bird's nests one morn- ing, and each nest had 7 eggs in it : how many eggs did she find? 3. There are 5 boys in a grammar class, and each boy has written 7 sentences : how many sentences have they all written? 4. If a horse trot 7 miles an hour, how far will he trot in 8 hours? 5. Kate picked 7 quarts of cherries, and sold them at 7 cents a quart: how many cents did she receive? 6. Jane is 7 years old, and her grandfather is 10 times as old as she is: how old is her grandfather? WRITTEN EXERCISES. Copy and complete these tables : (1) (2) (3) (4) (5) 7X1- 7X3 3X7 3 + 7 10 7 7X2 = 7X5 5X7 5 + 7 12 7 7X3 = 7X4 4X7 4 + 7 11 7 7X4 = . 7X6 6X7 6 + 7 13 7 7X5 = 7X8 8X7 8 + 7 15 7 7X6 = 7X7 1X7 1 + 7 8 7 7X7 = 7X9 9X7 9 + 7 16 7 7X8 = 7X2 2X7 2 + 7 9 7 7X9 = 7X1 7X7 7 + 7 14 7 To TEACHERS. Explain the sign of subtraction used in the 5th example, and teach the pupil to read it minus, as 10 minus 7. 108 PRIMARY ARITHMETIC. &.BSSON ORAL EXERCISES. 1. How many clusters of grapes are 2 times 8 clus- ters? 3 times 8 clusters? 4 times 8 clusters? 2. How many forks are 2 times 8 forks ? 3 times 8 forks? 4 times 8 forks? How many are 2 times 8? 3 times 8? 4 times 8? 3. How many fingers has one boy? 2 boys? 4 boys? 5 boys? 6 boys? 4. Five times 8 nuts are how many nuts ? 6 times 8 nuts? 7 times 8 nuts? How many are 5 times 8? 6 times 8? 7 times 8? 5. Here is a plate with 8 apples on it. How many apples are 7 times 8 apples? 8 times 8 apples? 6. How many are 7 times 8 stars? 7 times 8 men? 8 times 8 stars? 8 times 8 men? 7. How many are 9 times 8 apples? 9 times 8 pears? 10 times 8 apples? 10 times 8 pears? 8. How many are 6 times 8 ? 7 times 8 ? 8 times 8? 9 times 8? 10 times 8? 9. Five times 8 stars are how many stars ? 4 times 8 stars ? 6 times 8 stars ? 7 times 8 stars ? 10 times 8 stars? 3 times 8 stars? 9 times 8 stars ? PRIMARY ARITHMETIC. 109 How many are 1 time 8? 8 2 times 8? 88 3 times 8? 888 4 times 8? 8888 5 times 8? 88888 6 times 8? 888888 7 times 8?.... 8888888 8 times 8?... 88888888 9 times 8?. .888888888 10 times 8?. 8888888888 10. How many are 3 times 8? 5 times 8? 6 times 8? 7 times 8? 10 times 8? 9 times 8? 4 times 8? 2 times 8? 11. How many are 4 times 8? 8 times 4? 6 times 8? 8 times 6? 7 times 8? 8 times 7? 12. Five times 8 are how many? 8 times 5? 7 times 8? 8 times 7? 5 times 9? 9 times 5? 6 times 8? 8 times 6? 13. How many 8's in 16? 24? 40? 64? 48? 32? 72? 80? (l) WRITTEN EXERCISES. (2) (3) (4) (5) (6) (7) (8) Multiply 8 8 8 8 8 8 8 8 By ... 4 3 5 2 J7 8 9 6 (1) (?) (3) (4) (5) (6) (7) (S) ' Multiply 4 3 5 2 7 8 9 6 . By ... 8 8 8 8 8 8 8 8 (l) (2) (3) (4) (5) (0) Multiply 82 81 83 84 86 87 By ... J> J5 _4 3 1 2 (1) (2) (3) (4) (5) (6) Multiply 24' 26 43 36 33 25 By ... 11 12 13 15 14 16 110 PRIMARY ARITHMETIC. JL.JSSSOH ORAL EXERCISES. 1. A railroad car has 8 wheels : how many wheels has a train of 5 cars ? 2. There are 8 furlongs in a mile : how many fur- longs are there in 6 miles? 3. There are 4 rows of desks in a school-room, and 8 desks in each row : how many desks in all? 4. If a cow give 8 quarts of milk in one day, how many quarts will she give in 6 days? 5. There are 8 quarts in a peck : how many quarts are there in 9 pecks? 10 pecks? 6. What will 9 vests cost, at 8 dollars apiece? 7. What will 7 clusters of grapes cost, at 8 cents a cluster? WRITTEN EXERCISES. Copy and complete these tables : (1) (2) (3) (4) (3) 8X1=- 8X6 ' 6X8 6 + 8 14 8 8X2 = 8X4 4X8 4 + 8 10 S 8X3 = 8X2 2X8 2 + 8 12 S 8X4 = 8X1 1X8 3 + 8 13 G 8X5 = 8X3 3X8 5 + 8 15 9 8X6 = 8X5 5X8 7 + 8 16 8 8X7 = 8X7 7X8 9 + 8 17 9 8X8 = 8X9 9X-8 8 + 8* 18 9 8X9- 8X8 8X8 1+8 14 7 PRIMARY ARITHMETIC. Ill USS80N ORAL EXERCISES. 1. How many pine-apples are once 9 pine-apples? Twice 9 pine-apples? 3 times 9 pine-apples? 2. Jane picked 9 pinks, and Kate 2 times as many : how many pinks did Kate pick? How many are 2 times 9? 3 times 9? 3. Samuel has 3 book-shelves, and 9 books on each shelf: how many books has he? 4. How many books are 3 times 9 books? 4 times 9 books? 5 times 9 books? 6 times 9 books? 5. Four times 9 cents are how many cents? 5 times 9 cents? 6 times 9 cents? How many are 4 times 9 ? 5 times ? 6 times 9 ? H 6. Here are 8 banana trees. What long leaves they have! How many leaves are on each tree? 7. How many leaves are 7 times 9 leaves? 8 times 9 leaves ? 9 times 9 leaves ? 8. A fruit dealer bought 10 bunches of bananas, with 9 bananas in each bunch: how many bananas did he buy? 112 PRIMARY ARITHMETIC. 9. How many are 6 times 9 ? 7 times 9 ? 