'£ij^\'nmm:i':<'dif:i' UC-NRLF ii^i&SSIiifi^>. m I $B E7fl TM3 •.SiJidJlHBirftMiliMd'.li'W Ele^e^taj^y \TMA\EriC R? » :i'' ? 'i-\- W MEMOEEAM Irving Stringham Digitized by tine Internet Arciiive in 2007 witii funding from IVIicrosoft Corporation littp://www.archive.org/details/elementaryaritlimOOwentricli A^ ELEMEN^TARY ARITHMETIC, BY G. A. WENTVVORTH, A.M., Author of a Series of Text-Books in Mathematics. >o>«:;oc. — BOSTON, U.S.A.: PUBLISHED BY GINN & CO. 1894. Entered, according to Act of Congress, in the year 1893, by G. A. WENTWORTH, in the Office of the Librarian of Congress, at Washington. All Rights Reserved, Typography by J. S. Gushing & Co., Boston, U.S.A. Presswork by Ginn & Co., Boston, U.S.A. '^^C^ PREFACE. Teachers who have the power of putting themselves in the mental attitude of their pupils possess a most impor- tant gift. In the first stages of mental growth, as the mind works unseen, it is hard to realize the difficulties encoun- tered, and to decide what assistance can be judiciously given. There is no royal road to the knowledge of arith- metic, but the steps can be made short and easy. The little learner need not be wearied, if the exercise is not too long continued. He may also have the consciousness of eifort, as in learning to walk, and above all, the pleasure of suc- ceeding. This result can be secured only by observing the following fundamental principles : 1. All elementary teaching of arithmetic must be begun by the pupils observing and handling objects. It is surprising that school authorities in many places decline to furnish the money, however small the amount is, to purchase the simple apparatus required for each Primary School. They assert that they got on well enough without such aids when they were children, and they seem to be quite unconscious of the weakness of such an argument. The question is not whether children can do well without the aid of objects, but whether they can do better with them. Our fathers did well enough in travelling on horse- back and in coaches, but we do better with our express trains. Children may be able to grasp abstract ideas, after sufficient time, without the aid of concrete examples. It 8005&? iv PREFACE. is certain, however, that they grasp these ideas more firmly and more quickly if they are led to them by easy steps through objects that can be seen and handled. Besides, the use of objects saves children from the bondage of rules. With 6 blocks they can learn to add 4 and 2, to subtract 4 from 6, to multiply 3 by 2, to divide 6 by 2, without suspecting the existence of the fearful rules to be found in our text-books of arithmetic. They can also be taught to find ^ of 6 or | of 6, without even hearing of the terms, fraction, numerator, or denominator. 2. A knowledge of the processes of arithmetic should be acquired by using small numbers ; and each number should be treated in all its variations before the next higher number is considered. In the treatment of each number we must rely upon the sight of the pupil, and not upon his hearing. Furthermore, we must rely upon his activity. He must do as well as see. Listless repetition of 4 and 3 are 7, or the sing-song 4 times 3 are 12, makes no impression upon him. The next day he is quite likely to tell you that 4 and 3 are 6. If he is required to put 4 pegs in one row of the counting-board and 3 in another row, and to learn in this way that 4 and 3 are 7, he will remember it. This method of teaching has the very great advantage of keepmg the child's interest in his work fully alive, and of giving to the study of arith- metic the peculiar distinction that the learner can discover for himself, in case of doubt, whether his answer to any question is right or wrong, and can find the true answer, if he has given a wrong one. 3. Repetition is to be regular and systematic, combined with suitable variation. It cannot be too strongly urged that the first requisite of good teaching is repetition, the second requisite is repeti- tion, and the third requisite is repetition. The interest of PREFACE. V the pupil must be kept up by varying the application of the question. To find the sum of 3 horses and 5 horses is not the same thing to the child as to find the sum of 3 tops and 5 tops. Hence a lesson may be ^iven as many times as may be necessary by properly varying the questions. A table of different things, given opposite the first page of this book, will be found of great use in suggesting a suitable variety of questions. Care must be exercised to have the variation of a kind to fix knowledge. To ask the number of 3 ducks and 4 ducks, of 3 times 4 ducks, and \ of 12 ducks, in succession, is a variation, to be sure, but of a kind to distract the child's mind, as he cannot quickly pass from one conception to the other. The questions in Part I. of this book are specimen questions, which it is expected the Teacher will supplement by a great number and variety of other questions. 4. Lessons should be short, answers required should be simple, and the power to deal with numbers in the abstract should be acquired through concrete examples by regular gradation. Number work should be discontinued the moment the pupil's attention flags. It is far better to divide the time daily allotted to arithmetic into two or more lessons. Only simple, direct answers should be required. Of course, if objects are named in the question, they should be named in the answer. The answer to 5 birds + 3 birds should be 8 birds, and not simply 8. A knowledge of numbers in the abstract is obtained only by a comparison of different things. The child learns the number 5, for instance, by seeing and handling 5 familiar objects, by observing number pictures of 5 on the black- board or on cardboard, by answering questions about 5 familiar but unseen objects, and lastly about 5 in the abstract. Vi PREFACE. 5. The child must not be required to read questions that are difficult for him to read, or to solve problems that are difficult for him to analyze. The intention is to put this book into the hands of young pupils, hut only for them, to copy and do the nmnerical exer- cises. The other examples, usually called clothed examples by way of distinction, must be read by the Teacher, and only the answers be required of pupils. No child can become interested or successful in arithmetic if his mind is dis- tracted between the reading of a problem and the numerical calculation required for its solution. He can learn the simple processes of arithmetic while quite young ; he can learn to be accurate and reasonably rapid in these processes ; he can learn to be neat and orderly in the arrangement of his work ; and his interest will constantly increase, pro- vided he is kejyt master of his field of operations. At this early stage he cannot be exercised in logical analysis, and it is a great mistake to put problems before him that require too great an exercise of the reasoning faculty. Later he will form the habit of close attention, learn the meaning of logical inference, and acquire the power of sustained and continuous thought. Arithmetic rightly taught furnishes the very essence of intellectual training, and deserves the name of "The Logic of the People." G. A. WENTWORTH. EXKTEK, N.H. TABLE FOR VARYING QUESTIONS. Animals. . . . Dog, Puppy, Cat. Kitten, Rabbit, Cow, Calf, Pig, Horse, Colt, Sheep. Lamb, Goat, Kid, Fox, Mouse, Squirrel, Monkey. Birds o Robin, Sparrow, Swallow, Canary, Parrot, Crow, Blue- bird, Kingbird, Hawk, Owl, Jay, Loon, Swan, Pigeon. Clothes .... Hat, Cap, Bonnet, Coat, Vest, Dress, Socks, Boots, Shoes, Collar, Cuffs, Slippers, Rubbers, Mittens, Gloves. Flowers .... Rose, Pink, Daisy, Pansy, Lily, Geranium, Violet, Poppy. Fowls Hen, Chicken, Turkey, Duck, Goose, Gosling. Fruits Apple, Pear, Quince, Orange, Lemon, Peach, Grape, Fig. Garden Peas, Beans, Corn, Potatoes, Carrots, Parsnips. House Room, Door, Window, Chair, Table, Picture, Carpet, Cup, Plate, Saucer, Fork, Knife, Spoon, Pitcher, Clock. Insects Fly, Spider, Bee, Hornet, Butterfly, Beetle, Cricket. School Desk, Slate, Pencil, Pen, Book, Paper, Chair. Smallwares. . Buttons, Pins, Needles, Spools of Thread. Store Tea, Coffee, Sugar, Starch, Soap, Candles, Matches, Eggs, Axe, Rake, Pail, Spade, Hoe, Saw, Nails. Toy-Store. . . Doll, Top, Ball, Whip, Basket, Marbles, Whistle. Tradesmen. . Baker, Butcher, Grocer, Milkman, Blacksmith. Trees Apple, Oak, Cherry, Plum, Ash, Birch, Beech. Vehicles . . . Train, Car, Coach, Hack, Buggy, Wagon, Gig, Sleigh, Sled, Barge, Bus. • • t J • Elementary Arithmetic. Part I. Part T. is intended as a guide to teachers in oral and blackboard work for children before they can read. After they can read, a rapid review will help fix their knowledge of simple arithmetical processes. THINGS NEEDED. 1. Objects for Counters. Such as cents, blocks, buttons, spools, pencils, nails, little tin plates, cups and saucers, inch-squares of paste- board, foot-rules, yard-sticks, a set of tin measures for liquids, a set of wooden measures for dry articles, and a set of weights. 2. A Counting-Board. This is of great assistance in teaching arith- metical processes with small numbers. It is simply a smooth board with 100 holes about an inch apart, arranged in 10 rows of 10 holes each. Nails or wooden pins can be used for counters. Another way of making the counting-board is to drive 100 nails ill 10 rows of 10 nails each through a piece of board, at suitable dis- tances from each other, until they project about an inch, and use spools for counters, slipping them on the ends of the nails. LESSON 1. THE NUMBER ONE. Show me one finger ; one block ; one button. How many suns do we see by day ? How many moons by night ? We write the figure 1 for one. Note. The introduction of tigures may be postponed until after the number six is taught. In that case some variation in the language will be required. 1 2 LESSON 2. THE NUMBER TWO. How many fingers are one finger and one finger ? Hold up two fingers ; two hands. We write the figure 2 for two. NoTK, Pictures of balls, cups, tops, blocks, etc., are introduced in places where it is expected the Teacher will show objects of some kind. How many balls are C) and C) ? How many cups are "Q and Q* ? How many dolls are 1 doll and 1 doll \ How many horses are 1 horse and 1 horse ? How many are 1 and 1 ? Here are two blocks, B 8- Take away jB. How many are left ? 1 apple from 2 apples leaves how many ? 1 from 2 leaves how many ? How many more pears are ^ ^ than ^ ? How many more dolls are 2 dolls than 1 doll ? How many rings must you put with O to have O O • How many apples must you put with 1 apple to have 2 apples ? Note. The following plan is recommended to the Teacher, for the number-work of Part I. : 1. Show objects, and secure the desired result from them. 2. Draw pictures of blocks, squares, etc., on the board, and obtain the same result from the pictures. 3. Ask the same question on familiar but unseen objects. 4. Finish with abstract numbers. The Teacher can vary the questions at pleasure by using different objects and different pictures^ and by using the table of familiar objects given opposite the first page. LESSON 3. 3 THE NUMBER THREE. How many fingers are tivo fingers and one finger ? Hold up three fingers. We write the figure 3 for three. * Copy each card below, and write under it the figure for the number of dots in the card : • • • •*• Count the dots in these cards from left to right. Count the dots from right to left. What number follows 1 ? What number follows 2 ? What number comes before 2 ? before 3 ? What number is between 1 and 3 ? * Copy these pictures, and write under each group the figure for the number in the group. AAA DDD ••• XXX OOO *** How many pears are ^ and ^ and ^ ? How many balls are ® and © and © ? How many dogs are 1 dog and 1 dog and 1 dog ? How many boys are 1 boy and 1 boy and 1 boy ? How many are 1 and 1 and 1 ? How many stars are >|< if and >)< ? *NoTE. In this case and in similar cases tlie Teacher should put the number pictures on the board, and then require the pupils to follow the directions given. The Teacher should require the attention of the pupils only a few minutes at a time. One of these "Lessons" will make a great many lessons for the children. 4 LESSON 4. How many apples are C5 ^^^ ^ C3 ^ How many pinks are 1 pink and 2 pinks ? How many are 1 and 2 ? 2 and 1 ? Here are three blocks, 11 B HP Take 1 block away, how many will be left ? Take 2 blocks away, how many will be left ? Take 3 blocks away, how many will be left ? How many more blocks are 11811 than 8 B ? How many more cows are 3 cows than 2 cows ? How many more figs are 3 figs than 1 fig ? How many blocks must be put with || to make S IB S ^ How many baskets must be put with ^^ ^^ to make ^^ ^^ ^^ ? How many plums must be put with 2 plums to make 3 plums ? How many plums must be put with 1 plum to make 3 plums ? James may take 1 block ; then 1 more ; and then 1 more. How many times has James taken 1 block ? How many blocks has he ? Then 3 times 1 block are how many blocks ? How many chairs are 3 times 1 chair ? Here are 3 apples, C^ C5 ®- How many boys can each have 1 apple ? Here are 3 dolls. How many girls can each have 1 doll ? How many 07ies in 3 ? LESSON 5. 6 THE NUMBER FOUR. Three dots and one dot make four dots. Here arefoitr' dots, • • • • We write the figure 4 for four. Copy each card below, and write under it the figure for the number of dots in the card : • • • • • • • • • • Count the dots in these cards from left to right. Count the dots from right to left. What number follows 2 ? What number follows 3 ? What number comes before 4 ? before 3 ? What number is between 1 and 3 ? 2 and 4 ? Copy these pictures, and write under each group the figure for the number in the group : **** oooo How many sides has this square Q ? How many legs has a horse ? a frog ? a cow ? How many stars are >)c >)c >)< and >(< ? How many rings are O O O ^^^id Q ? How many crosses are + and + + + '^ Ho\^ many eggs are o and o o O ? How many boys are 3 boys and 1 boy ? How many mice are 1 mouse and 3 mice ? How many are 3 and 1 ? 1 and 3 ? 6 LESSON 6. How many stars are >|c >|< and >|c >|< ? How many marks are // and // ? How many brooms are 2 brooms and 2 brooms ? How many are 2 and 2 ? Here are four blocks, 11111111 Cover one block. How many can you see ? Then 1 from 4 leaves how many ? Cover two blocks. How many can you see ? Then 2 from 4 leaves how many ? Cover three blocks. How many can you see ? Then 3 from 4 leaves how many ? Cover all four blocks. How many can you see ? Then 4 from 4 leaves how many ? How many more tops are <)< >|< >|< >(c and >)< ? How many tops are ! "iiJP f: ***:+: >^ ////// AAAAAA xxxxxx oooooo nnnnna o o o o o o Copy each card below, and write under it tlie figure for the number of dots in the card : • • • • • • Count these dots from left to right. Count these dots from right to left. What number follows 4 ? What number follows 5 ? What number comes before 4 ? before 6 ? be- fore 5 ? before 3 ? before 2 ? What number is between 4 and 6 ? 3 and 5 ? How many balls are C) © © © © and © ? How many tops are ^ and ^ |c >|< >|c >)< and >♦< >|< ? How many rings are O O and O O O O '^ How many balls are © © and <© © aiid © © ? How many kittens are 4 kittens and 2 kittens ? How many horses are 4 horses and 2 horses ? How many buns are 2 buns and 4 buns ? How many pies are 2 pies and 4 pies ? How many are 4 and 2 ? 2 and 4 ? How many crosses are ►!< ►t" ♦ and ^ ^ «{^ ? How many apples are 3 apples and 3 apples ? How many are 3 and 3 ? Here are 6 blocks, fp fp H ip Cover 1 block. How many can you see ? Then 1 from 6 leaves how many ? Cover 2 blocks. How many can you see ? Then 2 from 6 leaves how many ? Cover 3 blocks. How many can you see ? Then 3 from 6 leaves how many ? Cover 4 blocks. How many can you see ? Then 4 from 6 leaves how many ? Cover 5 blocks. How many can you see ? Then 5 from 6 leaves how many ? Cover 6 blocks. How many can you see ? Then 6 from 6 leaves how many ? How many more dots are •••••• than •••••? How many more stars are ****** than **** ? How many more crosses are x x x x x x than x x x ? How many more marks are 1 1 1 1 1 1 than / / ? How many more tops are ^^^^^ than ^ ? 