8 times 9? 9 times 9? 10 times 9? 10. Three times 9 caps are how many caps? 5 times 9 caps? 7 times 9 caps? 9 times 9 caps? 8 times 9 caps? 6 times 9 caps? 4 times 9 caps? How tnany are 1 time 9? 9 2 times 9? 99 3 times 9? 999 4 times 9? 9099 5 times 9? 99999 6 times 9? 999999 7 times 9? 9999999 8 times 9?... 99999999 9 times 9?. .999999999 10 times 9?. 9999999999 11. How many are 3 times 9? 5 times 9? 2 times 9? 8 times 9? 6 times 9? 4 times 9? 10 times 9? 7 times 9? 9 times 9? 12. How many are 4 times 9 ? 9 times 4? 6 times 9? 9 times 6? 5 times 9? 9 times 5? 7 times 9? 9 times 7? 8 times 9? 9 times 8? 13. Six times 7 are how many? 6 times 8? 7 times 8? 8 times 9? 8 times 4? 6 times 6? 6 times 9? 9 times 9? 14. How many 9's in 18? 27? 45? 54? 36? 63? 72? 90? 81? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) (9) Multiply 9 9 9999999 By.. .3 5 4127686 PRIMARY ARITHMETIC. (1) (2) (3) (4) (5) (6) (7) Multiply 5 4 3 6 7 2 8 By ... 9 _9 9 9 9 9 9 (1) (2) (3) (4) (5) Multiply 92 93 95 94 96 By ... 7 8 6 5 J (l) (2) (3) (4) (5) Multiply 91 93 92 94 96 By . /. 17 16 15 14 13 113 (8) (9) 9 6 _9 _9 (6) 97 _4 (6) 95 12 USSSON ORAL EXERCISES. 1. Henry has copied 3 columns of figures on his slate, and each column contains 9 figures : how many figures has he copied in all? 2. A hunter shot 9 quails, and saw 4 times as many as he shot: how many quails did he see ? 3. How many melons in 6 baskets, if each basket contain 9 melons ? 4. If a window has 9 panes of glass, how many panes are there in 7 windows? 5. If one copy-book contain 9 sheets of paper, how many sheets will it take to make 10 copy-books? 6. A cow gives 9 quarts of milk a day : how many quarts of milk will she give in 8 days ? 7. What will 5 hogs cost, at 9 dollars apiece? 8. What will 9 combs cost, at 9 cents apiece? 9. What will be the cost of 8 yards of muslin, at 9 cents a yard? P. A. 8. 114 PRIMARY ARITHMKTIG. WRITTEN EXERCISES. Copy and complete these tables: (1) (2) (3) (4) (-5) 9X1 = 9X3 3X9 3 + 9 12 9 9X2 = 9X5 5X9 5 + 9 14 9 9X3 = 9X7 7X9 7 + 9 16 9 9X4 = 9X9 9X9 9 + 9 18 9 9X5- 9X1 1-X9 1 + 9 17 9 9X6- 9X2 2X9 2 + 9 16 9 9X7- 9X6 4X9 4 + 9 13 9 9X8- 9X8 6X9 6 + 9 15 9 9X9 = 9X4 . 8X9 8 + 9 11 9 3L.BSSOH ORAL EXERCISKS. 1. How many pears are 2 times 10 pears? 3 times 10 pears? 4 times 10 pears? 5 times 10 pears? 2. How many cents are 3 times 10 cents ? 5 times 10 cents? 4 times 10 cents? 2 times 10 cents? 3. How many are 2 times 10? 3 times 10? 4 times 10? 5 times 10? 4. How many are 6 times 10 shells? 7 times 10 shells? 8 times 10 shells? 9 times 10 shells? 10 times 10 shells? 5 times 10 shells? 5. Six times 10 nuts are how many nuts ? 8 times PRIMARY ARITHMKTIG. 115 10 nuts? 7 times 10 nuts? 9 times 10 nuts? 10 times 10 nuts? 5 times 10 nuts? 6. How many are 6 times 10? 8 times 10? 9 times 10? 10 times 10? How many are 1 time 10? 2 times 10? 3 times 10? 4 times 10? 5 times 10? 6 times 10? 7 times 10? 8 times 10? 9 times 10? 10 times 10? How many are, 10 times 1? 10 times 2? 10 times 10 times 10 times 10 times 10 times 10 times 10 times 3? 4? 5? 6? 7? 8? 9? 10 times 10? 7. How many are 3 times 10? 6 times 10? 5 times 10? 8 times 10? 7 times 10? 4 times 10? 9 times 10? 10 times 10? Multiply By ... (1) 25 22 (1) Multiply 22 By . .23 WRITTEN EXERCISES. (2) (3) (4) 33 14 17 22 22 33 (2) (3) (4) 25 34 44 33 15 13 (5) 20 34 (5) 18 18 (6) 15 25 (6) 17 17 3L.BSSOH REVIEW. 1. How many are 2 times 5? 3 times 2? 3 times 4? 2 times 7? 4 times 5? 2. How many are 3 times 8 ? 6 times 5 ? 3 times 10? 7 times 4? 6 times 4? 7 times 5? 116 PRIMARY ARITHMETIC. 3. How many are 5 times 6? 4 times 7? 7 times 6? 5 times 4? 8 times 6? 8 times 7? 7 times 2? 6 times 9? 9 times 6? 4. How many are 5 times 7? 6 times 8? 10 times 6 ? 7 times 9 ? 5 times 8 ? 6 times 7 ? 10 times 7 ? 5 times 9? 8 times 9? 5. How many are 3 times 7? 7 times 4? 9 times 3? 6 times 5? 8 times 2? 7 times 5? 6 times 7? 7 times 8? 8 times 7? 5 times 7? 6. How many are 4 times 6? 6 times 9? 9 times 7? 8 times 5? 7 times 3? 9 times 8? 7. How many are 2 times 6? 8 times 7? 7 times 6 ? 9 times 9 ? 7 times 9 ? 10 times 5 ? 8 times 8 ? 7 times 10? 8 times 9? 8. How many are 2 times 2? 3 times 2? 4 times 2? 3 times 3? 5 times 2? 4 times 3? 7 times 2? 5 times 3? 4 times 4? 9 times 2? 9. How many are 8 times 4? 3 times 7? 8 times 3? 5 times 3? 9 times 3? 7 times 4? 10 times 4? 8 times 4? 6 times 4? 10. How many are 5 times 5 ? 9 times 4? 4 times 10 ? 7 times 6 ? 9 times 5 ? 8 times 6 ? 11. How many are 7 times 7? 10 times 5? 