14 LESSON 14. How many more chairs are 6 chairs than 5 chairs? How many more boxes are 6 boxes than 4 boxes ? How many more cars are 6 cars than 3 cars ? How many more dogs are 6 dogs than 2 dogs ? How many more pears are 6 pears than 1 pear ? How many marks must be put with 1 1 1 1 1 to make//////? How many tops must be put with < |c>|<>)<>|c >ic>|< >|<)|< Copy each card below, and write under it the figure for the number of dots in the card. • • • • • • • • • • • • • • • • • • •• • ••• • ••• •••• Count the dots in these cards from left to right. Count the dots from right to left. What number follows 5 ? follows 7 ? What number comes before 8 ? comes before 5 ? What number is between 5 and 7 ? 6 and 8 ? Copy, and add dots enough to make 8 dots in each card below : X • • • • • • • • • • • • • • • • • How many blocks are 5 and 3 ? 6 and 2 ? 4 and 3 ? 4 and 4 ? 2 and 5 ? 2 and 6 ? 7 and 1 ? How many dots must be put with 5 to make 8 ? with 2 to make 8 ? with 3 to make 8 ? with 4 to make 8 ? with 7 to make 8 ? with 6 to make 8 ? How many more dots are 8 than 6 ? 8 than 3 ? 8 than 4 ? 8 than 2 ? 8 than 1 ? 8 than 5 ? LESSON 27. 27 Here are 8 blocks, liJB SB IIS SO If you take away 2 blocks, how many will be left ? If you take away 6 blocks, how many will be left ? If you take away 5 blocks, how many will be left ? If you take away 3 blocks, how many will be left ? If you take away 4 blocks, how many will be left ? If you take away I block, how many will be left ? If you take away 7 blocks, how many will be left ? Ellen may take 2 blocks at a time for 4 times. How many blocks has she ? How many blocks, then, are 4 times 2 blocks ? How many cups are 4 times 2 cups ? How many pears are 4 times 2 pears ? Erwin may take 4 blocks, and then 4 more. How many times has he taken 4 blocks ? How many blocks has he ? How many blocks, then, are 2 times 4 blocks? How many plums are 2 times 4 plums ? How many apples are 2 times 4 apples ? How many are 4 times 2 ? How many are 2 times 4 ? How many 2's in 8 ? How many 4's in 8 ? How many are 3 times 2 ? How many are 2 times 3 ? How many 2's in 6 ? How many 3's in 6 ? How many oranges are one-half of 6 oranges ? How many apples are one-third of 6 apples ? When we take one-half of 6 oranges, into how many equal parts do we divide the 6 oranges ? When we take one-third of 6 apples, into how many eqital parts do we divide the 6 apples? 28 LESSON 28. Here are 8 blocks, Sip jBli iHi ||g How many times must Nora go to bring these blocks to me if she brings just 2 blocks each time ? Then 8 blocks divided by 2 blocks = 4 times. But if Nora divides the blocks into two equal parts, how many blocks will there be in each part ? Then 8 blocks divided by 2 = 4 blocks. Note, The Teacher must illustrate in many ways the two different meanings of Division. When the divisor is a mere number, as 2, 3, 4, etc., the meaning of division then is the separation of the given num- ber of things into 2, 3, 4, etc., equal parts, and the quotient will signify a number of things like the dividend. When the divisor is a number of things like the dividend, the quotient will signify the number of times the divisor is contained in the dividend ; that is, the number of times the divisor can be taken from the dividend. How many times are 2 cents contained in 6 cents ? How many times are 2 cents contained in 8 cents ? How many times are 4 cents contained in 8 cents ? How many times are 3 cents contained in 6 cents ? What is the answer for 8 cents divided by 4 cents ? 8 pears divided by 2 pears ? 6 peaches divided by 2 peaches ? 6 plums divided by 3 plums ? 8 chairs divided by 2 chairs ? 8 oranges divided by 4 oranges ? This sign -t- stands for the words divided by. 4 dogs -^ 2 = ? 6 pears -^ 3 = 4 hens ^ 2 = ? 8 cents -^ 2 = 6 figs ^2 = ? 8 tops ^ 2 = LESSON 29. 29 Divide these eight dots tlms, ••/••/••/•• Into how msiny equal partshsive you divided them ? If a number of things is divided into four equal parts, each part is one-fourth of the number. How many dots in one-fourth of 8 dots ? How many dots in two-fourths of 8 dots ? How many dots in three-fourths of 8 dots ? How many dots in four-fourths of 8 dots ? How many dots in one-half of 8 dots ? How many dots in two-halves of 8 dots ? Fourths are often called quarters. Find one-quarter of 4 dollars ; of 8 cents. Find two-quarters of 4 dollars ; of 8 cents. Find three-quarters of 4 dollars ; of 8 cents. Find four-quarters of 4 dollars ; of 8 cents. Find one-half of 4 dollars ; of 8 cents ; of 8 pigs. What part of 8 blocks are 4 blocks ? are 2 blocks ? What part of 8 cents are 2 cents ? are 4 cents ? What part of 6 cups are 3 cups ? are 2 cups ? Which is greater, one-half of 8 cents or one-fourth of 8 cents ? one-half of 8 cents or one-quarter of 8 cents ? Which is greater, one-half of 8 cents or two- fourths of 8 cents ? one-half of 8 cents or three- fourths of 8 cents ? Here is a new way of writing one-half, thus, ^ ; one-third, thus, i ; one-fourth, thus, i. We write two-thirds, thus, § ; two-fourths, thus, i ; three-quarters, thus, f . 30 LESSON 30. Read :i;i;i;i;|;l;1 Write in figures : one-half ; one-third : two- thirds ; one-fourth ; three-quarters. Oral and slate exercises : 5 + 2 = 7-2 = 7-5 = 5 + 3 = 8-5 = 8-3 = 6 + 2 = 8-6 = 8-2 = 7 + 1 = 8-1 = 8-7 = 2 + 2 = 3 + 3 = 4 + 4 = 4-2 = 6-3 = 8-4 = 2x2 = 2x3 = 3x2 = 4-^-2 = 6^3 = 6^2 = 2x4 = 4x2 = 8-^2 = 8^4 = hoi 4: = iof6 = iof 8 = ^of 6 = lof8 = iof8 = ORSKS. iof8 = §of 6 = COLTS H MULES. 4 + = 7. 5 + =8. 7- = 3 4 + = 8. 7+ =8. 8- = 4 4 + = 6. 6+ =8. 8- = 1 4x = 8. 3+ =8. 8- = 6 2x = 8. 4+ =6. 8^ = 4 3x = 6. 8- =5. 6^ = 3 2x = 6. 8- =7. 8^ = 2 2x = 4. 8- =3. 6-^ = 2 5x = 5. 8- =2. 4^ = 2 LESSON 31. 31 If a melon is cut into four equal parts, what is one of the parts called ? What are three of the parts called ? How many quarters of a melon does it take to make a whole melon ? How many quarters of a melon does it take to make half of a melon ? How many quarters of a dollar does it take to make a dollar ? to make half of a dollar ? How many quarters of a dollar does it take to make 2 dollars ? How many quarters of a dollar does it take to make one dollar and a half ? How many quarters of a dollar does it take to make one dollar and a quarter ? If Sbjpie is cut into quarters, and Mary, Tom, and Harry each have a quarter, how many quarters will be left for Alice ? If half of a pie is cut into two equal parts, what part of the ivhole pie is each piece ? What part of the whole pie are the two pieces together ? How many fourths make one-half ? 32 LESSON 32. Which one of these measures is the smallest ? How many gills will the pint measure hold ? * Then four gills make one pint. At 1 cent a gill, what will a pint of milk cost ? At 2 cents a gill, what will a pint of syrup cost? How many gills in a half pint of water ? How many pints will the quart measure hold ? * Then two pints make one quart. At 4 cents a pint, what will a quart of milk cost ? At 3 cents a pint, what will a quart of oil cost ? At 6 cents a quart, what will a pint of berries cost ? What part of a quart is 1 pint ? How many gills make 1 quart ? How many quarts will the gallon measure hold ? * Then four quarts make one gallon. How many quart cans are needed for a gallon of milk ? How many two-quart cans ? At 2 cents a quart, what will a gallon of skim- milk cost ? What will a half-gallon cost ? What part of a gallon is one quart ? What part of a gallon are 2 quarts ? are 3 quarts ? At 8 cents a gallon, what will a quart of skim- milk cost ? What will a pint cost ? Note.* Let the pupil discover by trial the answer to this question. LESSON 33. 33 THE NUMBER NINE. Eight dots and one dot make nine dots. Here are nine dots, ••• • •• We write the figure 9 for nine. Copy these pictures, and write under each group the figure for the number in the group : ///////// * * * * * * * * * X X X X X X X X X O0OOOOOOO Copy these cards, and add dots enough to make 9 dots in each card, and write 9 under each card : • • • • • • • • • • • • • • • • ••• •••• •••• •••• • • • • • How many dots are 3 and 6 ? 5 and 4 ? 7 and 2 ? 1 and 8 ? 3 and 3 ? 2 and 7 ? 4 and 3 ? 4 and 5 ? 4 and 4 ? 6 and 3 ? 8 and 1 ? 5 and 3 ? How many dots must you put with 5 to make 9 ? How many dots must you put with 2 to make 9 ? How many dots must you put with 3 to make 9 ? How many dots must you put with 4 to make 9 ? How many dots must you put with 6 to make 9 ? How many dots must you put with 8 to make 9 ? How many dots must you put with 7 to make 9 ? How many more dots are 9 than 7 ? 9 than 6 ? 9 than 3 ? 9 than 4 ? 9 than 5 ? 9 than 2 ? 34 LESSON 34. Here are 9 blocks, SfBH BBB 181811 If you take away 3 blocks, how many will be left ? If you take away 6 blocks, how many will be left ? If you take away 5 blocks, how many will be left ? If you take away 4 blocks, how many will be left ? If you take away 7 blocks, how many will be left ? If you take away 2 blocks, how many will be left ? If you take away 1 block, how many will be left ? If you take away 8 blocks, how many will be left ? How many are : 8 minus 2 ? 8 minus 6 ? 8 minus 5 ? 8 minus 4 ? 8 minus 7 ? 9 minus 3 ? 9 minus 6 ? 9 minus 7 ? 9 minus 8 ? 9 minus 2 ? 7 minus 4 ? 7 minus 6 ? 7 minus 3 ? 7 minus 2 ? 7 minus 5 ? 9 minus 4 ? 9 minus 5 ? 8 minus 3 ? 9 minus 1 ? 6 minus 4 ? Emma may take 3 blocks at a time for 3 times. How many blocks has Emma ? How many blocks, then, are 3 times 3 blocks ? How many peaches are 3 times 3 peaches ? How many roses are 3 times 3 roses ? How many lambs are 3 times 3 lambs ? How many are 3 times 3 ? Here are 9 pears, e^ C^ ^ ddd ddd How many times can you take 3 pears from the 9 ? How many groups of 3 pears each can you make from the 9 ? 9 pears divided by 3 pears gives how many times ? 9 pears divided by 3 gives how many pears ? How many pears are 3 of 9 pears ? LESSON 35. 36 Here are 9 dots, ••••••••• Put your pencil between the second and third dots. How many dots are on the left of the pen- cil ? How many on the right of the pencil ? Put your pencil between the fourth and fifth dots. How many dots are on the left of the pen- cil ? How many on the right of the pencil ? Put your pencil between the fifth and sixth dots. How many dots on the left ? How many dots on the right ? If a boy goes up 8 steps 2 steps at a time, how many steps will he touch ? John had 9 flags, some of them red and the rest blue. If 4 of them were red, how many were blue ? Alice had 9 cents, and spent 3 cents. How many had she left ? George sells a newspaper for 2 cents, and receives a five-cent piece in payment. How many cents must he give back ? A hen had 9 chickens, but a hawk caught 2. How many chickens were left ? Miriam has 8 cents, and Hattie 3 less than Miriam. How many cents has Hattie ? Harry has 3 tops, and Tom has 6 more than Harry. How many tops has Tom ? I wanted 8 stamps for my letters, and had only 3. How many more must I buy ? Tom had 6 apples, and gave away a of them. How many had he left ? 36 LESSON 36. Florence had 8 apples on plates, 2 on a plate. How many plates were there ? How many twos in eight ? Annie had 8 pears on plates, 4 on a plate. How many plates were there ? How many fours in eight ? Hattie had 9 peaches, 3 on a plate. How many plates were there ? How many threes in 9 ? 8^2= 8^4= 9^3= i of 8 = i of 8 = ^ of 9 = Mary had 3 rows of buttons, 3 in a row. How many buttons had she ? If one orange costs 3 cents, what will 2 oranges cost ? What will 3 oranges cost ? If a quart of milk costs 6 cents, what will a pint cost ? What will 3 pints cost ? If a pint of vinegar costs 4 cents, what will a gill cost ? What will a quart cost ? If a pint of water will fill 4 gill cups, how many gill cups will a quart of water fill ? If a quart of milk will fill 2 pint cups, how many pint cups will a gallon of milk fill ? How many quart measures will a one-gallon can of milk fill ? will a two-gallon can fill ? A cook had 9 eggs, and used h of them for a pudding. How many eggs were left ? Harry had 8 oranges. He gave one-quarter of them to his sister Mary, one-quarter of them to his sister Alice, and one-quarter of them to his sister Ellen. How many did he keep for himself ? LESSON 37. 3T Oral and slate exercises : FIGS. BELLS. APPLES. 2 + 7 = 9-2 = 9-7 = 4 + 5 = 9-4 = 9-5 = 3 + 5 = 8-3 = 8-5 = 3 + 6 = 9-3 = 9-6 = 5 + 2 = 7-5 = 7-2 = 4 + 3 = 7-3 = 7-4 = 1 + 8 = 9-6 = 9-8 = 4 + 2 = 6-4 = 6-2 = 4 + 4 = 6 - 3 = 8-4 = 3x3 = iof4 = iof6 = hoi 2 = J of 3 = Jof 6 = J of 9 = iof8 = iof8 = SLEDS. ORANGES. LAMBS. 4 = 1 + 6 = 4 + 8 = 3 + 4 = 2 + 7 = 1 + 8 = 4 + 4 = 3 + 7 = 4 + 8 = 5 + 5 = 1 + 7 = 5 + 9 = 1 + 5 = 3 + - 7 = 3 + 9 = 8 + 5 = 4 + 7 = 6 + 9 = 2 + 5 = 2 + 7 = 2 + 9 = 7 + 6 = 3 + 8=1 + 9 = 3 + 6 = 1 + 8 = 6 + 9 = 6 + 6 = 2 + 8 = 7 + 9 = 4 + 6 = 5 + 8 = 2 + 9 = 5 + Note. Besides copying and completing these and similar exercises, the oral drill must be kept up until every one of the class can give the answers promptly. 38 LESSON 38. THE FIGURE ZERO. The figure is called zero, naught, or cipher. The figure means none to count. Four roses grew on a bush ; 2 were picked ; and then 2 more. Write the figure for the number left. Write the figure for the number of blocks left when you take away 5 blocks from 5 blocks. Write the figure for the number of oranges left if you had 4 oranges and gave them all away. Review of figures : You have now had all the figures used for writ- ing numbers, and have learned the meaning of each separate figure. Thus : The figure 1 is written for One. The figure 2 is written for Two. The figure 3 is written for Three. The figure 4 is written for Four. The figure 5 is written for Five. The figure 6 is written for Six. The figure 7 is written for Seven. The figure 8 is written for Eight. The figure 9 is written for Nine. The figure O is written for None. Draw a square, and write under it : then an- other square, and write 1 under it ; and so on to 9. Put in each square the number of dots indicated by the figure written under it. LESSON 39. 39 THE NUMBER TEN. Nine dots and one dot make ten dots. Here are ten dots, 2 J J J J We write the figures 10 for ten. I Ten ones make 1 ten. Draw these number pictures of ten, and write under each division the figure for the number of dots in the division : • • • • • • • • • • .... • • • • • • • • • • • • • • • • 9 + 1 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Look at these number cards, and answer the fol- lowing questions : How many must you add to 9 to make 10 ? to 8 to make 10 ? to 7 to make 10 ? to 6 to make 10 ? to 5 to make 10 ? to 4 to make 10 ? to 3 to make 10 ? to 2 to make 10 ? to 1 to make 10 ? How many more are 10 than 2 ? than 4 ? than 6 ? than 8 ? than 3 ? than 5 ? than 7 ? than 9 ? 40 LESSON 40. John found 3 eggs on Thursday, and 4 on Friday. How many eggs did he find ? There are 7 days in a week. When 2 are gone, how many are left ? There were 7 red roses on a rose bush, and 5 white roses on another bush. How many more red roses were there than white roses ? Susan had 3 apples, and James had 5 apples. How many apples had Susan and James together ? Alice had 8 dolls, and gave away 3 of them. How many had she left ? If a window has 4 panes of glass, how many panes of glass in 2 windows ? How many feet have 2 dogs ? 4 hens ? If you take 2 apples 4 times from a dish that has 8 apples in it, how many apples will be left ? There were 8 rooms in a house, half of them in the first story, and half in the second story. How many were there in each story ? John had 8 peaches, and gave aw^ay a quarter of them. How many peaches did he give away ? Frank bought 9 marbles, and gave away 4 of them. How many had he left ? There are 9 apples in a dish. How many boys can have 3 apples apiece ? At 3 cents apiece, how many oranges can you buy for 6 cents ? for 9 cents ? At 2 cents apiece, how many pears can you buy for 9 cents, and how many cents will be left ? i Part II. LESSON 1. 10 a 1 1 2 Look at the number picture on the right. What do you see over the 2 ? 2 ones. Over the 1 ? 1 ten. Then 12 means one ten and two ones. Look at the middle number. What do you see over the 1 at the right ? What do you see over the 1 at the left ? Then 1 1 means one ten and one. Look at the number picture on the left. What do you see over the ? What do you see over the 1 ? Then 10 means one ten and no ones. Note. The Teacher should proceed in Part II. as in Part I. ; show- ing objects, drawing number pictures on the board, and reading all the clothed exercises for the pupils. Pupils should have the books simply to copy and solve the numerical exercises. 41 42 LESSON 2, John may go to the counting-board. How many holes are there in the top row ? Put one nail in one of the holes of the top row. How many holes are left in the row ? Then how many must we add to 1 to make 10 ? Put in one more nail. How many nails are there now ? How many holes are left in the row ? Then how many must we add to 2 to make 10 ? Put in one more nail. How many nails are there now ? How many holes are left in the row ? How many must we add to 3 to make 10 ? Put in one more nail. How many nails are there now ? How many holes are left in the row ? How many must we add to 4 to make 10 ? Put in one more nail. How many nails in the row ? How many holes are left in the row ? How many must we add to 5 to make 10 ? Put in one more nail. How many nails in the row ? How many holes' are left in the row ? How many must we add to 6 to make 10 ? Put in one more nail. How many nails in the row ? How many holes are left in the row ? How many must we add to 7 to make 10 ? Put in one more nail. How many nails are there now ? How many holes are left in the row ? How many must we add to 8 to make 10 ? Put in one more nail. How many nails now in the row ? How many holes are left in the row ? How many must we add to 9 to make 10 ? LESSON 3. 43 Here are ten rings, OOOOOOOOOO I will put the end of the pointer between the second and third rings. How many rings on the left of the pointer ? How many rings on the right of the pointer ? How many are 2 and 8 ? How many are 10 less 2 ? 10 less 8 ? I will put the end of the pointer between the third and fourth rings. How many rings on the left of the pointer ? How many rings on the right of the pointer ? How many are 3 and 7 ? How many are 10 less 3 ? 10 less 7 ? , I will put the end of the pointer between the fourth and fifth rings. How many rings on the left of the pointer ? How many rings on the right of the pointer ? How many are 4 and 6 ? How many are 10 less 4 ? 10 less 6 ? I will put the end of the pointer between the fifth and sixth rings. How many rings on the left of the pointer ? How many rings on the right of the pointer ? How many are 5 and 5 ? How many are 10 less 5 ? How many are 10 less 1 ? 10 less 9 ? Note. Practise this exercise, putting the pointer in different posi- tions, until the pupils can readily name any two parts of 10, and the part left when one part is taken from 10. 44 LESSON 4. In each of the number pictures below, the bundle is a bundle of ten. Write the figures for the number in each case. I II III How many figures do you write for each number ? What does the figure on the left show ? What does the figure on the right show ? What is the number 11 called ? Eleven. What is the number 12 called ? Twelve. Note. It is absolutely necessary for the Teacher to show bundles of ten things (pencils, sticks, etc.) kept distinct by rubber bands, in order to show the compositions of numbers containing tens and ones ; and to show also that the counting of units of tens is exactly the same as the counting of single units. Oral and slate exercises : 8 + ?= 10. 6 + ? = 10. 5 + ? = 10. 1 + ?= 10. 3 + ? = 10. 7 + ? = 10. 2 + ? = 10. 4 + ?= 10. 9 + ?= 10. 5=1 + ? 5 = 2 + ? 4 = 2 + ? 4 = 1 + ? 6 = 1 + ? 6 = 3 + ? 6 = 4 + ? 7 = 6 + ? 7 = 4 + ? 7 = 5 + ? 7 = 3 + ? 8 = 2 + ? 8 = 3 + ? 8 = 4 + ? 9 = 3 + ? 9 = 5 + ? 9 = 2 + ? 9 = 8 + ? I Note. Continue these oral and slate exercises until every pupil can separate 10 into any two parts, and see at a glance the number to be added to any part to make 10 ; and also see the part required when] a number less than 10 and one of its parts is given. LESSON 5. 46 There were 5 birds in a tree, and 5 more flew in the tree. How many birds were in the tree then ? A teamster has 5 teams of 2 horses each. How many horses has he ? Harry brought in some wood twice. The first time he brought in 4 sticks, and the next time 5 sticks. How many sticks did he bring in ? There are 4 plates on each side of a table, and one plate at each end. How many plates in all ? If a table is 3 feet long and 2 feet wide, how many feet long are the 2 sides and 2 ends together ? A farmer brought 10 bushels of potatoes to put into his cellar. After he had put in 6 bushels, how many more bushels remained to be put in ? Daisy has 10 chickens. Five are white, and the rest brown. How many are brown ? A room is 10 feet high, and the top of the door is 7 feet from the floor. How many feet from the top of the door is the ceiling ? There were 10 saucers and only 8 cups. How many saucers were without cups ? I have 10 letters to mail, and only 1 stamp. How many stamps must I buy ? If a boy has 10 apples, and eats 2 apples a day, how many days will they last ? If a boy has 10 cents, and spends half of them, how many will he have left ? Note, These and similar questions can be made more intelligible and interesting by illustrating them with suitable number pictures. 46 LESSON 6. B 11 ELEVEN • • « • • t • • • — • • • • • • • • • • • • 12 TWELVE 13 THIRTEEN 14 FOURTEEN 15 FIFTEEN How many dots are 10 dots and 1 dot ? 10 dots and 2 dots ? 10 dots and 3 dots? 10 dots and 4 dots ? 10 dots and 5 dots ? How many sheep are 10 sheep and 1 sheep ? 10 sheep and 2 sheep ? 10 sheep and 3 sheep ? 10 sheep and 4 sheep ? 10 sheep and 5 sheep ? If you have 10 oranges, how many more must you buy to have 13 ? to have 14 ? How many blocks must you add to 10 blocks to have 15 ? to have 12 ? to have 11 ? How many twos are there in 8 ? in 10 ? Oral and slate exercises : 10 + 1 = ? 10 + 3 = ? 10 + 5 = ? 10 + 2 = ? 10 + 4 = ? 11 - 1 = ? 13 - 3 = ? 15-5 = ? 12-2 = ? 14 - 4 = ? CHICKKNS. 11-10 = ? 13 - 10 = ? 15-10 = ? 12 - 10 = ? 14 - 10 = ? LESSON 7. 47 • • • • 9_ 9 • • • _?. ^ JL -^ • • •* *_?. • ♦ • •• _?_-?_ — — — — • • •• •• •• 9^ 9_ • • •• •• •• • 9_ • • •• •• •• •• • • •• •• •• •• ZH S^ SB BS — k 16 17 18 19 20 SIXTEEN SEVENTEEN EIGHTEEN NINETEEN TWENTY How many dots are 10 dots and 6 dots ? 10 dots and 7 dots ? 10 dots and 8 dots ? 10 dots and 9 dots ? 10 dots and 10 dots ? If you have 10 cards, how many more must you have to make 16 cards ? to make 17 cards ? How many marbles must you put with 10 mar- bles to make 19 marbles ? to make 18 marbles ? How many cents have you if you have 10 cents, 5 cents, and 1 cent ? How many cents have you if you have ten cents, five cents, and two cents ? Oral and slate exercises : CROWS. 10 + 7 = ? 10+ 9 = ? 10 + 6 = ? 10+ 8 = ? 10 + 10 = ? 17- 7 = ? 19- 9 = ? 16 - 6 = ? 18- 8 = ? 20 - 10 = ? 17 - 10 =^ ? 19 - 10 = ? 16 - 10 = ? 18 - 10 = ? 15-10 = ? 48 LESSON 8. Write under the number pictures below the fig- ures for the number, and the name of the number. II III nil mil I In which place do we write the ones ? the tens ? Note. Tupils should be made familiar with the dime and all coins of smaller value ; and with the ten-cent postage stamp, and all stamps of smaller value. Annie has 2 five-cent pieces and a one-cent piece. How much money has Annie ? 2x5 + 1 = ? What two pieces of money together make 11 cents ? 10 -f- 1 -= ? What two pieces of money together make 12 cents ? 10 + 2 - ? What two pieces of money together make 15 cents ? 10 + 5 = ? Alice has 2 five-cent pieces and a two-cent piece. How much money has Alice ? 2x5 + 2 = ? Harry has 3 five-cent pieces. How much money has Harry ? 5 + 5 + 5 - ? What five pieces of money together make 14 cents ? 5 + 5 + 2 + 1 + 1-? What three pieces of money together make 13 cents ? 10 + 2 + 1 -- ? What four pieces of money together make 13 cents ? 5 + 5 + 2 + 1 = ? What four pieces of money together make 14 cents ? 5 + 5 + 2 + 2 = ? I LESSON 9. 49 Write under the number pictures below the fig- ures for the number, and the name of the number. In which place do we write the ones ? the tens ? How many tens and how many ones are there in 16? in 17? in 18? in 19? How many ones must we add to 9 ones to make 1 ten f to 7 ones to make 1 ten f to 6 ones to make 1 ten f to 8 ones to make 1 ten f How many tens and how many ones in 20 ? What does the figure mean in the number 20 ? How many twos in 10? XX XX XX XX XX How many fives in 10 ? XXXXX XXXXX How many more twos in 16 than in 10 ? How many twos in 16 ? How many more twos in 18 than in 10 ? How many twos in 18 ? How many twos in 12 ? How many more ones in 19 than in 17 ? How many more ones in 19 than in 16 ? How many more ones in 19 than in 10 ? How many more ones in 18 than in 10 ? How many more ones in 16 than in 10 ? How many more ones in 17 than in 10 ? How many more ones in 18 than in 16 ? How many more ones in 15 than in 10 ? How many more ones in 15 than in 12 ? 50 LESSON 10. Oral and slate exercises : SHEEP. LAMBS. MEN. 12 + 2 = ? 11 + 2 = ? 13 + 3 = ? 11 + 4 = ? 15 + 2 = ? 14 + 3 = ? 14 + 5 = ? 13 + 4 = ? 12 + 6 = ? 16 + 3 = ? 14 + 2 = ? 17 + 1 = ? 12 + 4 = ? 12 + 5 = ? 11 + 8 = ? 13 + 6 = ? 11 + 7 = ? 15 + 3 = ? 15 + 4 = ? 17 + 2 = ? 18 + 1 = ? 12 + 3 -- ? 11 + 3 12 + 7 -= ? 11 + 6 = ? 14 + 4 17 - 1 -= ? 15 - 3 - ? 14 - 2 = ? 13 - 2 -- ? 19 - 4 - ? 18 - 6 - ? 19 - 5 = ? 19 - 7 = ? 16 - 5 = ? 16 - 2 = ? 14 - 2 = ? 19 - 4 - ? 19 - 6 - ? 17 - 3 - ? 18 - 4 = ? 14 - 3 = ? 19 - 2 -^ ? 16 - 4 -= ? 15 -2-? 17-4==? 19-8 = ? 17 - 5 = ? 18 - 5 - ? 17 - 2 = ? 16-3 = ? 19-3 = ? 18~1 = ? Note. The above exercises, and similar exercises, should be worked aloud by each one of the class in turn ; and on blocks of paper or slates. Thus, the first example should be worked at first, as follows : 12 sheep and 2 sheep are 14 sheep. If a child makes a mistake, let the child himself correct it by the counting-board or by dots on the blackboacd. Care should be taken to have him clearly see that these operations are confined to the ones. Thus, in adding 2 to 12, let him fill the top row of holes in the coinit- ing-board with nails, and 2 holes more in the next row for the 12, tlien put two more nails in the row with the 2 nails already there. He will then see that 12 + 2 = 10 + 4 = 14. A LESSON 11. 51 How many cents are 12 cents and 5 cents ? How many days are 1 week and 3 days ? How many inches are 11 inches and 7 inches ? How many boys are 13 boys and 6 boys ? How many pinks are 15 pinks and 3 pinks ? One rose-bush has 17 roses, and another only 2. How many have both bushes together ? How many more has one bush than the other ? A farmer has 16 cows in the barn, and 3 in the stable. How many cows has he in all ? How many more in the barn than in the stable ? A man has 14 work horses and 2 driving horses. How many horses has he ? How many more work horses than driving horses ? James found 15 eggs in one nest, and 5 in an- other. How many eggs did he find in both nests ? The number 12 is sometimes called a dozen. When we say a dozen eggs, we mean tivelve eggs. Frank started with a dozen eggs from the barn, Ijut dropped and broke two before he reached the house. How many did he carry into the house ? John has a dozen chickens of one kind, and 6 of another kind. How many has he of both kinds ? Harry had a dozen oranges, but he gave away ten. How many had he left ? A watch dealer had 3 dozen gold watches the week before Christmas ; the day after Christmas he had 1 dozen left. How many dozen had he sold ? How many watches had he left ? 52 LESSON 12. Oral and slate exercises : CROWS. 9 + 3 - 10 + 2 - 9 + 8 -= 10 + ? = 9 + 4-10+ ? = 9 + 6 = 10+ ?- 9 + 6 = 10+ ? = 9 + 7-10+ ? = 9 + 2 - 10 + ? - 9 + 9 -^ 10 + ? = 8 + 3 -^ 10 + ? = 8 + 5 -^ 10 + ? - 8 + 7 = 10 + ? = 8 + 6 - 10 + ? = 8 + 4 = 10+ ? = 8 + 8 = 10 + ? = 8 + 9 = 10 + ? = 7 + 5 = 10 + ? = Note. When the sum of the ones is more than ten, we proceed as follows : Suppose we have to add 7 to 8. Call upon one of the children to put 8 nails in the top row of the counting-board, and 7 in the second row, and then ask. How many nails are there in the top row ? How many holes are left ? How many nails must we put in the top row to make ten ? Let him take 2 nails from the 7 in the sec- ond row and put in the holes left in the top row. How many nails now in the top row ? How many in the second row ? Then 8 and 7 are 10 and 5, or 15. Continue this practice, a few minutes at a time, until the children can dispense with the counting-board ; then continue it with the inter- mediate step until they can dispense with that step, and name instantly the sum of any two numbers that are each less than ten. 'i'his method may seem tedious, but it is the only method that gives complete mastery of addition. L2. ROBINS. 7 + 7 - 10 + 4 = 14 ? 7 + 4 = 10+ ? = ? ? 7 + 8 = 10 + ? = ? ? 6 + 6 = 10+ ? = ? ? 6 + 5 = 10+ ? = ? ? 6 + 7 = 10+ ? = ? ? 6 + 9 = 10 + ? = ? ? 6 + 8 = 10 + ? = ? ? 5 + 9 = 10 + ? = ? ? 5 + 7 = 10 + ? = ? ? 5 + 8 = 10+ ? = ? ? 6 + 6 = 10 + ? = ? ? 4 + 8 = 10+ ? = ? ? 4 + 7 = 10 + ? = ? ? 4 + 9 = 10 + ? = ? ? 3 + 8 = 10 + ? = ? LESSON 13. 53 Oral and slate exercises SPARROWS. 8 + 6 - 10 + ? = ? 7 + 4 == 10 + ? = ? 5 + 8 = 10 + ? = ? 8 + 7 =- 10 + ? = ? 9 + 3 - 10 + ? = ? 8 + 5 - 10 + ? = ? 6 + 5 = 10 + ? = ? 5 + 7 = 10 + ? = ? 4 + 9 = 10 + ? = ? 5 + 8 = 10 + ? = ? 7 + 6 = 10 + ? = ? 7 + 9 = 10 + ? = ? KINGBIRDS. 4 + 7 = 10 + ? = ? 8 + 4 = 10 + ? = ? 7 + 8 = 10 + ? = ? 2 + 9 = 10 + ? = ? 9 + 4 = 10+? = ? 9 + 9 = 10 + ? = ? 8 + 8 = 10 + ? = ? 7 + 7 = 10 + ? = ? 6 + 6 = 10 + ? = ? 8 + 9 = 10 + ? = ? 3 + 9 = 10 + ? = ? 2 + 9 = 10 + ? = ? 9 + 9 = ? 9 + 7 = ? 9 + 4 = ? 9 + 2 = ? 9 + 6 = ? 9 + 3 = ? 9 + 5 = ? 9 + 8 = ? 8 + 3 = ? 8 + 5 = ? 8 + 4 = ? 8 + 7 = ? 8 + 6 = ? 8 + 9^? 8 + 8 = ? 7 + 3 = ? 7 + 7 = ? 7 + 5 = ? 7 + 8 = ? 7 + 6 = ? 7 + 4 = ? 7 + 9 = ? 6 + 6 = ? 6 + 9 = ? 6 + 7 = ? 6 + 5 = ? CHICKENS. 6 + 8 = ? 6 + 4 = ? 5 + 5 = ? 5 + 8 = ? 5 + 6 = ? 5+7 = ? 5+9 = ? 4 + 7 = ? 4 + 9 = ? 4 + 8 = ? 3 + 8 = ? 3 + 9 = ? 2 + 9 = ? 54 LESSON 14, How many days are 1 week and 4 days ? 1 week and 5 days ? 1 week and 6 days ? 2 weeks ? John has 9 cents, and Mary 4 cents. How many have both ? How many are 9 and 4 ? 4 and 9 ? If one lamp is worth 6 dollars, and another 5 dollars, how much are both worth ? If there are 8 boys in one class, and 5 in another, how many are there in both classes ? If there are 6 boys in one class, and 7 in another, how many are there in both classes ? A farmer sold 6 sheep to one man, and 8 to an- other. How many sheep did he sell ? A farmer has 9 cows in one pasture, and 5 in another. How many cows has he in the two past- ures ? How many are 9 and 5 ? 5 and 9 ? Tom has two hens, one white, and the other black. The white hen has 9 chickens, and the black hen has 8 chickens. How many chickens have both hens ? How many are 9 and 8 ? 8 and 9? James saw 9 crows on the ground, and 7 more flying about. How many crows did he see ? There are 8 blocks in one pile, and 8 in another pile. How many blocks are there in both piles ? Tliere were 9 chickens roosting on one pole, and 6 on another pole. How many chickens were roost- ing on both poles ? How many are 9 and 6 ? If Harry paid 8 cents for his block of paper, and Ernest paid 7 cents for his, how many cents did the two blocks cost ? LESSON 15. 65 Oral and slate exercises : CHAIRS. BOXES. - 2 - 10 - 1 =- 9. 13 7 -^ 10 - 4 - 6. 3 - 10 - ? -= ? 13 - 8 = 10 - ? = ? - 4 = 10 - ? = ? 13 - 5 = 10 - ? = ? - 5 - 10 - ? - ? 14 - 6 - 10 - ? - ? - 6 - 10 - ? - ? 14 - 6 - 10 - ? = ? - 7 -^ 10 - ? = ? 14 - 7 = 10 - ? - ? -8-10-?-? 14 -8 = 10-?=? - 9 - 10 - ? - ? 14 - 9 = 10 - ? = ? 1 12 3 - 10 - ? - ? 15 - 6 - 10 - ? = ? 12 - 4 - 10 - ? - ? 15 - 7 = 10 - ? = ? 12 - 5 - 10 - ? - ? 15 - 8 = 10 - ? = ? 12 - 6 - 10 - ? - ? 15 - 9 = 10 - ? - ? 12 - 7 - 10 - ? - ? 16 - 7 = 10 - ? = ? 12 - 8 = 10 - ? == ? 16 - 8 = 10 - ? - ? 12 - 9 - 10 - ? -- ? 16 - 9 -= 10 - ? -^ ? 13 - 4 = 10 - ? - ? 17 - 8 - 10 - ? = ? 13 - 5 = 10 - ? - ? 17 - 9 - 10 - ? = ? 13 - 6 - 10 - ? = ? 18 - 9 - 10 - ? = ? Note. In Subtraction, the pupils may use the knowledge acquired in Addition. Thus, if 8 is to be subtracted from 15, the answer sought is obtained by discovering the number that must be added to 8 to make 15. But it is better to keep Subtraction distinct from Addition, and at this stage to take two steps, just as we did in Addition. Suppose we are required to take 8 from 15. Let one of the children put 10 nails in the top row of holes in the counting-board, and 5 in the next row below. We now ask the following questions : How many nails must we take away to leave 10 ? How many more than 5 are we required to take away ? And 3 nails from 10 nails leave ? Then 15-8 = 10-3 = 7. 