9 times 6? 4 times 5? 8 times 7? 5 times 9? 9 times 7? 8 times 8? 12. How many are 4 times 7? 9 times 8? 8 times 9? 9 times 7? 7 times 9? 9 times 10? 10 times 9? 10 times 10? 13. How many are 5 times 8? 7 times 8? 9 times 8? 8 times 8? 6 times 8? PRIMARY ARITHMETIC. 117 UBSSOH REVIEW. I. An ox has 2 horns: how many horns have 5 oxen? How many have 3 oxen? 6 oxen? 2. A bird has 2 wings : how many wings have 6 birds? 8 birds? 10 birds? 3. There are 3 seats in a stage-coach, and 3 men are sitting on each seat : how many men in the coach? 4. There are 3 feet in a yard: how many feet are there in 10 yards? 5. How many cherries, in 8 bunches, if each bunch has 3 cherries? 6. If John read 4 chapters a day, how many chap- ters will he read in 7 days? 7. If you give 4 marbles to each of 8 boys, how many marbles will you give to all? 8. An orchard contains 4 rows of trees, and each row has 8 trees : how many trees in the orchard ? 9. Edward attends school 5 days each week: how many days will he attend school in 6 weeks? 10. A stranger gave 7 boys 5 cents each: how many cents did he give to all? II. A house has 7 windows, and each window has 8 panes of glass : how many panes of glass in the house ? 118 PRIMARY ARITHMETIC. 12. Frank has 6 rows of blocks, and each row con- tains 7 blocks: how many blocks has he? 13. What will 2 bunches of grapes cost, at 8 cents a bunch ? 4 bunches ? 6 bunches? 3 bunches? 14. Joseph writes 10 lines each day: how many lines will he write in 6 days? In 5 days? In 7 days? 15. What will 10 slates cost, at 8 cents apiece? 16. If a man work 8 hours a day, how many hours will he work in 6 days? 17. There are 10 lines on a page of Ellen's primer, and each line contains 9 words : how many words on the page? 18. If it take 9 steps to cross a room once, how many steps will it take to cross the room 9 times? 19. A railway train runs 10 miles an hour: how many miles will it run in 9 hours? 20. An orchard contains 10 rows of trees, and each row contains 7 trees : how many trees in the orchard ? 21. What will 8 loads of wood cost, at 5 dollars a load? At 3 dollars a load? 22. If a man earn 9 dollars a week, how many dollars will he earn in 7 weeks? Multiplication is the process of taking a number one or more times. The result obtained by multiplying one number by another is called the Product. PRIMARY ARITHMKTIC. 119 UBSSOH EEVIEW. (1) (2) (3) (4) (5) (6) (7) (8) 8 18 7 17 24 16 16 18 7 7 6 6 3 5 6 9 (9) (10) (ll) (12) (13) (14) (15) (16) 27 36 47 38 45 34 56 27 4 5 3 6 8 9 7 8 (17) (18) (19) (20) (21) (22) m (24) 24 33 43 50 60 30 70 50 12 13 15 16 14 28 17 18 t (25) (26) (27) (28) (29) (30) (31) (32) 23 36 44 27 36 44 55 28 23 27 21 27 25 23 17 33 (33) (34) (35) (36) (37) (38) (39) (40) 205 304 107 109 106 108 103 108 3 2 6 8 5 4 7 9 (41) (42) (43) (44) (45) (46) (47) 21 24 15 27 16 17 24 30 40 50 20 _60 40 30 (48) (49) (50) (51) (52) (53) (54) 30 40 50 17 14 19 18 30 20 10 50 70 50 40 (55) (56) (57) (58) (59) (60) (61) 25 33 44 28 17 16 13 20 30 20 30 50 60 70 120 PRIMARY ARITHMETIC. DIVISION. USSSOSf ORAL EXERCISES. 1. Here is a gay winter scene. How many sleighs are in sight? How many times 1 sleigh are 2 sleighs? 2. How many boys are putting on their skates ? How many times 1 boy are 4 boys? 3. How many boys are coasting? How many times 1 boy are 7 boys? 4. How many times is 1 sled contained in 4 sleds? 1 sled in 6 sleds? 1 sled in 7 sleds? PRIMARY ARITHMETIC. 121 5. How many times is 1 skate contained in 8 skates ? 1 skate in 9 skates? 6. How many times is 1 contained in 2? 1 in 4? 1 in 6 ? 1 in 8 ? 1 in 7 ? 1 in 9 ? 1 in 10? Sow tnatty times 1 are 1? 1 are 2? 1 are 3? 1 are 4? 1 are 5? 1 are 6? 1 are 7? 1 are 8? 1 are 9? 1 are 10? How many times 1? 2? 3? 4? 5? 6? 7? 8? 1 in 9? 1 in 10 ? To TEACHERS. These two tables should be recited together, thus : Once Us 1: 1 in 1 once. Two times I are 2: 1 in 2 two times. Three times 1 are 3 : 1 in 3 three timeSj etc. The subsequent tables should be recited in the same manner. Division is here treated as the inverse of multiplication, but it may also be derived from subtraction. 4 is contained in 12 as many times as 4 can be taken from 12. At this point pupils may be taught the division of a material unit into halves, thirds, fourths, etc. They may also be taught to add and subtract halves, thirds, fourths, etc., and to find the fractional part of small numbers. 3UBSSOH ORAL EXERCISES. 1. How many times 2 horses are 4 horses? How many times 2 sleds are 4 sleds ? 