56 LESSON 16. Oral and slate exercises : BUTTONS. NEEDLES. PINS. 12 - 3 - 14-8 = 11-6 13 - 6 - 12-6 = 15-7 11-5 = 11-3 = 13-4 15 - 9 = 16-8 = 13-7 16-7 = 13-9 = 12-5 13-8 = 15-8 = 11-8 11-7 = 17-9 = 14-7 12-9 = 11-2 = 12-8 15-6 = 12-7 = 16-9 14-6 = 14-5 = 18-9 11-4 = 12-4 = 13-5 11-9 = 16-8 = 14-9 If you pay 17 dollars for a table, and 8 dollars for a chair, how many dollars more do you pay for the table than for the chair ? John has 16 marbles, and James has 9. How many more has John than James ? Take 1 week from 14 days. How many days are left ? How many weeks are left ? I have 17 miles to walk. After I have walked 9 miles, how many more have I to walk ? A milkman has 16 cows. If he sells 7, how many will be left ? A farmer had 16 turkeys, but a fox carried off 8 of them. How many were left for the farmer ? LESSON 17. 67 Alice has 15 chickens. If 6 are black, and the rest are white, how many are white ? If Ernest had 9 marbles more, he would have 15. How many marbles has he ? The first train in the morning had 7 cars, and the second train had 15 cars. How many more cars did the second train have than the first train ? Mary picked 15 quarts of blueberries, and George picked 8 quarts. How many more quarts did Mary pick than George ? George caught 14 trout, and his brother caught 8 trout. How many more did George catch than his brother ? Henry had 14 cents, but spent 6 cents for lem- ons. How many cents had he left ? Miriam is 14 years old. How old was she 7 years ago ? 9 years ago ? Lucy's father and mother together gave her 14 cents. Her father gave her 9 cents. How many cents did her mother give her ? There were 14 rolls on the table before break- fast, and only 5 after breakfast. How many rolls were eaten at breakfast ? Frank had 13 cents. He had one five-cent piece, and the rest one-cent pieces. How many one-cent pieces did he have ? Mary's mother had 13 eggs. She used 4 for a pudding. How many were left ? How many are 14 minus 6 ? 15 minus 8 ? ^^ LESSON 18. I sent by mail two books, and paid 13 cents postage. The postage for one was 8 cents. How much was the postage for the other ? A farmer had 13 lambs. How many had he left if he sold 6 ? if he sold 7 ? Tom had 13 oranges, but he gave away 9. How many had he left? Edna's class numbers 12. If 5 are boys, how many are girls ? Harry had 12 papers to sell. After he had sold 9, how many had he to sell ? Lucy had 12 plums, and Alice had 4. How many more had Lucy than Alice ? In two pods there were 12 peas. If there were 6 in one pod, how many were there in the other ? Erwin found a nest of 12 eggs. If he carried 3 of the eggs into the house, how many were left ? Fred had 12 cents. How many had he left if he spent 8 cents ? if he spent 7 cents ? Jane bought 11 yards of ribbon, and used 6 yards. How many yards had she left ? Lucy is 11 years old, and Mary 7. How many years older is Lucy than Mary ? Frank bought 3 oranges for 9 cents, and sold them for 11 cents. How many cents did he gain ? Grace had 11 cents, and paid 5 cents for car-fare. How many cents had she left ? There were 11 saucers on the table, but 3 had no cups. How many had cups ? LESSON 19. TWELVK. 12. (o) (ft) iiii III Look at the number picture marked (a). How many dots are there in each row ? How many rows are there ? How many dots in the three rows ? Then how many are 3 times 4 dots ? A line of dots running up and down the page is called a column. How many dots in each column ? How many columns are there ? How many dots in the four columns ? Then how many are 4 times 3 dots ? How many 3's in 12 ? How many 4's in 12 ? Look at the number picture marked (b). How many dots are there in each row ? How many rows are there ? How many dots in the two rows ? Then how many are 2 times 6 dots ? How many dots are there in each column ? How many columns are there ? How many dots in the six columns ? Then how many are 6 times 2 dots ? How many 2's in 12 ? How many 6's in 12 ? Find i of 12 ; i of 12 ; i of 12 ; * of 12. 12^2 = ? 12^3 = ? 12^4 = ? 12^6-? 2x3 = ? 2x4 = ? 2x5 = ? 2x6 = ? 3x3 = ? 3x4 = ? 4x3 = ? 6x2 = ? 60 LESSON 20. THE FOOT-RULE AND THE YARD-STICK. Measure the yard-stick with the foot-rule. How many feet long is the yard-stick ? A carpet is a yard wide. How many feet wide is the carpet ? How many yards in 3 feet ? in 6 feet ? in 9 feet ? in 12 feet ? How many feet in 2 yards ? in 3 yards ? in 4 yards ? in i of a yard ? If the distance between two windows is 3 yards, how many feet is the distance ? Your foot-rule is marked off into 12 divisions. What is each division called ? How many inches, then, make a foot ? How many inches in ^ a foot ? i of a foot ? i of a foot ? f of a foot ? I of a foot ? What part of a foot are 6 inches ? 4 inches ? How many more inches are 10 inches than 6 inches ? than 5 inches ? than 3 inches ? than 7 inches ? than 2 inches ? Remember : 12 inches make 1 foot. 3 feet make 1 yard. If there are 8 yards of wall-paper in a roll, how many yards are there in i of a roll ? If it takes 2 yards of ribbon to trim a hat, how many yards will it take to trim 6 hats ? Edna's mother had 8 yards of velvet. She used i of her velvet. How many yards were left ? LESSON 21. 61 Measure with the foot rule :" 1. The length of a page of your reader. 2. The length of the top of your desk. 3. The length of a pane of glass in the window. 4. The width of a pane of glass in the window. 5. The length of your slate. 6. The width of your slate. 7. The length of the face of the blackboard. 8. The width of the face of the blackboard. 9. The length of a page of your copybook. Measure with the yard stick : 10. The width of the floor of this room. 11. The length of the floor of this room. Draw on the board a line 12 inches long, as nearly as you can without measuring. Measure this line, and tell me how long it really is. Draw a line 6 inches long, as nearly as you can. Measure the line, and tell me how long it really is. Draw a square, one inch on each side. Draw a square with its sides 2 inches long, and divide it into four smaller squares. How many square inches in a square, the sides of which are 2 inches long ? How many square inches in a square, the sides of which are 3 inches long ? Draw a square with its sides 3 inches long, and divide it into nine smaller squares. Note. The Teacher should give exercises in measuring daily. 62 LESSON 22. FOURTEEN. 14. (a) (6) I • • Look at the number picture marked (a). How many dots are there in each row ? How many rows are there ? How many dots in the two rows together ? How many dots, then, are 2 times 7 dots ? How many cokimns are there of 2 dots each ? How many dots in the seven columns ? How many dots, then, are 7 times 2 dots ? If you divide 14 dots into two equal numbers, how many will there be in each number ? 14^2 = ? iofl4--? 2x7-? 7x2 = ? Count by 2's to 14. How many 7's in 14 ? How many skates are 7 pairs of skates ? Alice has 7 two-cent pieces. How many apples at one cent each can she buy ? How many weeks do 1 4 days make ? 2x2-? 2x5 = ? 4^2 = ? 10-^5 = ? 2x3 = ? 2x6 = ? 6-^3 = ? 12 ^ 2 = ? 2x4 = ? 2x7 = ? 8^2 = ? 14^7-? 8 + 4 = ? 6 + 5 = ? 9 + 5 = ? 8 + 9 = ? 9 + 6 = ? 7 + 6 = ? 5 + 7 = ? 8 + 5 = ? 7 + 8 = ? 9 + 4 = ? 6 + 9 = ? 7 + 9 = ? 14 ~ 8 = ? 17-8 = ? 14 - 5 = ? 16 - 7 = ? 15-7 = ? 14-9 = ? 13-6 = ? 13 -7-? 16-9 = ? 13 - 5 = ? 12-7 = ? 18 - 9 = ? LESSON 23. 63 FIFTEEN. 16. (a) (b) • • • Look at the number picture marked (a). How many dots are there in each row ? How many rows of dots are there ? How many dots in the three rows ? How many dots, then, are 3 times 5 dots ? How many dots are there in each cohimn of dots ? How many columns of dots are there ? How many dots in the five columns ? How many dots, then, are 5 times 3 dots ? Look at the number picture marked (h). How many sets of 5 each in 15 ? Count by 3's to 15. Count by 5's to 15. 15^5 = ? 15^3-? •iofl5--? iofl5-? If one orange cost 3 cents, how many cents will 5 oranges cost ? will 4 oranges cost ? How many pencils at a cent each can you buy with 3 five-cent pieces ? with 2 five-cent pieces ? Find i of 15 oranges ; i of 15 oranges. Emily has 15 cents in five-cent pieces. How many five-cent pieces has she ? How many feet long is a string that is 5 yards long ? 4 yards long ? 3 yards long ? 2 yards long? What part of 15 pears are 5 pears ? 3 pears ? How many inches are there in 1 foot and i of a foot ? in 1 foot and e of a foot ? 64 LESSON 24. SIXTEEN. 16. (a) (6) • • • • • • • • • • • • • • • • I Look at the number picture marked (a). How many dots are there in each row ? How many rows are there ? How many dots in the four rows ? How many dots, then, are 4 times 4 dots ? Look at the number picture marked (b). How many dots are there in each row ? How many rows are there ? How many dots in the two rows ? How many dots, then, are 2 times 8 dots ? How many columns of 2 dots each are there ? How many dots in the eight columns ? How many dots, then, are 8 times 2 dots ? Count by 2's to 16. Count by 4's to 16. How many 2's in 16 ? How many 4's in 16 ? 4x4 = ? 2x 8-^? 8x2 = ? 16^4 = ? 16^2-? 16^8 = ? 15^3 = ? 15^5 = ? i of 16 = ? * of 16 = ? i of 16 = ? i of 15 = ? At 4 cents a quart, how many quarts of milk can you buy for 16 cents ? At 2 cents a pint, how many pints of milk can you buy for 16 cents ? At 8 cents a quart, how many quarts of berries can you buy for 1 6 cents ? LESSON 25. 66 OUNCES IN A POUND. How many ounces make a pound ? It takes 16 ounces to make 1 pound. How many ounces in ^ of a pound ? How many ounces in i of a pound ? What part of a pound are 8 ounces ? What part of a pound are 4 ounces ? How many ounces in a quarter of a pound of tea ? How many ounces in a half of a pound of tea ? What will a pound of prunes cost, if half of a pound costs 8 cents ? What will a pound of raisins cost, if a quarter of a pound costs 4 cents ? If I buy three-quarters of a pound of candy, how many ounces of candy do I buy ? How many 4-ounce weights are equal to a pound weight ? How many 8-ounce weights ? How many 2-ounce weights ? How many 1-ounce weights ? What part of a pound are 2 ounces ? 4 ounces ? How many 1-ounce weights are equal to a 2-ounce weight ? a 4-ounce weight ? an 8-ounce weight ? If 1 egg weighs 2 ounces, how many eggs will it take to weigh a pound ? a half-pound ? 66 LESSON 26. EIGHTEEN. 18. (a) (6) I How many dots in each row of dots marked (a) ? How many rows are there ? How many dots in the three rows ? How many dots, then, are 3 times 6 dots ? How many cohimns of dots are there ? How many dots in each column ? How many dots in the six cokimns ? How many dots, then, are 6 times 3 dots ? How many 6's in 18 ? How many 3's in 18 ? Look at the dots marked (b). How many dots in the top row ? in the bottom row ? in the two row^s ? How many dots, then, are 2 times 9 dots ? How many columns of 2 dots each are there ? How many dots, then, are 9 times 2 dots ? How many 2's in 18 ? How many 9's in 18 ? Count by 2's to 18. 2+2+2 + 2+2 + 2 + 2+2 + 2. Count by 3's to 18. 3 + 3 + 3 + 3 + 3 + 3. Count by 6's to 18. 6 + 6 + 6. 2x4-? 2x5 = ? 2x6 = ? 2x7 = ? 2x8==? 2x9 = ? 18^2 = ? 18-^3 = ? 18^6--? 18^9 = ? 9 + 9 = ? 18-9 = ? ^ofl8 = ? ^ofl8=? * of 18 = ? iof 18 = ? What part of 18 is 9 ? What part of 18 is 6 ? What part of 18 is 3 ? What part of 18 is 2 ? LESSON 27. 67 TWENTY. 20. (a) (b) How many dots in each row of dots marked (a)? How many rows are there ? How many dots in the four rows ? How many dots, then, are 4 times 5 dots ? How many columns of dots are there ? How many dots in each cohnnn ? How many dots in the five columns ? How many dots, then, are 5 times 4 dots ? How many 5's in 20 ? How many 4's in 20 ? Count by 4's to 20. Count by 5's to 20. Look at the number picture marked (b). How many dots in the top row ? How many dots in the bottom row ? How many dots in the two rows ? How many dots, then, are 2 times 1 dots ? How many columns of 2 dots each are there ? How many dots in the 10 cohimns ? How many dots, then, are 10 times 2 dots ? How many lO's in 20 ? How many 2's in 20 ? 4x5-=? 5x4 = ? 2x10 = ? 10x2 = ? 20^4 = ? 20^5 = ? 20^ 2 = ? 20^10 = ? Count by 2's to 19, beginning 1, 3, 5, etc. Count by 3's to 19, beginning 1, 4, 7, etc. Count by 3's to 20, beginning 2, 5, 8, etc. 68 LESSON 28. ADDITION TABLE. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 7 8 9 3 3 3 3 3 3 3 3 3 3 1 2 3 4 5 6 7 8 9 4 4 4 4 4 4 4 4 4 4 1 2 3 4 5 6 7 8 9 5 5 5 5 6 5 5 5 5 5 1 2 3 4 5 6 7 8 9 6 6 6 6 6 6 6 6 6 6 1 2 3 4 5 6 7 8 9 7 7 7 7 7 7 7 7 7 1 2 3 4 5 6 7 8 9 8 8 8 8 8 8 8 8 8 8 1 2 3 4 5 6 7 8 9 9 9 9 9 9 9 9 9 9 9 1 2 3 4 5 6 7 8 9 Note. The Teacher should copy this addition table on the board, and require each pupil in turn to name the sums as she touches the examples at random with a pointer. She should continue the drill daily until every pupil is absolutely certain of the required answer. LESSON 29. 69 James had 2 peaches, and Tom had 5 peaches. How many did they have together ? Harry bought a quart of peanuts for 6 cents, and a lead pencil for 2 cents. How much money did he spend ? There are 7 apples on one limb, and 2 apples on another. How many apples on both limbs ? Susie has 8 white roses, and Alice has 2 red roses. How many roses have they together ? Nine boys are at play, and 2 boys are looking on. How many boys in all ? John had 10 marbles, and found 2 more. How many had he then ? Mary had 7 cherries, and her brother gave her 3 more. How many had she then ? Alice had 8 white chickens, and 3 brown chick- ens. How many chickens had she in all ? A farmer sold 9 bushels of corn at one time, and 3 bushels at another time. How many bushels did he sell in all ? Harry saw 5 birds sitting on a fence, and 4 birds on the ground. How many birds did he see ? Nora bought a quart of peanuts for 6 cents, and an orange for 4 cents. How much money did she spend ? A boy paid 3 cents for an orange, and 8 cents for some bananas. How much did he pay in all ? The cook used 6 eggs for a pudding, and 7 eggs for cake. How many eggs did she use ? 70 LESSON 30. Kate bought half a quire of note paper for 6 cents, and a bunch of envelopes for 5 cents. How much did she pay for the paper and envelopes ? Ernest found 7 eggs in one nest, and 4 eggs in another nest. How many eggs did he find in all ? Emma picked 8 quarts of berries, and Frank 4 quarts. How many quarts did they both pick ? There are 9 apples in one dish, and 4 apples in another. How many apples are there in all ? A farmer had 9 red cows, and 5 red and white cows. How many cows had he ? A boy rode 8 miles, and walked 5 miles. How many miles did he go ? A man paid 7 dollars for a ton of coal, and 5 dollars for a cord of wood. How many dollars did he pay for the coal and wood together ? A man worked 6 days one week, and 5 days the next week. How many days did he work in all ? School begins at 9 o'clock in the morning, and continues 3 hours. What o'clock is it when school is dismissed ? John had 6 cents, and earned 6 cents more. How much money had he then ? Jane paid 9 cents for a slate, and 4 cents for some paper. How much did the slate and paper together cost ? Olive paid 5 cents for a spool of silk, and 9 cents for two yards of ribbon. How much did she pay in all ? LESSON 31. 71 A farmer sold 7 lambs at one time, and 6 lambs at another time. How many lambs did he sell ? A milkman has 8 Dutch cows, and 6 Durham cows. How many cows has he ? James paid 9 dollars for a coat, and 6 dollars for a vest. How much did he pay for both ? In a school one class has 9 girls, and another has 7 girls. How many girls have the two classes ? Harry caught 8 trout, and Tom caught 7 trout. How many did they catch in all ? There are 8 yards of ribbon in one roll, and 9 yards in another. How many yards are there in the two rolls ? In a game of baseball 9 persons play on one side, and 9 persons on the other side. How many persons does it take to play the game ? If a boy buys an orange for 4 cents, a pear for 3 cents, and an apple for 2 cents, how much does he pay for all ? Alice bought a postage stamp for 5 cents, another for 4 cents, and another for 3 cents. How much did she pay for the three stamps ? A 5-cent piece, a 2-cent piece, and 9 single cents are equal to how many cents ? Tom paid 3 cents for a top, 2 cents for a ball, and 7 cents for a book. How much did he pay ? James hoed 4 rows of potatoes, George hoed 5 rows, and Oscar hoed 6 rows. How many rows did they all hoe ? 