2. How many persons in each sleigh? (See picture.) How many times 2 persons are 6 persons? How many times is 2 contained in 2? 2in4? 2in 6? 2 in 8? 122 PRIMARY ARITHMETIC. 3. How many times 2 blocks make 10 blocks? How many times are 2 blocks contained in 10 blocks? 4. How many times are 2 marbles contained in 10 marbles? 2 marbles in 12 marbles? How many times is 2 contained in 10? 2 in 12? 5. How many times 2 grape-clusters make 14 grape-clusters? 16 grape-clusters? 6. How many times are 2 clusters contained in 14 clusters? 2 clusters in 16 clusters? How many times is 2 contained in 14? 2 in 16? 7. How many times 2 boys make 18 boys? How many times are 2 boys contained in 18 boys? 8. How many times are 2 men contained in 18 men? 2 men in 20 men? How many times is 2 contained in 18? 2 in 20? How many times 2 are 2? 2 are 4? . 2 are 6? 2 are 8? 2 are 10? 2 are 12? 2 are 14? 2 are 16? 2 are 18? 2 are 20? w many times 2 in 2? 2 in 4? 2 in 6? 2 in 8? 2 in 10? 2 in 12? 2 in 14? 2 in 16? 2 in 18? 2 in 20? PRIMARY ARITHMETIC. 123 9. How many times 2 make 4? 6? 10? 14? 12? 16? 20? 18? 10. How many times is 2 contained in 4? 2 in 6? 2 in 10? 2 in 8? 2 in 14? 2 in 20? 11. How many times is 2 contained in 12? 2 in 16? 2 in 14? 2 in 18? 12. How many times is 1 contained in 8? 2 in 8? 1 in 12? 2 in 12? 1 in 14? 2 in 14? WRITTEN EXERCISES. 1. Divide 12 by 2, thus: 2)12 QAns. (2) (3) (4) (5) (6) 2)8_ 2)6_ 2)10 2)14 2)16 (7) (8) (9) (10) (11) 2)12 2)18 2)20 2)22 2)24 (12) (13) (14) (15) (16) 2J28 2)42 2)82 2)62 2)44 Copy and complete: (i) (2) 2-J-2 = 2-4-2 4-v-2 = 6-4-2 6-^2 = 10-^-2 84-2 = 14-4-2 10 -f- 2 = 18-^-2 12 -4- 2 = 8-5-2 14-4-2 = 4-4-2 16 -T- 2^ 12-- 2 18-*- 2 = 16 H- 2 20-i-2 = 20-^2 UESSOH ORAL EXERCISES. 1. How many times 3 pears make 6 pears? 9 pears? 12 pears? 2. How many times are 3 pears contained in 6 pears? 3 pears in 9 pears? 3 pears in 1*2 pears? How many times is 3 contained in 6? 3 in 9? 124 PRIMARY ARITHMETIC. 3. How many times 3 oak leaves make 15 oak leaves? 18 oak leaves? 4. How many times are 3 acorns contained in 15 acorns? 3 acorns in 18 acorns? How many times is 3 contained in 15? 3 in 18? 5. How many times 3 nuts make 21 nuts? 24 nuts? 27 nuts? 30 nuts? 6. How many times are 3 balls contained in 21 balls? 3 balls in 15 balls? 3 balls in 27 balls? 3 balls in 24 balls? 7. How many times are 3 cents contained in 24 cents? 3 cents in 30 cents? 3 cents in 27 cents? 3 cents in 21 cents? 0^00 Hotv many titties 3 are 3? 3 are 6? 3 are 9? 3 are 12? 3 are 15? 3 are 18? 3 are 21? 3 are 24? 3 are 27? 3 are 30? Sow tnany times 3 in 3? 3 in 6? 3 in 9? 3 in 12? 3 in 15? 3 in 18? 3 in 21? 3 in 24? 3 in 27? 3 in 30? 8. How many 3's in 6? 12? 18? 24? 30? 9. How many times is 3 contained in 9? 3 in 15? 3 in 6? 3 in 12? 3 in 18? 3 in 24? 3 in 27? 3 in 21? 3 in 30? 10. How many times is 2 contained in 12? 3 in 12? 2 in 18? 3 in 18? 2 in 16? PRIMARY ARITHMETIC. 125 ORAL EXERCISES. 1. It takes 2 boots to make a pair : how many pair of boots will 6 boots make ? 2. Two ducks make a pair : how many pair will 10 ducks make ? 3. How many peaches at 2 cents each can you buy for 20 cents? 4. If John step 2 feet at a time, how many steps must he take to go 16 feet? 5. There are 3 feet in a yard: how many yards are there in 18 feet? 6. If a man walk 3 miles an hour, how many hours will it take him to walk 27 miles? 7. How many sheep at 3 dollars a head can be bought for 24 dollars? tt (5) 3)6_ (9) 3)15 (13) 3)66 (2) 3)15 (6) 3)12 (10) 3)27 (14) 3)99 WRITTEN EXERCISES, (3) 3)21 (4) 3)18 Copy (i) and complete : (2) 3 3 = 6 -*-3 CO (8) 6 _i_ 3^ 12 -:-3 3)24 3)30 9 _i_ o 18 -*-3 12 _i_ 9 -5-3 (11) (12) 15 -:- 15 -f-3 3)33 3)36 18 21 -j- 3^ = 21 30 . 3 4-3 24 -;- 3 = 24 ^-3 (15) (16) 27 3 = 27 -^-3 3)63 3)69 30 H- 3 -f-3 126 PRIMARY ARITHMETIC. USSSCBS ORAL EXERCISES. 1. Here are 8 rabbits in 2 groups. 8 rabbits are how many times 4 rabbits ? 2. How many times are 4 ducks contained in 4 ducks? 4 ducks in 8 ducks? How many times is 4 contained in 4? 4 in 8? 3. How many times 4 quails make 12 quails? 16 quails? 20 quails? 4. How many times are 4 pigeons contained in 12 pigeons? 4 pigeons in 16 pigeons? How many times is 4 contained in 12? 4 in 16? 5. How many times 4 keys are there in 20 keys? In 24 keys? In 28 keys? How many times is 4 contained in 20? 4 in 24? 4 in 28? 6. How many times 4 boys make 28 boys? 32 boys? 36 boys? 40 boys? 7. How many times is 4 contained in 28? 4 in 32? 4 in 36? 4 in 40? 8. How many times are 4 pages contained in 8 pages? 4 pages in 20 pages? 