72 LESSON 32. There are 7 pies on one shelf, and 9 pies on another shelf. How many pies are there on the two shelves ? There are 6 eggs in one nest, 4 in another, and 3 in another. How many eggs are there in the three nests together ? Nora paid 9 cents for ribbon, 5 cents for buttons, and 3 cents for pins. How much did she pay for all? A lady bought a dress for 9 dollars, a hat for 4 dollars, and a parasol for 3 dollars. How much did she pay for all ? If a table is 8 feet long and 5 feet wide, what is the number of feet in one side and the two ends ? Harry had 7 five-cent pieces, 4 two-cent pieces, and 8 one-cent pieces. How many pieces of money had he in all ? Alice picked 6 quarts of berries, Kate 6 quarts, and Florence 5 quarts. How many quarts did they all pick together ? In a certain garden there are 6 pear trees, 7 peach trees, and 5 cherry trees. How many trees are there in the garden ? James picked 7 boxes of strawberries on Monday, 3 boxes on Tuesday, and 6 boxes on Wednesday. How many boxes did he pick ? Frank bought a pencil for 4 cents, a penholder for 3 cents, and a block of paper for 9 cents. How much did he have to pay for all ? LESSON 33. 73 SUBTRACTION TABLE. 123456789 10 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 3 4 5 6 7 8 9 10 11 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 3 4 5 6 7 8 9 10 11 12 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 4 5 6 7 8 9 10 11 12 13 -4 -4 -4 -4 -5 -5 -5 -5 -5 -5 5 6 7 8 9 10 11 12 13 14 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 6 7 8 9 10 11 12 13 14 15 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 7 8 9 10 11 12 13 14 15 16 -7 -7 -7 -7 -7 -7 -7 -7 -7 -7 8 9 10 11 12 13 14 15 16 17 -8 -8 -8 -8 -8 -8 -8 -8 -8 -8 9 10 11 12 13 14 15 16 17 18 -9 -9 "9 -9 -9 -9 -9 -9 -9 -9 10 11 12 13 14 15 16 17 18 19 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 Note. The Teacher should copy this substraction table on the board, and require each pupil in turn to name the differences as she touches the examples at random with a pointer. She should continue the drill daily until every pupil is absolutely certain of the required answer. 74 LESSON 34. Kobert had 9 cents, and spent 4 of them for an orange. How many cents had he left ? From a string 14 inches long, 4 inches were cut off. How many inches remained ? A hen had 11 chickens. A hawk caught 4 of them. How many chickens were left ? There were 13 crows on the groimd. Four of them flew away. How many were left ? A baker sold 10 loaves of bread in the morning, and 7 loaves in the afternoon. How many more loaves did he sell in the morning than in the afternoon ? A farmer raised 19 barrels of apples, and sold 9 barrels ? How many barrels had he left ? From a dozen cans of tomatoes three cans were used. How many cans were left ? Alice has 7 dolls. How many more must she get in order to have 10 dolls ? Ernest has 14 ducks and 6 geese. How many more ducks has he than geese ? Ellen is 11 years old, and Susan is 7 years old. How many years older is Ellen than Susan ? A carpenter had a board 15 feet long. He sawed off a piece 7 feet long. How many feet long was the other piece ? A farmer sold a calf for 11 dollars, and a pig for 3 dollars. How much more did he receive for the calf than for the pig ? How much did he receive for the calf and pig together ? LESSON 35. 76 A milkman has 13 cows. Six of them are dark red cows, and the rest are black and white. How many of them are black and white ? Robert has to travel 16 miles. How many miles remain after he has gone 7 miles ? How many eggs must you put with 7 eggs in order to have a dozen eggs ? There were 12 rats in the stable, but 5 of them were caught in a trap. How many rats escaped ? In a pigeon house there were 16 pigeons, but 9 flew away. How many pigeons remained ? Mary hemmed 15 handkerchiefs, and Ellen only 7. How many more did Mary hem than Ellen ? A farmer had 17 lambs. He sold 8 of them. How many lambs had he left ? A sitting hen had 13 eggs under her, but only 9 chickens came out. How many eggs had no chickens ? Seventeen spiders waited for flies, but 7 spiders waited without catching any. How many spiders caught flies ? John had 13 cents, and paid 5 cents for car fare. How many cents had he left ? George earned 13 cents, and spent 8 cents. How many cents had he left ? Florence had 16 pinks. Eight were red, and the rest w^ere white. How many were white ? Bertha had 18 chickens. Nine were white, and the rest were black. How many were black ? 76 LESSON 36. Peter raised 13 melons, and sold 9 of them. How many were left ? There were 15 eggs in a nest, but 9 of them were carried into the house. How many were left ? Fourteen lilies were growing in a field, but a boy picked 9 of them. How many lilies were left ? Harry has earned 9 cents by selling newspapers. How many more cents must he earn in order to have 16 cents ? Kobert had 17 rows of peas. He has hoed 9 rows. How many more rows has he to hoe ? From a dozen cans of j)eaches 9 cans were used. How many cans were left ? A gardener raised 11 dozen cabbages, and sold 9 dozen. How many dozen had he left ? A farmer had 10 oxen, but he sold one pair of them. How many oxen had he left ? A butter dealer had 11 pounds of butter, and sold 8 pounds. How many pounds were left ? A tea merchant bought 14 chests of tea. When he had sold 8 chests, how many had he left ? From 14 yards of cloth a merchant sold 5 yards. How many yards were left ? Richard had 10 lambs. He sold 3 of his lambs to one man, and 2 to another man. How many lambs remained ? Florence had 15 roses. Three of the roses were yellow, three were white, and the rest were red. How many red roses did she have ? LESSON 37. 77 TENS. Illllll NINETY 90 SEVENTY 70 tlltll ONE HUNDRED lOO What do we call 2 tens ? 3 tens ? 4 tens ? 5 tens ? 6 tens ? 7 tens ? 8 tens ? 9 tens ? 10 tens ? How many tens make ninety ? thirty ? one hun- dred ? seventy ? fifty ? forty ? sixty ? eighty ? If I pay 6 ten-cent pieces for peaches, and 3 ten- cent pieces for pears, how many cents do I spend ? If I have 6 ten-cent pieces in one pocket, and 4 in another, how much money have I ? How many tens are 3 tens and 4 tens ? 5 tens and 2 tens ? 4 tens and 4 tens ? 5 tens and 5 tens? How many ten-cent pieces make a dollar ? Twenty is sometimes called a score. How many years are 2 score years ? How old is a man who is 4 score years old ? How many years are 3 score and ten years ? 78 LESSON 38. Copy, and write the results : 20 20 50 70 30 60 50 +50 +60 +30 +20 +40 +30 +40 70 +30 80 +10 40 +40 50 +50 60 +40 80 +20 90 +10 50 -20 60 30 70 -10 80 -50 90 -20 30 -20 50 -30 70 -30 90 -70 80 40 70 -20 90 -30 80 -60 40 -20 3x20 = ? 4x20-? 3x30 = ? 4x10 = ? 80 20 60 90 4 = ? 2 = ? 3 = ? 3 = ? 2x 20 = ? 5x20 = ? 2 X 30 = ? 2 X 40 = ? 60 40 80 100 2 = ? 4 = ? 10 = ? 10 = ? 5x10 = ? 5 X 20 = ? 9 X 10 = ? lOx 10 = ? ^of40 = ? ^ of 60 = ? J of 80 = ? i of 50 = ? You have already learned that we write the fig- ure for the number of tens in the second place from the right. In what place, counting from the right, do we write the hundreds of a number ? Write on the board the number that contains six hundreds, no tens, and five ones. If you rub out the 0, what does the number become ? LESSON 39. 79 Two tens and one make twenty-one, 21. Two tens and two make twenty-two, 22. Two tens and three make twenty-three, 23. Two tens and four make twenty-four, 24. Two tens and five make twenty-five, 25. Two tens and six make twenty-six, 26. Two tens and seven make twenty- seven, 27. Two tens and eight make twenty-eight, 28. Two tens and nine make twenty-nine, 29. What are the names of the numbers made up of 3 tens and 1 ? 3 tens and 2 ? 3 tens and 3 ? 3 tens and 4 ? 3 tens and 5 ? 3 tens and 6 ? 3 tens and 7 ? 3 tens and 8 ? 3 tens and 9 ? What are the names of the numbers made up of 4 tens and 1 ? 4 tens and 2 ? 4 tens and 3 ? 4 tens and 4 ? 4 tens and 5 ? 4 tens and 6 ? 4 tens and 7 ? 4 tens and 8 ? 4 tens and 9 ? What are the names of the numbers made up of 5 tens and 1 ? 5 tens and 2 ? 5 tens and 3 ? 5 tens and 4 ? 5 tens and 5 ? 5 tens and 6 ? 5 tens and 7 ? 5 tens and 8 ? 5 tens and 9 ? What are the names of the numbers made up of 6 tens and 1 ? 6 tens and 2 ? 6 tens and 3 ? 6 tens and 4 ? 6 tens and 5 ? 6 tens and 6 ? 6 tens and 7 ? 6 tens and 8 ? 6 tens and 9 ? What are the names of the numbers made up of 7 tens and 1 ? 7 tens and 2 ? 7 tens and 3 ? 7 tens and 4 ? 7 tens and 5 ? 7 tens and 6 ? 7 tens and 7 ? 80 LESSON 40. Kead the numbers: 78; 79; 81; 82; 83; 84; 85; 86; 87; 88; 89. Read the numbers: 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 200; 300; 400. How many more tens has the number 84 than 72 ? 63 than 31 ? 55 than 15 ? 42 than 2 ? 95 than 80 ? 65 than 50 ? 94 than 43 ? 99 than 39 ? Copy, and complete : 18 = 10 + ? 26 = = 2x10 + ? 67- = 6x10 + ? 14-^10 + ? 37 = = 3x10 + ? 84- = 8x10 + ? 13 = 10 + ? 24- = 2x10 + ? 85- = 8x10 + ? 19 = 10 + ? 35 = = 3x10+? 89- = 8xl0 + ? 12 = 10 + ? 39 = = 3x10 + ? 86- = 8x10 + ? 15 = 10 + ? 41- = 4x10 + ? 88- = 8x10 + ? 16 = 10 + ? 47 = -4x10 + ? 95- = 9x10 + ? 17 = 10 + ? 43 = = 4xl0 + ? 97 = = 9x10 + ? 11 = 10 + ? 55 = = 5x10 + ? 93 = 9X10 + ? 20 = 10 + ? 59 = = 5x10 + ? 96 = = 9xl0 + ? 50 = 10 + ? 51 = = 5x10 + ? 98 = = 9 X 10 + ? 70 = 10 + ? 52 = = 5x10 + ? 99 = = 9x10 + ? Copy, and add : 5 6 2 3 3 5 8 7 9 9 2 4 7 5 5 7 3 4 2 5 7 4 6 6 6 9 2 5 6 4 7 8 5 7 2 6 4 9 6 4 3 5 5 6 2 1 7 4 3 3 4 5 6 5 4 3 7 6 6 8 LESSON 41. 81 Copy, and add, adding the 07ies first : 22 31 33 25 18 35 21 33 11 21 30 11 23 12 13 11 21 21 32 23 31 22 20 22 34 60 40 41 36 23 12 17 25 34 21 22 30 12 13 13 20 32 13 10 11 10 12 11 Copy, and subtract, subtracting the ones first : 65 87 98 78 63 77 43 -55 -67 -52 -51 -35 99 76 95 46 37 89 -44 -66 -54 -22 -21 -65 62 71 92 85 74 52 -40 -50 -70 -30 -43 -50 Copy, and multiply, multiplying the 07ies first : 21 32 13 24 34 42 2 2 2 2 2 2 31 23 33 43 44 30 2 2 2 2 2 2 11 10 23 12 32 33 3 3 3 3 3 3 10 11 12 20 21 22 4 4 4 4 4 4 82 LESSON 42. TWENTY-ONE. 21. (a) (6) II • • • How many dots in each row of dots marked (a) ? How many rows of dots ? How many dots in the three rows together ? How many dots, then, are 3 times 7 dots ? How many dots in each cohimn of dots ? How many columns of dots ? How many dots in the seven columns ? How many dots, then, are 7 times 3 dots ? How many 3's in 21 ? Look at the number picture marked (b). How many 7's in 21 ? 3x7-=? 21^3 = ? iof21-? 7x3 = ? 21^-7 = ? ^of21-? If a pair of boots costs 7 dollars, what will 3 pairs of boots cost ? 2 pairs of boots ? If an orange costs 3 cents, what will 7 oranges cost ? 6 oranges ? 5 oranges ? 4 oranges ? Divide 21 oranges equally among 3 boys. How many oranges will each boy have ? Divide 21 oranges equally among 7 boys. How many oranges will each boy have ? There are 21 apples in a basket, and James takes one-third of them. How many apples does he take ? If he had taken t of them, how many would he have taken ? LESSON 43. 83 TWENTY-FOUR. 24. (a) (h) • ••••••• • ••••• • ••••• How many dots in each row of dots marked (a) ? How many rows of dots ? How many dots in the three rows ? How many dots, then, are 3 times 8 dots ? How many dots in each column of dots ? How many cohimns are there ? How many dots in the eight columns ? How many dots, then, are 8 times 3 dots ? Look at the dots marked (b). How many dots in each row ? How many rows of dots ? How many dots in the four rows ? How many dots, then, are 4 times 6 dots ? How many dots in each column of dots ? How many columns are there ? How many dots in the six columns ? How many dots, then, are 6 times 4 dots ? 3x8 = ? 8x3-=? 4x6 = ? 6x4 = ? How many 3's in 24 ? How many 8's ? How many 4's ? How many 6's ? 24^3 = ? 24^4 = ? 24^6 = ? 24^8 = ? i of 24 = ? i of 24 = ? * of 24 = ? * of 24 = ? 4x2=? 4x3=? 4x4=? 4x5=? 4x6=? 5x2=? 5x3=? 5x4=? 6x3=? 6x4=? 84 LESSON 44. TWENTY-FIVE. 26. (a) (b) How many dots in each row of dots marked (a) ? How many rows are there ? How many dots in the five rows ? How many dots, then, are 5 times 5 dots ? How many 5's in 25 ? iof2o = ? 25-^5-? Count by 5's to 25 ? Count by 4's to 24. Note. Assist the pupil by dots to count by 3's, 4's, etc., but only so long as such assistance is necessary. Count by 3's to 24. Count by 2's to 24. Count by 6's to 24. Count by 8's to 24. ' Count by 3's to 25, beginning 1, 4, etc. Count by 3's to 23, beginning 2, 5, etc. Count by 4's to 25, beginning 1, 5, etc. Count by 4's to 22, beginning 2, 6, etc. Count by 4's to 23, beginning 3, 7, etc. There are 5 plates in a row, and each plate has 5 apples on it. How many apples on the 5 plates ? If you divide 25 oranges equally among five lit- tle girls, how many oranges will each girl have ? If you have 25 oranges, how many times can you give away oranges if you give 5 each time ? How many eggs make a dozen ? a half-dozen ? How many inches make a foot ? How many feet a yard ? How many quarts a gallon ? LESSON 45. 85 TWENTY-SEVEN. 27. («) (6) How many dots in each row of dots marked (a) ? How many rows are there ? How many dots in the three rows together ? How many dots, then, are 3 times 9 dots ? How many dots in each column of dots ? How many cohimns are there ? How many dots in the nine columns ? How many dots, then, are 9 times 3 dots ? How many 3's in 27 ? How many 9's ? 27^3-? lof27-^? 27-9 = ? iof27-? How many three-cent stamps can I buy for 27 cents ? for 24 cents ? for 21 cents ? In one yard there are 3 feet. How many feet in 9 yards ? in 8 yards ? in 7 yards ? in 6 yards ? At 9 cents a quart, how much will 3 quarts of berries cost ? 2 quarts of berries ? 2xl = ? 3x1 = ? 4x2 = ? 6x2 = ? 2x2 = ? 3x2 = ? 4x3 = ? 6x3 = ? 2x3-? 3x3 = ? 4x4 = ? 6x4 = ? 2x4 = ? 3x4 = ? 4x5 = ? 7x2 = ? 2x6 = ? 3x5 = ? 4x6 = ? 7x3 = ? 2x6 = ? 3x6 = ? 5x2 = ? 8x2 = ? 2x7 = ? 3x7 = ? 5x3 = ? 8x3 = ? 2x8 = ? 3x8=? " 5x4 = ? 9x2 = ? 2x9 = ? 3x9 = ? 5x5 = ? 9x3 = ? 86 LESSON 46. TWENTY-EIGHT. 28. (a) (6) • • • • • • • • • • • !•{•<• How many dots in each row of dots marked (a) ? How many rows are there ? How many dots in the four rows together ? How many dots, then, are 4 times 7 dots ? How many dots in each cohimn ? How many columns of dots are there ? How many dots in the seven columns ? How many dots, then, are 7 times 4 dots ? How many 4's in 28 ? How many 7's in 28 ? 4x7 = ? 7x4 = ? 28-^4 = ? 28-^7 = ? At 4 cents a quart, what will 6 quarts of milk cost ? What will 7 quarts cost ? At 6 cents a quart, what will 4 quarts of berries cost ? What will 3 quarts cost ? At 7 cents a quart, what will 4 quarts of berries cost ? What will 3 quarts cost ? At 7 cents a cake, how many cakes of maple sugar can you buy for 28 cents ? If it takes 4 men 7 days to dig a certain ditch, how long will it take 1 man to dig the ditch ? If it takes a man 28 days to build a certain wall, how many days will it take him to build a quarter of the wall ? Three-quarters of the wall ? What part of 28 is 7 ? What part of 24 is 4 ? What part of 24 is 8 ? What part of 27 is 9 ? LESSON 47. 87 THIRTY. 30. (a) • • • < How many dots in each row of dots marked (a) ? How many rows are there ? How many dots hi the five rows ? How many dots, then, are 5 times 6 dots ? How many dots in each column of dots ? How many cohunns of dots are there ? How many dots in the six columns ? How many dots, then, are 6 times 5 dots ? How many 6's in 30 ? How many 5's in 30 ? What part of 30 is 6 ? What part of 30 is 5 ? 5x6-^? 6x5--? 30-^5==? 30^6 = ? How many cents ai'e 6 five-cent pieces ? How many five-cent stamps can you buy for 30 cents ? for 25 cents ? for 20 cents ? When berries are 6 cents a quart, how many quarts can you buy for 30 cents ? for 24 cents ? How many more is i of 30 than ^ of 30 ? How many tens in 30 ? How many fives in i of 30 ? in -h of 30 ? m i of 30 ? How many sixths of 30 must you take to have i of 30 ? to have J of 30 ? How many sixths of any number must you take to have i of the number ? to have ^ of the number ? How many inches in 3 of a foot ? in I of a foot ? How many inches in ^ of a foot ? in f of a foot ? 88 LESSON 48. SLATE ADDITION. Add 8 ones to 6 tens and 7 ones. Write the 6 tens and 7 ones 67 Then write the 8 ones under the 7 ones . . . 8 Add the ones. 75 How many are 8 ones and 7 ones ? 15. How many tens and how many ones in 15 ? Write the 5 ones in the ones' place under 8. What shall be done with the 1 ten ? Add it to the 6 tens, and we have 7 tens. Now write the 7 tens in the tens' place. Read the answer. Howmany tensandonesin 75? Add 7 ones to 2 tens and 8 ones. Add 8 ones to 2 tens and 5 ones. Add 6 ones to 3 tens and 7 ones. Add 4 ones to 4 tens and 9 ones. Add 9 ones to 4 tens and 7 ones. Add 5 ones to 5 tens and 5 ones. Add 7 ones to 7 tens and 3 ones. 68 +8 76 + 5 47 + 6 28 + 4 35 + 8 24 + 9 56 + 4 57 + 9 65 + 7 69 + 4 63 + 8 55 + 5 84 + 7 87 + 3 88 + 9 79 + 6 88 + 8 79 + 9 33 ±1 46 + 8 57 + 7 64 + 9 77 + 9 86 + 9 LESSON 49. 89 Add 3 tens and 7 ones to 4 tens and 6 ones. Write the 4 tens and 6 ones 46 Then the 3 tens and 7 ones 37 Add the ones. 83 How many are 7 ones and 6 ones ? 13. How many tens and how many ones in 13 ? Write the 3 ones in the ones' place under the 7. What shall be done with the 1 ten in 13 ? Add it to the tens. 1 ten and 3 tens are ? and 4 tens more ? Write the 8 in the tens' place. Therefore the sum of 46 and 37 is 83. Add 5 tens and 3 ones to 1 ten and 8 ones. Add 7 tens and 6 ones to 1 ten and 5 ones. Add 3 tens and 7 ones to 3 tens and 6 ones. Add 3 tens and 3 ones to 3 tens and 9 ones. Add 2 tens and 5 ones to 5 tens and 5 ones. Add 4 tens and 9 ones to 4 tens and 8 ones. Add 6 tens and 4 ones to 1 ten and 9 ones. Add 3 tens and 8 ones to 4 tens and 7 ones. 64 18 48 29 76 18 57 19 35 56 56 24 55 38 28 36 55 29 35 16 68 19 39 26 48 32 65 19 53 28 57 35 48 27 34 28 90 LESSON 50. Add: 67 74 57 29 39 59 19 16 38 34 47 38 36 19 32 17 23 18 14 46 28 23 19 57 20 18 47 27 30 35 14 36 15 22 17 17 17 23 18 25 49 24 34 49 56 38 28 18 16 24 26 27 34 57 12 15 16 27 39 19 25 23 39 47 39 35 28 28 14 22 23 39 27 35 27 17 26 14 38 19 38 39 26 25 28 57 25 12 19 37 35 18 28 14 17 14 16 18 29 38 45 26 18 19 25 34 39 19 27 24 36 24 12 45 27 37 56 17 19 28 28 19 12 19 29 38 35 25 22 44 39 18 LESSON 51. 91 THIRTY-TWO. 32. (a) (6) mil A A 1 A A • • • • • • • • How many dots in each row of dots marked (a) ? How many rows of dots ? How many dots in the 4 rows ? How many dots, then, are 4 times 8 dots ? How many dots in each column of dots ? How many columns of dots are there ? How many dots in the eight columns ? How many dots, then, are 8 times 4 dots ? 4x8-? 8x4-? 32-4 = ? 32 ^8 = ? How many shoes will a blacksmith need to shoe 8 horses all round ? A teamster has 32 horses. How many four- horse teams can he form ? How many eight-horse teams ? At 4 cents a quart, how many quarts of milk can you buy for 32 cents ? for 28 cents ? At 8 cents a pint, how many pints of cream can you buy for 32 cents ? for 24 cents ? Four weeks make a lunar month. How many weeks are there in 8 lunar months ? in 7 ? in 6 ? At 8 cents a pound, how much will 4 pounds of sugar cost ? 3 pounds ? 2 pounds ? How many pears in i of 32 pears ? in i of 32 pears ? in i of 24 pears ? in f of 24 pears ? 92 LESSON 52. THE PECK. QUART. Note. These wooden measures are used for measuring dry articles, such as oats, wheat, beans, potatoes, etc. How many pints in one quart ? How many quarts make one peck ? * Eight quarts make one peck. How many 2-quart measures of oats will a peck measure hold ? How many 4-quart measures ? One quart of oats is what part of a peck of oats ? Two quarts of oats are what part of a peck ? four quarts ? How many quarts in 2 pecks ? in 4 pecks ? If the peck measure is half-full of beans, how many more quarts of beans will it hold ? If the peck measure is a quarter-full of oats, how many more quarts will it hold ? If the peck measure is three-quarters full of cranberries, how many quarts of cranberries are in it ? How many more quarts will it hold ? How many quarts in ^ of a peck ? in i of a peck ? in I of a peck ? At 2 cents a quart, what will a peck of corn cost ? At 3 cents a quart, what will a peck of nuts cost ? At 4 cents a quart, what will a peck of peas cost ? * Let the pupil discover the answer hy trial. LESSON 53. THE BUSHEL,. 93 How many pints make a quart ? How many quarts make a peck ? How many pecks make a bushel ? Four pecks make one bushel. How many pecks in a half-bushel ? One peck of corn is what part of a bushel of corn ? Two pecks are what part of a bushel ? Three pecks are what part of a bushel ? How many quarts in a peck of berries ? How many quarts in a half-bushel of berries ? How many quarts in a bushel of berries ? How many quarts in three-quarters of a bushel? In 24 quarts how many pecks ? In 32 quarts how many pecks ? If a bushel basket is half-full of apples, how many more pecks of apples will it hold ? If a bushel basket is three-quarters full of apples, how many more pecks of apples will it hold ? A bushel of oats weighs 32 pounds. How much does a peck weigh ? How much do 4 quarts weigh ? What part of a bushel are 4 quarts ? 8 quarts ? 94 («) LESSON 54. THIRTY-FIVE. 35. (&) • • • • • • • • • • • • • • • • • • • • • • • • How many dots in each row of dots marked (a) ? How many rows of dots ? How many dots in the five rows ? How many dots, then, are 5 times 7 dots ? How many dots in each column of dots ? How many columns of dots ? How many dots in the seven columns ? How many dots, then, are 7 times 5 dots ? How many 7's in 35 ? How many 5's in 35? 5x7 = ? 7x5 = ? 35^7 = ? 35^5 = ? How many halves of a number make the entire number ? How many thirds ? How many fourths ? How many fifths ? How many sixths ? How many sevenths ? ^ of 12 - ? ? 9 i of 10 i of 20 = ? i of 24 = ? i of 25 = ? ? i of 35 = ? ? I of 35 = ? At seven dollars a cord, how many cords of wood can be bought for 35 dollars? for 21 dollars ? At 5 cents a ride, how many street-car rides can be taken for 35 cents ? for 25 cents ? for 15 cents? 2" Oi ±^ iof 14 ioi 16 iof 18 4 of 15 iof 18 iof 21 i of 24 LESSON 55. 95 THIRTY-SIX. 36. (a) (6) How many dots in each row of dots marked (a) ? How many rows ? How many dots in the four rows ? How many dots, then, are 4 times 9 dots ? How many dots in each column of dots ? How many columns ? How many dots in the nine columns ? How many dots, then, are 9 times 4 dots ? How many dots in each row of dots marked (6) ? How many rows ? How many dots in the six rows ? How many dots, then, are 6 times 6 dots ? 4x9^? 9x4-? 6x6 = ? 36-4 = ? 36^9 = ? 36^6 = ? iof36 = ? ^of36 = ? How many four-cent stamps can I buy for 36 cents ? for 28 cents ? for 32 cents ? for 24 cents? At 9 cents a yard, how many yards of calico can I buy for 36 cents ? for 18 cents ? for 27 cents ? At 6 cents a quart, how many quarts of milk can I buy for 36 cents ? for 24 cents ? for 30 cents ? 4x2 = ? 4x4 = ? 4x6 = ? 4x8 = ? 4x3 = ? 4x5 = ? 4x7 = ? 4x9 = ? 96 (a) LESSON 56. FORTY. 40. I (&) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • How many dots in each row of dots marked (a) ? How many rows ? How many dots in the five rows ? How many dots, then, are 5 times 8 dots ? How many dots in each column of dots ? How many columns ? How many dots in the eight columns ? How many dots, then, are 8 times 5 dots ? How many 5's in 40 ? How many 8's in 40 ? 5x8=-? 8x5 = ? 40^5 = ? 40-^8==? At 5 dollars a barrel, how many barrels of flour can you buy for 40 dollars ? for 35 dollars ? At 8 cents a bottle, how many bottles of ink can you buy for 40 cents ? for 32 cents ? If one loaf of bread is worth 5 cents, how many cents are 8 loaves worth ? 6 loaves ? If a melon is worth 8 cents, how many cents are 5 melons worth ? 4 melons ? How much will a boy earn in 9 weeks, if he earns 4 dollars a week ? i of 20 - ? i of 16 = ? i of 16 - ? iof 30==? i of 32 == ? i of 32 = ? iof 40-? i of 40 - ? 4 of 40 = ? LESSON 57. 97 SLATE SUBTRAC.TIOX. The result obtained from subtracting a smaller number from a larger is called the remainder or difference. The smaller number is called the sub- trahend ; and the larger number, the minuend. From 5 tens and 3 ones take 2 tens and 8 ones. Write the 5 tens and 3 ones 53 Write the 2 tens and 8 ones below 28 Draw a line underneath 25 We cannot take 8 ones from 3 ones. We there- fore take 1 of the 5 tens and put with the 3 ones. Note. Illustrate this. Let the pupil take a bundle of ten, and slip- ping off the rubber bands put the ten ones with the three ones. We now have 13 ones, and 8 ones from 13 ones leave 5 ones. We write the 5 in the ones* place. As we have taken 1 ten from the 5 tens, we have only 4 tens left, and 2 tens from 4 tens leave 2 tens. We write the 2 in the tens' place, and have for the remainder 2 tens and 5 ones ; that is, 25. Note. The entire work may be shown as follows : 63 40 + 13 28 20+8 25 20 + 5 = 25. The pupils, however, must be taught from the first to do the work without any change of the figures, 75 23 33 31 37 86 -6-4-5-3 -8 ^ 67 35 37 32 46 82 -8 -9 -9 -7 -7 -3 98 LESSON 58. Slate exercises : . 75 42 33 64 83 92 -37 -25 -16 -28 -38 -29 50 41 42 56 35 52 -29 -24 -15 -27 -26 -28 48 42 62 55 61 72 -19 -29 -33 -27 -37 -36 70 52 85 75 85 60 -37 -39 -16 -36 -28 -48 98 96 73 86 83 57 -69 -27 -57 69 -27 -18 74 67 85 91 80 61 -37 -19 -38 -64 -55 • -28 64 73 81 80 43 82 -45 -26 -33 -43 -26 -57 94 72 91 80 51 90 -18 -19 -29 -37 -22 -23 •87 95 93 90 73 83 -19 -26 -38 -43 -37 -35 LESSON 59. 99 Out of 16 eggs 7 were used for cooking. How many eggs were left ? In a class of 14 pupils there are 5 boys. How many girls are there in the class ? In a class of 13 pupils there are 6 girls. How many boys are there in the class ? Out of 15 signal flags, 8 are white, and the rest blue. How many flags are blue ? One package of tea weighs 16 ounces, and another weighs 8 ounces. How many more ounces in one package than in the other ? How much deeper is a well 21 feet deep than a well 18 feet deep ? How many more are 13 ducks than 9 ducks ? A man has 17 miles to go. After he has gone 9 miles, how many more has he to go ? From a board 16 inches long, a piece 9 inches long was cut off. How many inches long was the other piece ? A farmer had 13 lambs and sold 5 of them. How many had he left ? In a brood of 14 chickens 6 are white, and the rest brown. How many chickens are brown ? There were 13 crows on the ground. 7 flew away. How many were left on the ground ? What number must you add to 9 to get 12 ? What number must you add to 3 to get 11 ? What number must you take from 11 to get 5 ? What number must you take from 14 to get 8 ? 100 LESSON 60. The number 259 is read two hundred ffty-nine, and is composed of 2 hundreds, 5 tens, and 9 ones. Read, and give the number of hundreds, of tens, and of ones, in the following numbers : 362 715 826 987 567 571 157 628 789 657 263 751 682 879 765 623 286 307 978 576 175 268 703 798 675 517 862 370 897 756 Write in figures the following numbers : One hundred twenty-nine. One hundred nine. Two hundred thirty-six. Seven hundred eight. Two hundred twenty-four. Five hundred six. Two hundred twenty-two. Four hundred seven. Five hundred nineteen. Three hundred five. Seven hundred thirteen. Two hundred four. Six hundred eighteen. Four hundred three. Nine hundred eleven. Three hundred two. Three hundred twelve. Four hundred one. Three hundred sixteen. Four hundred ten. In any number containing hundreds, tens, and ones. The ones are called units of the first order. The tens are called units of the second order. The hundreds are called units of the third order. Remember that any standard by which we count or measure is called a unit. LESSON 61. >lOlc Find the sums : 128 136 215 320 357 362 204 32Y 267 198 416 473 296 376 276 317 218 375 427 576 207 219 293 291 197 327 397 189 198 189 229 379 263 327 183 292 125 362 279 136 376 268 185 202 181 Find the remainders : 362 416 473 327 355 128 137 279 158 278 811 624 821 583 725 258 527 279 283 196 615 209 913 467 916 529 874 389 767 488 531 451 937 873 726 253 184 690 565 339 657 567 765 576 675 386 897 798 703 370 862 218 517 175 726 528 904 208 703 307 102 LESSON 62. FORTY-TWO. 42. (a) • ••••• (6) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • How many dots in each row of dots marked (a) ? How many rows ? How many dots in the six rows ? Haw many dots, then, are 6 times 7 dots ? How many dots in each cokimn of dots ? How many columns ? How many dots in the seven columns ? How many dots, then, are 7 times 6 dots ? How many 7's in 42 ? How many 6's in 42 ? 6x7=-? 7x6 = ? 42-7-=? 42-6 = ? At 6 cents a pound, what will 7 pounds of sugar cost ? 6 pounds ? 5 pounds ? 4 pounds ? At 7 cents a quart, how many quarts of blue- berries can you buy for 42 cents ? At 6 dollars a ton, how many tons of coal can be bought for 42 dollars ? At 7 cents each, what will 6 melons cost ? Count by 2's to 42. Count by 3's to 42. Count by 4's to 40. Count by 5's to 40. Count by 6's to 42. Count by 7's to 42. How many 7's in 28 ? 35 ? 42 ? 21 ? 14 ? How many 6's in 24 ? 30 ? 36 ? 42 ? 18 ? How many 5's in 25 ? 30? 35? 40? 20? LESSON 63. 103 FORTY-FIVE. 46. («) (ft) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • How many dots in each row of dots marked (a) ? How many rows ? How many dots in the five rows ? How many dots, then, are 5 times 9 dots ? How many dots in each cohmm of dots ? How many cohimns ? How many dots in the nine columns ? How many dots, then, are 9 times 5 dots ? How many 9's in 45 ? How many 5's in 45 ? 5x9-^? 9x5---? 45^5^? 45-^9 = ? At 5 cents a pound, how many pounds of sugar can be bought for 45 cents ? for 40 cents ? At 9 cents a pound, how many pounds of candy can be bought for 45 cents ? for 36 cents ? Copy, and write the answers : 2x2--? 3x2 = ? 4x2 = ? 5x2 = ? 2x3 = ? 3x3 = ? 4x3 = ? 5x3 = ? 2x4-^? 3x4 = ? 4x4 = ? 5x4 = ? 2x5 = ? 3x5 = ? 4x5 = ? 5x5=? 2x6 = ? 3x6 = ? 4x6 = ? 5x6 = ? 2x7 = ? 3x7 = ? 4x7 = ? 5x7=? 2x8 = ? 3x8 = ? 4x8 = ? 5x8=? 2x9 = ? 3x9 = ? 4x9 = ? 5x9 = ? 104 LESSON 64. Copy, and write the answers : 4- -2 = ? 6- ^3 = = ? 8- -4 = ? 10- -5 = ? 6- -2-? 9- -3 = = ? 12- -4-? 15- -5 = ? 8- -2 = ? 12 -3 = = ? 16- -4-? 20- -5 = ? 10- -2 = ? 15- -3 = -? 20- -4-? 25- -5 = ? 12- -2-? 18- -3 = -? 24- -4-? 30- -5 = ? 14 -2=-? 21- 3^ - ? 28 - -4-^? 35- -5==? 16- -2 = ? 24 -3- = ? 32- -4 = ? 40- -5 = ? 18- -2-^? 27- -3 = = ? 36- -4 = ? 45- -5 = ? 20- -2 = ? 30- -3^ = ? 40- -4^? 50- -5 = ? Find i of 4. iof 6. k of 8. i of 10. i of 12. iof 6. i of 9. i of 12. i of 15. i of 18. iof 8. * of 12. i of 16. i of 20. i of 24. i of 10. i of 15. i of 20. i of 25. i of 30. i of 12. i of 18. i of 24. i of 30. J of 36. h of 14. i of 21. i of 28. i of 35. i of 42. i of 16. i of 24. I of 32. i of 40. 1 of 42. i of 18. * of 27. i of 36. i of 45. 1 of 35. h oi E20. ^ of 3 0. i of 40. i of 50. 1 T of 28. When we multiply one number by another, the result is called the product ; the number multiplied is called the multiplicand ; and the number by which we multiply is called the multiplier. Name two numbers whose product is : 15 ; 12 ; 18; 24; 21; 32; 28; 25; 35; 45; 42; 27; 20. The product of two equal numbers is called a square number. With 16 buttons make a square. LESSON 65. 105 Multiply 234 by 2. Write the multiplicand 234 Under the ones write the multiplier 2 Draw a line below. AfKQ. Multiply in order the ones, tens, and hundreds, and write ^^^ the result at each step : Twice 4 ones are 8 ones, twice 3 tens are 6 tens, twice 2 hundreds are 4 hundreds. The product, therefore, is 468. Find the products : 342 123 2 2 243 2 334 2 321 2 424 2 123 132 3 3 323 3 213 3 312 3 212 3 111 112 4 4 121 i 211 4 212 4 222 4 When we divide one number by another, the result is called the quotient ; the number divided is called the dividend ; and the number by which we divide is called the divisor. Divide 648 by 2. Write the divisor at the left of the dividend with a 2) 648 curved line between them, and draw a line underneath. — ooT Divide in order the hundreds, tens, and ones, and write oZ4: the result at each step : 2 in 6 hundreds, 3 hundreds ; 2 in 4 tens, 2 tens ; 2 in 8 ones, 4 ones. The quotient, therefore, is 324. Find the quotients : 2)428 2 )684 2 )468 2 )864 2)248 3 )369 3 )639 3 )396 3 )693 3)936 3 )963 4 )444 4 )484 4 )448 4)i844 106 LESSON 66 KOMAN NUMERALS. The Roman method of writing numbers uses these seven capital letters : I = 1; V = 5; X=10; L = 50 ; C = 100; D = 500; M=1000. Other numbers are written by putting two or more of these letters together. A letter written before another of greater value signifies the difference of the values of the letters used. Thus, IV = 4; IX = 9; XL = 40; XC = 90. A letter written after another of the same or greater value signifies the sum of the values of the letters used. Thus, VI = 6; Xl = ll; LX = 60; CX=110; II = 2; 111 = 3; VII = 7; VIII = 8 ; XX = 20; XXX = 30; LXX = 70; CCC = 300. Numbers from 10 to 20 are written : 11-X + I =XI; 16-X + VI -XVI; 12-^X + II -XII; 17-X + VII -XVII; 13 - X + III - XIII ; 18 = X + VIII - XVIII ; 14 = X + IV-XIV; 19-X + IX -XIX. 15-X + V =XV; * In like manner : 25-XX + V -XXV; 46 - XL + VI -XL VI; 29 - XX + IX -XXIX; 69-LX + IX=LXIX. LESSON 67. 