4 pages in 16 pages? PRIMARY ARITHMETIC. 127 4 pages in 28 pages ? 4 pages in 1 2 pages ? 4 pages in 24 pages ? *-f*-*^*. tv many times 4 are 4? . 4 are 8 ? 4 are 12? 4 are 16? 4 are 20? 4 are 24? 4 are 28? 4 are 32 ? 4 are 36? 4 are 40? How many times 4 in 4? 4 in 8? 4 in 12? 4 in 16? 4 in 20? 4 in 24? 4 in 28? 4 in 32 ? 4 in 36? 4 in 40? in 4 in ^ are iu : i in iu r 9. How many times is 4 contained in 12? 4 i 16? 4 in 24? 4 in 8? 4 in 20? 4 in 28? 4 i: 36? 4 in 32? 10. How many times 2 in 18? 3 in 21? 4 in 40? 2 in 20? 2 in 14? 3 in 27? 3 in 18? 4 in 16? 4 in 28? 3 in 24? 3 in 30? ORAL EXERCISES. 1. If 4 girls can sit on one settee, how many settees will be required to seat 12 girls ? 2. A wagon has 4 wheels : how many wagons will 16 wheels furnish? 3. Four quarts make a gallon: how many gallons are there in 32 quarts? 4. At 4 cents apiece, how many lemons can you buy for 40 cents? 32 cents? 5. If a load of wood cost 4 dollars, how many loads can be bought for 12 dollars? 128 PRIMARY ARITHMETIC. 6. If there be 4 trees in a row, how many rows will 36 trees make? 7. If a man can build 4 rods of fence in a day, how long will it take him to build 40 rods of fence ? 8. There are 4 pecks in a bushel : how many bush- els are there in 20 pecks ? 4)12 (5) 4)8_ (9) 2)44 (13) 3)36 (2) 4)20 (6) 4)28 (10) 2)66 3)66 WRITTEN EXERCISES. (3) 4)16 (4) 4)24 Copy and (i) complete : (2) 4-^-4 8-^4 (7) (8) 8^-4 12 --3 4)36 4)32 12-^4 18 4-2 16-^4 20 --4 (11) (12) 20^-4 24 --3 2)88 2)22 24 --4 28 --4 28-4-4 36-f-4 32 -4- 4 21-^-3 (15) (16) 36-4-4 40-4-4 3)99 3)39 40^-4 20-4-2 ORAL EXERCISES. 1. How many groups of 5 tops each will 10 tops make? 15 tops? 2. Harry has 15 blocks: how many rows of 5 blocks in each will they make? How many times is 5 contained in 5? 5 in 10? 5 in 15? PRIMARY ARITHMKTIG. 129 3. Charles has 25 marbles: how many groups of 5 marbles each will they make? *> JQ *j) J *) JQ *> jQ ^-^ jQ 4. How many times are 5 marbles contained in 25 marbles? 5 marbles in 30 marbles? How many times is 5 contained in 25? 5 in CO? 5. A violet has 5 leaves or petals : how many vio- lets will together have 35 petals ? 40 petals ? 6. How many times are 5 pinks contained in 35 pinks? 5 pinks in 40 pinks? 5 pinks in 45 pinks? 5 pinks in 50 pinks? How many times is 5 contained in 35? 5 in 40? 7. How many times are 5 cents contained in 20 cents ? 5 cents in 30 cents ? 5 cents in 25 cents ? 5 cents in 35 cents? 5 cents in 45 cents? Hotv many times 5 are 5? 5 are 10? 5 are 15? 5 are 20? 5 are 25? 5 are 30? 5 are 35? 5 are 40? 5 are 45? 5 are 50? How many times 5 in 5? 5 in 10? 5 in 15? 5 in 20? .5 in 25? 5 in 30? 5 in 35? 5 in 40? 5 in 45? 5 in 50? 8. How many 5's in 20? 30? 50? 45? 35? 25? 9. How many times is 5 contained in 15? 5 in 25? 5 in 35? 5 in 40? 5 in 50? 5 in 45? 5 in 20? P. A. 9. 130 PRIMARY ARITHMETIC. 3UESSOK ORAI EXERCISES. 1. Charles has 30 blocks: how many groups of 5 blocks each can he make from them? 2. If a squirrel eat 5 chestnuts a day, how many days will 40 chestnuts last it? 3. If a boat sail 5 miles an hour, how many hours will it take to sail 50 miles? 4. Edward goes to school 5 days each week : in how many weeks will he attend school 35 days? 5. How many oranges at 5 cents apiece can be bought for 45 cents? 6. How many hours will it take a horse to travel 25 miles, if he travel 5 miles an hour? 7. At 5 cents apiece, how many pencils can be bought for 35 cents? 8. How many times can you take 5 from 20? 4 from 32? 3 from 18? 4 from 28? 5 from 35? (i) 5)15 (5) 5)10 (9) 4)44 (13) 5)55 (2) 5)25 (6) 5)35 (10) 4)88 5)50 WRITTEN EXERCISES. (3) 5)30 (4) 5)45 Copy and complete : ~~ (i) (2) 5- -5 50-^-5 (7) (8) 10- -5 35 --5 5)40 5)50 15- -5 25 --5 20- -5 40 --5 (11) (12) 25- -5 36^-4 3)63 3)69 30- 35- -5 -5 27^-3 32 -f- 4 40- -5 21 --3 (15) (16) 45- -5 24 -=-4 4)48 3)96 50- -5 20^-5 PRIMARY ARITHMETIC. 131 ORAL EXERCISES. 1. How many times 6 bunches of cherries make 12 bunches? 18 bunches? 2. How many times are 6 plums contained in 12 plums ? 6 plums in 18 plums ? 6 plums in 24 plums ? How many times 6 in 12? 6 in 18? 6 in 24? 3. Here are 30 books : how many shelves holding 6 books each, will they fill? 4. How many times 6 books make 30 books ? 36 books? 42 books? 5. How many times 6 sheets of paper in 30 sheets ? 6 sheets in 36 sheets? 6 sheets in 42 sheets? How many times 6 in 30? 6 in 36? 6 in 42? 6. Lucy has 48 spools : how many piles will they make if she put 6 spools in each pile ? 7. How many times 6 spools in 48 spools? 