1 Complete with Roman numerals : 1 = 11 = 21 35 = 64 2 = 12= - 22 45 = 36 3 = 13= 23 55 = 46 4 = 14= 24 65 = 77 5 = 15 = 25 75 = 88 6 = 16 = 26 85 = 97 7 = 17 = 27 95 = 39 8 = 18 = 28 34 = 98 9 = 19= 29 44 = 89 10 = 20= 30 54 = 99 Complete with figures : 1 = XV = XXIX = XCI 11 = XVI = XXX = XCII 111 = XVII = XL = XCIII IV- XVIII = XLV = XCIV V = XIX = LI = XCV VI = XX = LII = XCVI VII = XXI = L1II = XCVII VIII = XXII = LIV =- XCVIII IX = XXIII = LV = XCIX x = XXIV = LVI = CVIII XI = XXV = LVII = CL XII = XXVI = LVIII = CCIX XIII = XXVII = LIX = CCXX XIV = XXVIII = LX = CCXLV 107 108 LESSON 68. MEASURE OF TIME. When the smallest hand of the clock has gone round the little circle, a minute has passed. The little circle has 60 spaces, and the hand goes over one space every second. Hence, Sixty seconds make a minute. When the longest hand of the clock has gone round the large circle, an hour has passed. How many spaces are marked on the large circle ? The longest hand goes over one space every minute. Hence, Sixty minutes make an hour. The letters I, II, etc., mark the hour spaces. How many hours have passed when the hour- hand has gone entirely round the face of the clock ? The hour-hand goes round twice from sunrise to sunrise. Hence, Twenty-four hours make a day. LESSON 69. 109 How many minutes in a half of an hour ? in a quarter of an hour ? in a third of an hour ? in three-quarters of an hour ? What part of an hour are 30 minutes ? 15 min- utes ? 20 minutes ? 10 minutes ? 45 minutes ? How many hours in a half of a day ? in a quar- ter of a day ? in a third of a day ? What time of day is shown on the clock-face ? What time of day will be shown on the clock- face when the minute-hand reaches I ? II ? Ill ? mi? V? VI? VII? VIII? IX? X? XI? XII? What time of day will be shown on the clock- face when the minute-hand is one minute-space beyondl? II? III? V? VI? VIII? IX? X?XI? What time of day will be shown on the clock- face when the minute-hand is two minute-spaces beyond I? II? III? IIII ? VI? IX? X? XI? What time of day will be shown on the clock- face when the minute-hand is three minute-spaces beyond I ? Ill ? V ? VII ? IX ? X ? XI ? What time of day will be shown on the clock- face when the minute-hand is four minute-spaces beyond II ? Ill ? V ? VI ? VII ? VIII ? IX ? X ? What time of day will be shown on the clock- face when the minute-hand is at XII and the hour- hand at I ? II ? Ill ? V ? VI ? VII ? VIII ? IX ? At what letters does the minute-hand point at half-past four ? at quarter-past four ? at quarter of five ? at 20 minutes to five ? 110 LESSON 70. If a man works 8 hours a day, what part of the day (24 hours) does he work ? What part of 24 hours are 4 hours ? 6 hours ? 8 hours. ? 12 hours ? 2 hours ? If a man can dig one-quarter of a certain ditch in 8 hours, how many hours will it take him to dig the whole ditch ? If 2 men can mow a certain field in 8 days, how many days will it take one man to mow it ? If one man can mow a certain field in 24 days, how many men will it take to mow the field in 6 days ? in 4 days ? in 8 days ? in 3 days ? How many minutes are there in 2 hours ? in 3 hours ? in 4 hours ? in 5 hours ? in 6 hours ? How many seconds are there in 2 minutes ? in 4 minutes ? in 5 minutes ? in 6 minutes ? What part of a minute are 30 seconds ? 15 sec- onds ? 12 seconds ? 20 seconds ? 40 seconds ? 45 seconds ? 50 seconds ? If a man walks a mile in 20 minutes, how many miles at that rate will he walk in an hour ? If a man walks a mile in 15 minutes, how many miles at that rate will he walk in an hour ? At the rate of one mile in 10 minutes, how many miles will a horse go in an hour ? At the rate of one mile in 6 minutes, how many miles will a horse go in one hour ? At the rate of one mile in 2 minutes, how many miles will a railway train go in an hour ? ■ Part III. LESSON 1. FORTY-EIGHT. 48, How many dots are there in each row ? How many rows are there ? How many dots in the six rows ? How many dots, then, are 6 times 8 dots ? How many dots are there in each column ? How many columns are there ? How many dots in the eight columns ? How many dots, then, are 8 times 6 dots ? 6x8 = ? 8x6 = ? 48 -^8 = ? 48 -^6 = ? 1 of 48 = ? 1 of 48 = ? I of 48 = ? ^ of 48 = ? At 6 dollars a ton, what will 8 tons of coal cost ? At 8 dollars apiece, what will 6 hats cost ? If a cow gives 8 quarts of milk a day, in how many days will she give 48 quarts ? Ill 112 LESSON 2. FORTY-NINE. 49. How many dots are there in each row ? How many rows are there ? How many dots in the seven rows ? How many dots, then, are 7 times 7 dots ? Count by 7's to 49. Count by 8's to 48. 7x7 = ? 49 ^7 = ? -fof49 = ? 2x7 = ? '3x7=? 4x7=? '5x7=? 6x7=? 7 + 7 = ? 49-7 = ? 42-7=? 35-7 = ? 28-7 = ? 21-7 = ? 14-7 = ? 7-7 = ? At 7 cents a pound, what will 7 pounds of rice cost ? 6 pounds ? 5 pounds ? 4 pounds ? 3 pounds ? Copy and subtract : 418 -166 219 -184 607 -235 729 -327 839 -ebb 905 -461 806 -235 704 -194 603 -162 502 -171 213 -151 314 -182 415 -193 516 -264 617 -255 526 -275 425 -283 324 -193 635 -383 639 -379 LESSON 3. FIFTY-FOUR. 64. 113 How many dots are there in each row ? How many rows are there ? How many dots in the six rows ? How many dots, then, are 6 times 9 dots ? How many dots are there in each column ? How many columns are there ? How many dots in the nine columns ? How many dots, then, are 9 times 6 dots ? Coimt by 6's to 54. Count by 9's to 54. 6x9 = ? 9x6 = ? 54 ^ 6 = ? 54 - 9 = ? J of 54 = ? 1 of 54 = ? I of 54 = ? -J- of 54 = ? 2x6 = ? '6x6 = ? 12 H- 6 = ? 36 -^ 6 = ? 3x6 = ? 7x6 = ? 18 ^ 6 = ? 42 -5- 6 = ? 4x6 = ? 8x6 = ? 24 - 6 = ? 48 ^ 6 = ? 5x6 = ? 9x6 = ? 30 -i- 6 = ? 54 H- 6 = ? How many tens and how many ones in 54 ? 54 _ 6 = ? 48 - 6 = ? 42 - 6 = ? 36 - 6 = ? 30-6 = ? 24-6=? 18-6=? 12-6 = ? 54 _ 9 = ? 45 _ 9 = ? 36 _ 9 _ 9 27 - 9 = ? At 6 cents a quart, what will 9 quarts of milk cost ? 8 quarts ? 7 quarts ? 6 quarts ? 4 quarts ? At 9 cents a pint, what will 6 pints of sirup cost ? 5 pints ? 4 pints ? 3 pints ? 2 pints ? 114 LESSON 4. If we divide 25 by 4, we have 6 for the quotient and 1 for the remainder. The quotient and remainder may be written as a complete quotient, thus, 6i. In this quotient, the part i is written by writ- ing the remainder above the divisor with a line between them. Divide, and write the complete quotient under the dividend in each case : 2)13 3) 20 3)29 5)21 6)13 2)15 31 22 4)21 5)27 5)32 2)17 ^1 23 4)23 5)33 6)39 2)19 ' 3) 25 4)33 5)34 6)40 3)19 3) 26 4)35 5)37 6)47 3)17 3) 28 4)^7 5)44 6)53 2)123 3)123 4) 124 6)126 2)143 3)153 4)128 6)128 2)167 3)157 4)160 6)186 2)165 3)159 4)166 6)180 2)169 3) 127 4)168 6)248 2)182 3)128 4)204 6)249 2)184 3)187 4)247 6)306 2)187 3)189 4)289 6)368 LESSON 5. FIFTY-SIX. 56. 115 i of 56 = ? How many dots are there in each row ? How many rows are there ? How many dots in the seven rows ? How many dots, then, are 7 times 8 dots ? How many dots in each column ? How many cohimns are there ? How many dots in the eight columns ? How many dots, then, are 8 times 7 dots ? 7x8 = ? 8x7 = ? 56h-7 = ? 56 ^8 } of 56 = ? I of 56 = ? ^ of 56 = ? If I of 56 is 14, and ^ of 56 is 7, how many eighths of 56 are equal to i of 56 ? How many eighths of 56 are equal to J of 56 ? Count by 8's to 56. Count by 7's to 56. If a man works 8 hours a day, how many hours will he work in 5 days ? in 6 days ? in 7 days ? What will 7 yards of print cost, at 8 cents a yard ? at 7 cents a yard ? at 6 cents a yard ? At 8 cents a yard, how many yards of cambric can be bought for 40 cents ? for 48 cents ? At 7 dollars a ton, how many tons of coal can be bought for 49 dollars ? for 56 dollars ? 116 LESSON 6. SIXTY-THREE. 63. How many dots are there in each row ? How many rows are there ? How many dots in the seven rows ? How many dots, then, are 7 times 9 dots ? How many dots are there in each cohimn ? How many columns are there ? How many dots in the nine columns ? How many dots, then, are 9 times 7 dots ? 7x9 = ? 9x7 = ? 63 -^7 = ? 63-9 = ? I of 63 = ? -i-of63 = ? iof63 = ? | of 63 = ? How many ninths of 63 are equal to i of 63 ? Count by 7's to 63. Count by 9's to 63. At 9 cents a foot, what will 7 feet of lead pipe cost ? 6 feet ? 4 feet ? 5 feet ? 3 feet ? How many days are there in 9 weeks ? At 7 dollars a week, how many weeks' board can be had for 56 dollars ? for 63 dollars ? At 9 cents a quart, how many quarts of cran- berries can be bought for 54 cents ? for 63 cents ? How many quarts of oats in 7 pecks of oats ? How many dozen eggs in 48 eggs ? How many gallons of milk in 36 quarts of milk ? LESSON 7. 117 7 X 2 = ? 7x3 = ? 7x4 = ? 7x5 = ? 7x6 = ? 7x7 = 7x8 = 7x9 = 14 H- 7 = ? 21 ^ 7 = ? 28 -H 7 = ? 35 H- 7 = ? Copy, and find the products : 12 12 11 11 11 3 4 5 6 7 42 ^ 7 = ? 49 + 7 = ? 56 -f- 7 = ? 63 ^ 7 = ? 11 8 11 9 41 3 41 4 41 5 41 6 41 7 41 8 41 9 60 3 60 4 60 5 60 6 60 7 60 8 60 9 31 3 31 4 31 5 31 6 31 7 31 8 31 9 70 3 70' 4 70 5 70 6 70 7 70 8 70 9 80 3 80 4 80 5 80 6 80 7 50 8 60 9 91 3 91 4 91 5 91 6 91 7 71 8 61 9 80 3 80 4 80 5 80 6 80 7 80 8 80 9 81 7 71 8 61 9 91 6 61 8 41 7 31 6 118 LESSON 8. A fly has 6 legs. How many legs have 9 flies ? A spider has 8 legs. How many legs have 7 spiders ? 6 spiders ? 4 spiders ? 3 spiders ? An ox has 8 hoofs. How many hoofs have 6 oxen ? 5 oxen ? 4 oxen ? 3 oxen ? A man bought 9 cords of wood at 4 dollars a cord, and gave 4 ten-dollar bills in payment. How much change should he receive ? James had 7 cents, and his father gave him six times as much. How many cents had he then ? Ernest has 9 five-cent pieces and 3 cents. How much money has he ? What will 9 sheep cost, at 6 dollars each ? At 7 cents a yard, what will 9 yards of cotton cloth cost ? What will 8 yards cost ? A farmer sold 9 lambs for 45 dollars. How much apiece did he get for them ? How many lengths of 9 yards each can be cut from a piece of silk 63 yards long ? In a schoolroom there were 63 seats arranged in 7 rows. How many seats in each row ? Find the cost of a dozen peaches at 3 for 5 cents. Find the cost of a dozen pears at 3 for 4 cents. A bushel of oats weighs 32 pounds. How many pounds will a peck weigh ? 3 pecks ? A bushel of corn weighs 56 pounds. How many pounds will a peck weigh ? 2 pecks ? At 56 cents a peck, how much must be paid for a quart of beans ? 2 quarts ? 4 quarts ? 6 quarts ? LESSON 9. SIXTY-FOUR. 64. 119 How many dots are there in each row ? How many rows are there ? How many dots in the eight rows ? How many dots, then, are 8 times 8 dots ? Count by 8's to 64. 8x8 = ? 64 ^ 8 = ? I of 64 = ? A man receives 8 dollars a week for work. How much does he receive in 8 weeks ? There are 8 pints in a gallon. How many pints are there in 8 gallons ? in 7 gallons ? When flour is 6 dollars a barrel, what will 8 bar- rels cost ? 9 barrels ? 7 barrels ? 4 barrels ? When blueberries are 8 cents a quart, what will 7 quarts cost ? 8 quarts ? 6 quarts ? 5 quarts ? At 7 cents a quart, what will a peck of beans cost ? What will 9 quarts cost ? What will 6 quarts cost ? What will 4 quarts cost ? If a freight train averages 8 miles an hour, in how many hours will it run 64 miles ? 56 miles ? 64-8 = ? 56-8 = ? 48-8 = ? 40-8 = ? 32 - 8 = ? 24 - 8 = ? 16 - 8 = ? 8 - — ? 120 LESSON 10. SEVENTY-TWO. 72. How many dots are there in each row ? How many rows are there ? How many dots in the eight rows ? How many dots, then, are 8 times 9 dots ? How many dots are there in each column ? How many columns are there ? How many dots in the nine columns ? How many dots, then, are 9 times 8 dots ? 9x8 = ? 1 of 72 = ? 72 - 8 = ? 72 -. 9 = ? 1 of 72 = ? iof 72 8 X 9 = ? J of 72 = ? At 8 dollars apiece, what will be the cost of 9 calves ? 7 calves ? 8 calves ? 6 calves ? At 9 cents a yard, what will be the cost of 8 yards of cambric ? 7 yards ? 6 yards ? A farmer sold 8 calves for 72 dollars. How much did he get apiece ? If 9 yards of muslin cost 72 cents, what is the price of the muslin a yard ? How many 9's in 36 ? in 54 ? in 63 ? in 45 ? in 72? in 27? in 18? How many dozen in 24 ? in 36 ? in 48 ? in 72 ? LESSON 11. 121 2x8 = =? 6x8 = ? 16-^2 = ? 48^6=? 3x8 = = ? 7x8 = ? 24h-3 = ? 56^7 = ? 4x8 = =? 8x8 = ? 32-^4 = ? 64^8 = ? 5x8 = = ? 9x8 = ? 40-5 = ? 72-9 = ? iofl6 = _? i-of 32 = ? ^of 48 = ? ^of 64 = ? 1 of 16 = _? |of 32 = ? I of 48 = ? 1 of 64 = ? i of 24 = = ? J of 40=? ^of 56 = ? iof72 = ? iof24 = =? iof 40 = ? jof 56=? i of 72 = ? Add; 23 31 27 36 47 75 35 49 33 67 51 24 47 36 29 73 68 37 72 53 32 21 33 22 36 67 76 89 98 57 84 74 88 37 65 84 39 38 31 53 29 37 46 21 19 27 37 18 Find the differences 225 87 313 56 321 28 337 89 235 88 312 147 482 279 663 392 671 289 817 465 476 279 567 378 676 387 576 378 637 239 122 LESSON 12. EIGHTY-ONE. 81. How many dots are there in each row ? How many rows are there ? How many dots in the nine rows ? How many dots, then, are 9 times 9 dots ? Comit by 9's to 81. 9x9 = ? 81-9 = ? If it takes 9 yards of cloth for a dress, how many yards will be required for 9 dresses ? If a family uses 9 pounds of sugar a week, how many weeks will 81 pounds last the family ? If it takes 7 eggs for a cake, how many eggs will be required for 9 cakes ? How many days are there in 9 weeks ? If it takes 9 yards of print for a dress, how many dresses can be made from 54 yards ? If you sleep 8 hours every night, how many hours will you sleep in 9 nights ? 2x9=? 6x9=? 18-9=? 54-9=? 3x9=? 7x9=? 27^9=? 63-9=? 4x9=? 8x9=? 36-^9=? 72-9=? 5x9=? 9x9=? 45^9=? 81^9=? LESSON 13. MULTIPLICATION TABLK. 123 2 3 1 4 5 TIMES TIMES TIMES TIMES 1 ARE 2 1 ARE 3 1 ARE 4 1 ARE 5 2 ARE 4 2 ARE 6 2 ARE 8 2 ARE 10 3 ARE 6 3 ARE 9 3 ARE 12 3 ARE 15 4 ARE 8 4 ARE 12 4 ARE 16 4 ARE 20 5 ARE 10 5 ARE 15 5 ARE 20 6 ARE 25 6 ARE 12 6 ARE 18 6 ARE 24 6 ARE 30 7 ARE 14 7 ARE 21 7 ARE 28 7 ARE 35 8 ARE 16 8 ARE 24 8 ARE 32 8 ARE 40 9 ARE 18 9 ARE 27 9 ARE 36 9 ARE 45 6 7 8 9 TIMES TIMES TIMES TIMES 1 ARE 6 1 ARE 7 1 ARE 8 1 ARE 9 2 ARE 12 2 ARE 14 2 ARE 16 2 ARE 18 3 ARE 18 3 ARE 21 3 ARE 24 3 ARE 27 4 ARE 24 4 ARE 28 4 ARE 32 4 ARE 36 5 ARE 30 5 ARE 35 5 ARE 40 5 ARE 45 6 ARE 36 6 ARE 42 6 ARE 48 6 ARE 54 7 ARE 42 7 ARE 49 7 ARE 56 7 ARE 63 8 ARE 48 8 ARE 56 8 ARE 64 8 ARE 72 9 ARE 54 9 ARE 63 9 ARE 72 9 ARE 81 124 LESSON 14. Kobert bought 2 postage stamps at 3 cents apiece. How much did he pay for them ? A buggy has 4 wheels. How many wheels are needed for 2 buggies ? At 5 cents each, how much will 2 car tickets cost ? At 6 cents a quart, how much wdll 2 quarts of peanuts cost ? At 7 cents a pound, what will be the cost of 2 pounds of loaf sugar ? At 8 cents a yard, what will 2 yards of calico cost? At 9 cents a cake, what will 2 cakes of soap cost ? If a horse goes 9 miles an hour for 3 hours, how many miles will he go in all ? A box has eight corners. How many corners have 3 boxes together ? If a pair of boots costs 7 dollars, how many dollars will 3 pairs of boots cost ? If an orange costs 3 cents, how many oranges can you buy for 21 cents ? for 27 cents ? for 24 cents ? for 18 cents ? for 12 cents ? At 3 cents apiece, how much will 4 oranges cost ? If a hat costs 4 dollars, how much will 4 hats cost? At 5 dollars a barrel, what will be the cost of 4 barrels of flour ? At 6 cents a quart, what will be the cost of a gallon of milk ? LESSON 15. 125 At 7 cents apiece, what will be the cost of 4 yard-sticks ? At 9 dollars a barrel, what will be the cost of 4 barrels of brown sugar ? At 8 dollars a load, what will 4 loads of bricks cost ? A farmer sold 5 pigs for 3 dollars apiece. How much did he get for his pigs all together ? A farmer sold 6 barrels of apples at 3 dollars a barrel. How much did the 6 barrels bring ? If one desk has 8 drawers, how many drawers will 5 desks of the same pattern have ? How many yards long is a piece of cloth that is 24 feet long ? How many pints of milk will a two-gallon can hold? How many quarts of oysters in 6 gallons of oysters ? The cook used 2 dozen eggs in making six pud- dings. How many eggs on the average did she use for each pudding ? At 5 cents apiece, how many bananas can be bought for 30 cents ? At 4 cents apiece, how many oranges can be bought for 24 cents ? At 3 cents apiece, how many can be bought for 24 cents ? At 6 cents a quart, how many quarts of berries can you buy for 18 cents ? for 36 cents ? for 30 cents ? for 24 cents ? for 42 cents ? for 48 cents ? 