6 spools in 54 spools? 6 spools in 60 spools? How many times 6 in 48? 6 in 54? 6 in 60? 8. How many times are 6 dimes contained in 18 dimes? 6 dimes in 30 dimes? 6 dimes in 42 dimes? 6 dimes in 54 dimes? 6 dimes in 48 dimes? 132 PRIMARY ARITHMETIC. JETotv many times 6 are 6? 6 are 12? 6 are 18? 6 are 24? 6 are 30? 6 are 36? 6 are 42? 6 are 48? 6 are 54? 6 are 60? How many tunes 6 in 6? 6 in 12? 6 in 18? 6 in 24? 6 in 30? 6 in 36? 6 in 42? 6 in 48? 6 in 54? 6 in 60? 9. How many times 6 are 12? 30? 42? 54? 36? 10. How many times is 6 contained in 30? 6 in 24? 6 in 42? 6 in 54? 6 in 60? 6 in 48? 11. How many times is 4 contained in 24? 3 in 24? 6 in 24? 5 in 30? 6 in 30? 4 in 36? usssoxt ORAL EXERCISES. 1. If a column contain 6 words, how many col- umns will contain 12 words? 2. If a cart have 6 stakes, how many carts will 18 stakes supply ? 3. If a window contain 6 panes of glass, how many win- dows will contain 30 panes of glass ? 4. An orchard contains 48 trees, and has 6 trees in each row : how many rows of trees in the orchard ? 5. At 6 cents apiece, how many lead-pencils can be bought for 42 cents? PRIMARY ARITHMETIC. 133 6. Joseph writes 6 lines a day : how many days will it take him to write 60 lines ? 7. A farmer bought 48 young peach trees : how many rows will they make if he set 6 trees in a row? 8. How many sheep, at 6 dollars a head, can be bought for 54 dollars? 9. How many 'times can you take 5 from 25? 4 from 24? 3 from 18? 6 from 18? (1) 6)12 (5) 6)54 (0) 4)48 (13) 6)72 (2) 6)24 (6) 6)66 (10) 4)84 (14) 6)84 WRITTEN EXERCISES. (3) 6)36 (4) 6)48 Copy and complete : (!) (2) 6 6 54 --6 (7) (8) 12- -6 42-4-6 6)90 6)60 18- -6 45 --5 24- -6 36^-4 (11) (12) 30- -6 50 -T- 5 4)88 3)69 36- 42- -6 -6 35-i-5 27-^-3 48- -6 24 -f- 4 (15) (16) 54- -6 32---4 6)96 6)78 60- -6 30-4-5 ORAL EXERCISES. 1. If each nest contain 7 eggs, how many nests will contain 14 eggs? 21 eggs? 2. How many times are 7 nuts contained in 14 nuts? 7 nuts in 21 nuts? 7 nuts in 28 nuts? How many times 7 in 14? 7 in 21? 7 in 28? 134 PRIMARY ARITHMKTIC. 3. This pretty leaf has 7 points. How many times 7 points make 35 points? 42 points? 4. How many times are 7 leaves contained in 35 leaves? 7 leaves in 42 leaves? How many times is 7 contained in 35? 7 in 42? 5. Charles has 49 cherries, and he wishes to put them up in bunches of 7 cherries each to sell : how many bunches will they make? 6. How many times are 7 cherries contained in 49 cherries? 7 cherries in 56 cherries? 7 cherries in 63 cherries? 7 cherries in 70 cherries? 7. How many times is 7 contained in 49? 7 in ^56? 7 in 63? 7 in 70? JETotr many times How many times 7 are 7? 7 in 7? 7 are 14? 7 in 14? 7 are 21? 7 in 21? 7 are 28? 7 in 28? 7 are 35? 7 in 35? 7 are 42? 7 in 42? 7 are 49? 7 in 49? 7 are 56? 7 in 56? 7 are 63? 7 in 63? 7 are 70? 7 in 70? 8. How many times 7 are 14? 28? 42? 56? 49? 70? 9. How many times is 7 contained in 21? 35? 7 in 56? 7 in 28? 7 in 63? 7 in 14? n PRIMARY ARITHMETIC. 135 ORAL EXERCISES. 1. How many bunches of 7 cherries each will 14 cherries make? 2. How many quarts of milk, at 7 cents a quart, can be bought for 21 cents ? 3. There are 7 days in one week : how many weeks are there in 28 days? 4. A horse travels 7 miles an hour: how many hours will it take him to travel 42 miles? 5. Frank has 35 blocks : how many rows will they make if he place 7 blocks in each row ? 6. At 7 cents apiece, how many melons can be bought for 42 cents ? 7. If 7 words make a line, how many lines will 70 words make? 77 words? 8. How many settees will seat 49 boys, if each settee seat 7 boys? WRITTEN EXERCISES. (1) 7)28 (2) 7)42 (3) 7)56 (4) 7)63 Copy and (i) complete : 7-^7 36 -5-6 (5) (6) (7) (8) 14-^-7 48-5-8 7)84 7)77 7)91 7)98 35 -v- 7 42 -r- 6 42 -r- 7 45-^5 (0) (10) (11) (12) 28 -H7 28-^-4 7)147 7)217 7)357 7)497 21 -r-7 49 -f- 7 30-^-6 40 -f- 5 6S 7 27 -f- 3 (13) (14) (15) (16) 56 4- 7 36-^-4 7)154 7)161 7)175 7)182 70-^-7 54 -f- 6 136 PRIMARY ARITHMETIC. ORAL EXERCISES. 1. How many times 8 fingers make 16 fingers? 24 fingers? 32 fingers? 40 fingers? 2. How many times are 8 trees contained in 16 trees? 8 trees in 24 trees? 8 trees in 32 trees? 3. How many times is 8 contained in 16? 8 in 24? 8 in 32? 8 in 40? 4. Here arc 48 'apples : Low many plates will they fill if each plate hold 8 apples? 5. How many times 8 apples in 48 apples? In 56 apples? 64 apples? 72 apples? 80 apples? Holt' many times 8 are 8? 8 are 16? 8 are 24? 8 are 32? 8 are 40? 8 are 48? 8 are 56? 8 are 64? 8 are 72? 8 are 80? How many times 8 in 8? 8 in 16 ? 8 in 24? 8 in 32 ? 8 in 40 ? 8 in 48 ? 8 in 56? 8 in 64? 8 in 72? 8 in 80? 6. How many times 8 are 16? 32? 48? 56? 40? 64? 80? 72? 7. How many times 8 in 24? 8 in 16? 8 in 32? 8 in 40? 8 in" 56? 8 in 72? 8 in 64? PRIMARY ARITHMETIC. 137 ORAL EXERCISES. 1. If 8 panes of glass will fill one window, how many windows will 24 panes fill? 2. If a railroad car has 8 wheels, how many cars will 40 wheels supply? 3. If a horse travel 8 miles an hour, in how many hours will it travel 56 miles? 4. How many days will it take a man to work 48 hours, if he work 8 hours a day ? 5. At 8 cents apiece, how many slates can be bought for 80 cents? WRITTEN EXERCISES. (1) 8)24 (2) (3) (4) (5) (6) 8)40 8)64 8)72 8)88 8)96 (7) 8)192 (8) 8)120 (9) 8)168 (10) 8)248 (11) 8)208 (12) 8)272 (13) 8)264 (14) 7)147 (15) 7)154 (16) 7)112 (17) 7)301 (18) 7)245 (19) 7)252 3UBSSOH ORAL EXERCISES. 1. How many times 9 crowns make 18 crowns? 27 crowns? 36 crowns? 45 crowns? How many times is 9 contained in 27? 9 in 45? 138 PRIMARY ARITHMETIC. 2. Harry has gathered 54 acorns : how many piles of 9 acorns each will they make ? 3. How many palm trees will bear 72 leaves, if each tree bear 9 leaves? 4. How many times are 9 nuts contained in 63 nuts? 9 nuts in 72 nuts? 9 nuts in 81 nuts? How many times How many times 9 are 9? 9 in 9? 9 are 18? 9 in 18? 9 are 27? 9 in 27? 9 are 36? 9 in 36? 9 are 45? 9 in 45? 9 are 54? 9 in 54? 9 are 63? 9 in 63? 9 are 72? 9 in 72? 9 are 81? 9 in 81? 9 are 90? 9 in 90? y are y\) i v m vv i 5. How many times 9 are 18? 36? 27? 72? 19 K49 4K9 SI 9 63? 54? 45? 81? 6. How many times is 9 contained in 27? 45? 9 in 81? 9 in 36? 9 in 54? 9 in 63? How many times How many times 10 are 10? 10 in 10? 10 are 20? 10 in 20? 10 are 30? 10 in 30? 10 are 40? . 10 in 40? 10 are 50? N 10 in 50? 10 are 60? 10 in 60? 10 are 70? 10 in 70? 10 are 80? 10 in 80? 10 are 90? 10 in 90? 10 are 100? 10 in 100? n 7. How many times is 10 contained in 70? 10 in 50? 10 in 80? 10 in 60? 10 in 90? PRIMARY ARITHMETIC. 139 ORAL EXERCISES, 1. If a copy-book contain 9 sheets of paper, how many copy-books will 27 sheets of paper make? 2. If 9 words fill a line, how many lines will 45 words fill? 36 words? 3. If a train of cars run 9 miles an hour, in how many hours will it run 90 miles? 4. If 9 melons fill a basket, how many baskets will 63 melons fill? 5. If a pupil write 9 lines a day, how many days will it take him to write 54 lines ? WRITTEN EXERCISES. (1) 9)54 (2) (3) (4) (5) 9)72 9)81 9)45 9)90 (6) 9)108 (7) 9)117 (8) 9)180 (9) 9)288 (10) 9)225 (11) 9)396 (12) 9)549 (13) 10)70 (14) 10)90 (15) 10)60 (16) 10)200 (17) 10)500 (18) 10)400 (19) 10)250 (20) 10)360 (21) 10)480 (22) 10)570 (23) 10)430 (24) 10)270 3UESSOH EEVIEW. 1. There are 3 feet in a yard: how many yards are there in 30 feet? 2. If Mary read 4 chapters a day, in how many days will she read 32 chapters? 140 PRIMARY ARITHMETIC. 3. There are 7 days in a week : how many weeks are there in 70 days? 4. Willis picked 72 cherries, and tied them .up in bunches of 8 cherries each : how many bunches did they make? 5. There are 8 quarts in a peck : how many pecks are there in 56 quarts ? 6. At 9 cents a bushel, how many bushels of coal can be bought for 90 cents ? 7. If a steamer sail 9 miles an hour, how long will it be in sailing 63 miles? 8. At 10 dollars a barrel, how many barrels of flour can be bought for 70 dollars ? Division is the process of finding how many times one number is contained in another. The result obtained by dividing one number by another is called the Quotient. WRITTEN EXERCISES. (1) 2)118 (2) 2)676 (3) 3)588 (4) 3)231 (5) 4)872 (6) 4)804 (7) 5)450 (8) 5)665 (9) 5)725 (10) 6)174 (ii) 6)906 (12) 6)474 (13) 7)231 (14) 7)266 (15) 7)476 (16) 7)189 (17) 7)329 (18) 7)840 (19) 8)272 (20) 8)408 (21) 8)512 (22) 8)328 (23) 8)504 (24) 8)960 (25) 9)279 (26) 9)396 (27) 9)477 (28) 9)648 (29) 9)864 (30) 9)387 PRIMARY ARITHMETIC. 141 GENERAL REVIEW. 3UESSGH 3CC. ORAL EXERCISES. Study and recite these examples across the page, thus : 2 and 7 are 9; 2 from 9 leaves 7 2 times 7 are 14; 2 in 14, 7 1. 2 and 7? 2 from 9? 2 times 7? 2 in 14? 2, 3 and 9? 3 from 12? 3 times 9? 3 in 27? 3. 4 and 8? 4 from 12? 4 times 8? 4 in 32? 4. 5 and 7? 5 from 12? 5 times 7? 5 in 35? 5. 6 and 9? 6 from 15? 6 times 9? 6 in 54? 6. 7 and 8? 7 from 15? 7 times 8? 7 in 56? 7. 7 and 4? 7 from 11? 7 times 4? 7 in 28? 8. 8 and 6? 8 from 14? 8 times 6? 8 in 48? 9. 8 and 7? 8 from 15? 8 times 7? 8 in 56? 10. 9 and 5? 9 from 14? 9 times 5? 9 in 45? 11. 9 and 7? 9 from 16? 9 times 7? 9 in 63? WRITTEN EXERCISES. (1) (2) (3) (4) (5) (6) (7) (8) 2 24 48 64 121 135 233 450 3 35 64 43 132 144 246 108 4 46 77 57 140 155 328 200 5 5 39 46 135 166 344 306 6 24 48 68 124 177 422 437 7 43 56 39 155 188 346 330 8 66 66 47 166 199 166 149 Add _9 27 44 84 143 145 222 128 (9) (10) (11) (12) (13) (14) (15) From 407 564 640 702 506 547 603 Take 289 347 518 486 389 388 486 142 PRIMARY ARITHMETIC. (16) Multiply 270 By ... 3 345 6 (18) 383 4 (19) (20) 209 460 6 5 (21) 244 7 (22) (23) (24) (25) (26) (27) Divide: 3)408 4)760 5)565 6)876 7)945 8)904 bBSSOM XCI ORAL EXERCISES. 1. 2 and 9? 9 from 11? 2 times 9? 2 in 18? 2. 3 and 8? 3 from 11? 3 times 8? 3 in 24? 3. 4 and 7? 4 from 11? 4 times 7? 4 in 28? 4. 5 and 9? 5 from 14? 5 times 9? 5 in 45? 5. 6 and 8? 6 from 14? 6 times 8? 6 in 48? 6. 6 and 7? 6 from 13? 6 times 7? 6 in 42? 7. 7 and 9? 7 from 16? 7 times 9? 7 in 63? 8. 8 and 6? 8 from 14? 8 times 6? 8 in 48? 9. 9 and 8? 9 from 17? 9 times 8? 9 in 72? 10. 9 and 9? 9 from 18? 9 times 9? 9 in 81? WRITTEN EXERCISES. 1. Add 234, 275, 366, and 484. 2. Add 244, 412, 561, 308, and 445. 3. Add 327, 303, 482, 206, 409, and 292. 4. From 865 subtract 336. 5. From 642 subtract 516. 6. From 736 subtract 345. 7. Multiply 241 by 4, and 5. 8. Multiply 165 by 3, 4, and 6. 9. Multiply 250 by 4, 5, and 6. 10. Divide 248 by 2, 4, and 8. PRIMARY ARITHMETIC. 143 11. Divide 512 by 4, 8, and 2. 12. Divide 864 by 3, 6, and 9. 13. Divide 492 by 3, 4, and 6. 14. What is the sum of 486 and 237? 15. What is the difference between 486 and 237? 16. What is the product of 348 multiplied by 6? 17. What is the quotient of 348 divided by 6? bJSSSOH XLCH. ORziL EXERCISES. 1. William bought 8 marbles, and Edward gave him 6 : how many marbles had he then ? 2. A cooper made 15 barrels, and sold 7 of them: how many had he left? 3. Sarah found 12 eggs, and Kate found 9: how many eggs did both find? 4. Albert has 21 plums : if he give 8 of them to Alice, how many plums will he have left? 5. There are 7 days in a week : how many days are there in 9 weeks? 6. There are 8 quarts in one peck: how many quarts in 10 pecks? In 8 pecks? 7. If a man earn 8 dollars a week, in how many weeks will he earn 64 dollars? 8. If a cord of wood cost 5 dollars, how many cords can you buy for 35 dollars? ). How long will it take a steamer to run 90 miles at the rate of 9 miles an hour ? 144 PRIMARY ARITHMETIC. WRITTEN EXERCISES. 1. There are 267 boys, and 289 girls in a school : how many pupils in the school? 2. A drover bought 564 sheep, and sold 288 of them: how many had he left? 3. A merchant had 408 yards of cloth, and sold 184 yards: how many yards had he left? 4. There are 338 apples on one tree, 467 apples on another, and 169 apples on another : how many apples on all the trees? 5. A miller made 467 barrels of flour, and sold 237 of them : how many barrels remain unsold ? 6. There are 320 rods in a mile : how many rods are there in 3 miles ? 7. If a steamship can sail 290 miles in a day, how far can it sail in 6 days? 8. There are 7 days in a week : how many weeks are there in 427 days ? 9. If 3 bushels of apples will fill a barrel, how many barrels will 468 bushels fill? 10. A farmer bought 26 cows at 18 dollars a head: how much did they cost? 11. If a man build 8 rods of fence in a day, in how many days will he build 464 rods? 12. If a man can walk 28 miles a day, how far can he walk in 24 ^^ VA 02442 UNIVERSITY OF CALIFORNIA LIBRARY NEW GEOGRAPHIES, IFTJIBIITSIKIEID ILSON, INKLS &' O. The Eclectic Series of Geographies, consisting three books, by A KIXWEHR and D. G. BRINTOJ No. l f The frlntar) ^geography, is adapted to the of pupiti^rcommencing the study. The language is sin and clear ; the definitions and descriptions are exact ; plan of the book is natural, and the copper-plate maps wonderfully clear and definite. No. 2, The Intermediate Geography, is intended the use of the higher classes in Graded Schools, aivl cont the leading principles of the science, so arrange as to s , t correct ideas to pupils, and, at the ire aid from the teacher than any other b. b contains full instructions in map-drawing. \0. 3, The SchOOl Geography, embraces a iv ematical, Political, and Physical descript : on of the Ea: and is intended for the highest classes in this branch study. The maps, which are the basis of all geograph study, are models of clearness. The physical features :itry are fully brought out, and it is thus made j. /ely.