126 LESSON 16. If a quarter of a pound of candy costs 9 cents, what will a pound cost ? I have 40 cents in 5-cent pieces. How many 5- cent pieces have I ? At 10 cents a quire, how many quires of paper can be bought for 40 cents ? James has 50 cents in 10-cent pieces. How many 10-cent pieces has he ? If 36 pounds of starch are put up in 4-pound packages, how many packages will there be ? John has 54 cents. How many quarts of pea- nuts can he buy at 6 cents a quart ? Emma has 54 cents. How many yards of ribbon can she buy at 9 cents a yard ? At 8 cents a quart, what will 7 quarts of berries cost? At 7 cents a yard, what will 8 yards of cloth cost? Robert has 56 cents. How many packages of candy can he buy if each package is 8 cents ? An orchard has 56 trees, and there are 7 equal rows. How many trees in each row ? A certain schoolroom has 7 rows of desks, with 9 desks in each row. How many desks in the 7 rows ? A man can build 9 yards of fence in a day. How many days will it take him to build 63 yards? A dealer sold 7 plows for 63 dollars. What was the price of one plow ? LESSON 17. 127 A man took 6 eggs at a time seven times from a box of eggs. How many eggs did he take out ? If a ton of coal costs 6 dollars, how much will 9 tons cost ? If a cord of oak wood is worth 7 dollars, how much will 9 cords cost ? On a table there are 9 plates, and each plate has 9 peaches. How many peaches are on the table ? If one dozen buttons cost 8 cents, how much will 9 dozen buttons cost ? Ernest has 64 buttons. How many rows of 8 buttons each can he make ? If a box of butter weighs 7 pounds, how much will 8 boxes weigh ? It takes 6 candles to weigh a pound. How many pounds will 54 candles weigh ? At 7 dollars a pair, how many pairs of boots can be bought for 56 dollars ? for 63 dollars ? If three men together earn 9 dollars a day, in how many days will they earn 54 dollars ? If a man earns 8 dollars a week, in how many weeks will he earn 56 dollars ? There are 6 working days in a week. How many working days are there in 7 weeks ? If 9 persons ride in a coach, how many coaches will be required to carry 72 persons ? If a man has 48 horses, how many 6-horse teams can he form ? How many pecks in 56 quarts ? 128 LESSON 18. Copy and multiply : 94 2 43 3 62 4 51 5 71 7 81 8 71 9 91 8 81 7 61 6 31 5 92 4 920 3 930 2 610 9 710 8 910 7 810 6 210 9 310 8 710 7 910 6 810 5 920 4 622 4 911 5 711 6 911 7 811 8 911 9 913 3 944 2 811 5 810 7 101 8 901 9 Copy and divide : 2 )266 3 )273 7 )567 8 )648 3 )213 4 )484 5 )550 6)546 7 )567 9)549 6)546 7 )721 4)364 5)455 6)546 9)729 7)637 5)405 2)468 6)606 8)808 9)909 8)568 7)777 4)884 5)500 8)568 8)856 9)972 4)836 LESSON 19. 129 Count to a number greater than 100 : By 2's, beginning with 1 ; with 2. By 3's, beginning with 1 ; with 2 ; with 3. By 4's, beginning with 1 ; with 2 ; with 3 ; with 4. By 5's, beginning with 1 ; with 2 ; with 3 ; with 4 with 5. By 6's, beginning with 1 ; with 2 ; with 3 ; with 4 with 5 ; with 6. By 7's, beginning with 1 ; with 2 ; with 3 ; with 4 with 5 ; with 6 ; with 7. By 8's, beginning with 1 ; with 2 ; with 3 ; with 4 with 6 ; with 6 ; with 7 ; with 8. By 9's, beginning with 1 ; with 2 ; with 3 ; with 4 with 5 ; with 6 ; with 7 ; with 8 ; with 9. Note. Practice the above drill- exercise until every pupil can go through it readily. In counting by 2's, beginning with 2, we obtain 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc. These numbers are called even numbers. In counting by 2's, beginning with 1, we obtain 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, etc. These numbers are called odd numbers.' With what figures do even numbers end ? With what figures do odd numbers end ? Does any even number when divided by 2 give a remainder ? Which of the following numbers are odd, and which even ? 5, 7, 10, 26, 36, 38, 47, 50, 51, 55. 130 LESSON 20. How many ll's in 22 ? in 33 ? in 44 ? in 55 ? in 66? in 77? in 88 ? in 99 ? in 110? in 121 ? in 132 ? How many 12's in 24 ? in 36 ? in 48 ? in 60 ? in 72 ? in 84 ? in 96 ? in 108 ? in 120 ? in 132 ? in 144 ? How many eggs are 2 dozen eggs ? 3 dozen ? 4 dozen ? 5 dozen ? 6 dozen ? 7 dozen ? 8 dozen ? 9 dozen? 10 dozen? 11 dozen? 12 dozen? 2x11=? 7x11=? 2x12=? 7x12=? llx 2=? llx 7=? 12x 2=? 12x T= ? 3x11=? 8x11=? 3x12=? 8x12=? llx 3=? llx 8=? 12x 3=? 12x 8=? 4x11=? 9x11=? 4x12=? 9x12=? llx 4=? llx 9=? 12x 4=? 12x 9=? 5x11=? 10x11=? 5x12=? 10x12=? llx 5=? 11x10=? 12x 5=? 11x12=? 6x11=? 11x11=? 6x12=? 12x11= ? llx 6=? 11x12=? 12x 6=? 12x12=? At 12 cents each, what is the cost of 11 slates ? At 12 dollars each, what is the cost of 12 coats ? If a man works 9 hours a day, how many hours will he work in 2 weeks ? in one week and a half ? Twelve months make a year. How many months in 2 years ? in 7 years ? How many years in 36 months ? in 96 months ? Thirty-six inches make a yard. How many inches in 1 yard ? in I of a yard ? in 5 of a yard ? in § of a yard ? in 3 of a yard and i of a foot ? in i of a yard and h of a foot ? LESSON 21. 1 SQUARE FOOT. 131 This square represents a square foot. How many inches long is a side of the square ? How many square inches are there in the square ? 144 square inches make 1 square foot. A square the side of which measures 1 yard is called a square yard. If the side of a certain square is 1 yard long, how many feet long is it ? If you cut a square yard of brown paper into strips a foot wide, how many strips will you have ? How many square feet in each strip ? How many square feet in the three strips ? How many square feet, then, in a square yard ? 9 square feet make 1 square yard. How many square inches in a square 4 inches on a side ? 6 inches ? 7 inches ? 8 inches ? 9 inches ? How many square feet in a square 2 feet on a side ? 3 feet ? 4 feet ? 5 feet ? 6 feet ? 7 feet ? 132 LESSON 22. How many pecks in 8 quarts ? in 24 quarts ? How many pecks in 16 quarts ? in 32 quarts ? How many bushels in 8 pecks ? in 12 pecks ? How many bushels in 4 pecks ? in 16 pecks ? Add, and give the answers in bushels : 5 bu. 3 pks. 3 qts. 3 bii. 2 pks. 6 qts. 4 2 4 7 3 6 6 15 8 17 8 4 6 3 5 How many quarts in 2 pints ? in 6 pints ? How many quarts in 4 pints ? in 8 pints ? How many gallons in 8 quarts ? in 12 quarts ? Add, and give the answers in gallons : 5 gals. 3 qts. 1 pt. 8 gals. 2 qts. 1 pt. 6 2 1 6 3 7 2 1 9 3 1 8 3 1 7 3 How many feet in 12 inches ? in 24 inches ? in 36 inches ? in 48 inches? in 60 inches ? How many yards in 3 feet ? in 6 feet ? in 9 feet ? in 12 feet ? in 21 feet ? in 27 feet ? in 36 feet ? Add, and give the answers in yards : 6 yds. 1 ft. 9 in. 12 yds. 2 ft. 3 in. 5 2 7 ^ 7 2 6 3 2 2 How many square feet in 144 square inches ? How many square yards in 9 square feet ? in 18 square feet ? in 27 square feet ? in 36 square feet ? 15 1 4 13 2 3 19 2 LESSON 23. 133 The coins of the United States are made of gold, silver, nickel, or bronze. The double-eagle, the eagle, the half -eagle, and the quarter-eagle are made of gold. Twenty dollars make a double-eagle. Ten dollars make an eagle. Five dollars make a half-eagle. Two and one-half dollars make a quarter-eagle. The dollar, the half-dollar, the quarter-dollar, and ten-cent piece are made of silver. How many cents make a dollar ? One hundred cents make a dollar. How many cents make a half-dollar ? How many cent« make a quarter-dollar ? A ten-cent piece is often called a dime. How many cents make a dime ? The five-cent piece is made of nickel. A five-cent piece is often called a nickel. How many cents make a nickel ? The one-cent piece is made of bronze. A one-cent piece is often called a penny. How many dimes make a half-dollar ? How many nickels make a quarter-dollar ? How many quarter-dollars make a half-dollar ? How many nickels make a half-dollar ? How many quarter-dollars make a dollar ? How many dimes make a dollar ? How many nickels make a dollar ? 134 LESSON 24. The sign $ is called the dollar sign, and is placed before the figures. One dollar is written $ 1, or $ 1.00. Eleven dollars and twenty-five cents is written $11.25. The dot after the $ 11 in $ 11.25 means that the two figures on the right of it stand for cents, and the figures on the left of it stand for dollars. The dot between the figures for dollars and the figures for cents is called the decimal point. Read: $5.03; $7.27; $42.56; $12.23; $13.67; $67.53; $18.91; $98.01; $107.31; $121.02. How many places do the cents occupy? The cents always occupy two places. Write in figures : Three dollars and five cents. Forty-five dollars and seventy-three cents. Thirty-five dollars and sixty-seven cents. Nineteen dollars and eighteen cents. Eighty-nine dollars and ten cents. One hundred five dollars and two cents. One hundred seventeen dollars and one cent. One hundred three dollars and three cents. One hundred nine dollars and five cents. One hundred one dollars and one cent. Two hundred seventy dollars and nine cents. Two hundred dollars and eight cents. Three hundred dollars and twenty-five cents. Two hundred dollars and fifty cents. LESSON 25. 135 Add: $2.03 3.04 3.21 5.51 $8.12 7.32 5.13 6.41 $12.12 13.13 21.21 32.32 $14.05 11.10 31.32 23.50 $30.03 20.02 40.01 50.50 $5.43 1.27 3.19 $9.34 2.18 6.25 $8.27 9.36 10.19 $11.17 25.25 37.37 $13.37 72.26 87.19 Subtract . . $7.45 $7.89 $8.59 $9.33 $36.55 -5.03 -4.63 -5.26 -7.29 -28.00 $9.51 $5.65 $6.41 $6.73 $17.44 -3.28 -1.27 -2.38 -1.09 -8.36 Multiply : $1.13 $2.24 $5.10 $8.12 $9.08 3 4 5 6 7 $11.07 $12.09 $9.07 $7.09 $6.08 8 9 9 7 8 Divide : $16.08 by 2. $12.24 by 6. $56S6 by 8. $12.24 by 2. $24.12 by 6. $64.08 by 8. $18.36 by 3. $35.35 by 7. 854.54 by 9. $24.12 by 4. $49.42 by 7. $81.09 by 9. $25.05 by 5. $56.56 by 7. $63.72 by 9. 136 LESSON 26. Ten mills make 1 cent. What part of a cent is one mill? 2 mills? 3 mills ? 5 mills ? 7 mills ? 10 mills ? Since 1 mill is 1 tenth of a cent, how many cents are twenty mills ? 30 mills ? 50 mills ? We write mills on the right of cents. Two dollars 87 cents and 5 mills are written $2,875. Thirty-seven cents and 5 mills are written $ 0.375. Read: $3,607; $5,546; $18,364; $0,253. Write in figures : Seven dollars sixty cents and eight mills. Eleven dollars seventy-five cents and five mills. Twenty-one dollars two cents and two mills. Ninety-nine cents and seven mills. A ten-cent piece is often called a dime. Ten dimes make a dollar. What part of a dollar is 1 dime ? 2 dimes ? 3 dimes ? 4 dimes ? 5 dimes ? 6 dimes ? 10 dimes ? How many tenths of a dollar make the dollar ? How many tenths of a cent make the cent ? How many tenths of any unit whatever make the whole unit ? Tenths occupy one place, the first place to the right of the decimal point. • The number seven and three-tenths is written 7.3. The number 6.5 is read six and five tenths. The number 0.7 is read seven tenths. LESSON 27. 137 Since 100 cents make a dollar, 1 cent is 1 hun- dredth of a dollar. How many hundredths of a dollar are 2 cents ? 3 cents ? 5 cents ? 10 cents ? 25 cents ? 50 cents ? How many tenths of a dollar are 10 cents ? How many hundredths of a dollar are 10 cents ? How many hundredths, then, make 1 tenth ? 10 hundredths make 1 tenth. 10 tenths make 1 unit. The number, three and five hundredths, is writ- ten, 3.05. The number, two and sixty-four hun- dredths, is written, 2.64. Hundredths always occupy two places. Read: 5.08; 7.21; 10.54; 17.27; 65.65; 7.6; 6.07; 8.9; 8.09; 7.8; 7.08; 90.9; 90.09; 81.81. Write in figures : Five and five tenths. Seventy-five and eighty-six hundredths. Nine hundred one and nine hundredths. Seventy-six and twenty-five hundredths. Fifty-five and fifty hundredths. How many hundredths are : 8 hundredths + 9 hundredths ? 14 hundredths - 5 hundredths ? 16 hundredths - 7 hundredths ? 3x4 hundredths ? i of 63 hundredths ? 7x8 hundredths ? I of 56 hundredths ? 6x9 hundredths ? i of 36 hundredths ? 138 LESSON 28. The number denoted by figures at the right of the decimal point is called a decimal number, or simply a decimal. In adding or subtracting numbers containing decimals loe j^ut the decimal point in the result directly under the column of decimal points in the give7i number's. Add: 51.8 36.2 47.6 15.5 26.7 37.5 62.5 54.7 36.3 57.3 25.6 47.5 63.8 38.6 32.7 87.9 8.15 2.63 7.46 5.51 7.62 7.35 2.65 4.57 6.33 3.57 5.26 7.45 3.68 6.38 2.37 7.89 8.51 -2.36 7.62 -3.57 6.33 -3.75 8.63 -6.83 92.3 -35.7 64.7 -26.5 62.5 -45.7 75.4 -b5.b 9.32 -7.25 6.74 -2.65 2.56 -1.19 7.37 -2.89 3.77 -1.98 81.2 -36.9 47.6 -28.7 56.2 -19.5 LESSON 29. 139 A farmer paid $160 for a horse and i as niucli for a cow. How much did he pay for the cow ? A lady bought some blankets for $ 15 and some silk for $25. She gave ten-dollar bills in pay- ment. How many bills did she give ? A boy bought a pair of boots for $4.25. He gave a five-dollar bill in payment. How much change did he receive ? A man earned in a week $19.50, and spent $ 12.25. How much did he save ? James earned $6.25, and his brother gave him enough to make $ 10. How much did his brother give him ? What will 9 barrels of flour cost at $6.10 a barrel ? What will 8 sheep cost at $6.10 apiece ? What will 5 hats cost at $3.10 apiece ? A lady bought a shawl for $11.50, and a hat for $ 8. She gave a twenty-dollar bill in payment. How much change did she receive ? Henry bought 3 pounds of beefsteak at 23 cents a pound, and gave a dollar-bill in payment. How much change did he receive ? At $ 0.50 a pound, how many pounds of Jersey butter can be bought for $2.50 ? How many pounds of coffee at $0.30 a pound can be bought for $ 0.90 ? At 8 cents a pound, how many pounds of rice can be bought for $0.56 ? 140 LESSON 30. THE YEAR. How many months make one year ? Twelve months make a year. The names of the months in order are : January, February, March, April, May, June, July, August, September, October, November, De- cember. The spring months are March, April, May. The summer months are June, July, August. The autumn months are September^ October, November. The winter months are December, January, Feb- ruary. Spring, summer, autumn, winter, are called the four seasons of the year. Thirty days have September, April, June, and November. Febiniary has 28 days, and in leap years 29 days. The other months have 31 days each. Three hundred sixty-five days make a year. Three hundred sixty-six days make a leap year. When the date of the year can be divided by 4 without remainder, or in case the date ends in two zeros by 400, the year is a leap year. Which of these years are leap years ? 1800 ; 1860; 1872; 1890; 1893; 1892; 1900; 2000. In a common year, how many days from the be- ginning of the year to February 15 ? to March 31 ? to April 7 ? to May 1 ? to June 14 ? to July 20 ? LESSON 31. 141 THOUSANDS. The number, 10 hundred, is called a thousand. A thousand is written 1,000. A thousand and one is written 1,001. Ten thousand and ten is written 10,010. One hundred twenty thousand four hundred is written 120,400. How many thousands and how many ones in 7,632 ? 50,023 ? 41,701 ? 417,203 ? 500,230 ? Write in figures and read all the numbers from 4,002 to 4,020; from 80,997 to 81,010; from 537,091 to 537,102 ; from 748,987 to 749,000. Read: 5,430; 3,072; 1,010 ; 45,320 ; 70,045; 40,309; 36,008; 113,079; 273,002; 182,012; 811,200; 100,256; 500,005; 300,023; 608,300. Write in figures : Four thousand. Three thousand seven. Six thousand ten. Five thousand fifteen. Eight thousand three. Nine thousand seven hundred. Six thousand twenty-eight. Seventy-four thousand six hundred. Fifteen thousand five hundred. Sixty-nine thousand thirty-two. Seventy-three thousand five hundred forty-six. Eight hundred thousand seven hundred five. Ninety-six thousand eight hundred fifty-six. Two hundred fifty thousand two hundred fifty. Two hundred five thousand two hundred five. 142 LESSON 32. MIT^LIONS. When we write numbers which contain thousands and ones, we generally leave a little space after the last figure of the thousands, and put a comma in this space. Thus, 236 347 is written 236,347. This comma divides the figures into two periods, the period of thousands and the period of ones. Forty-eight thousand and thirty-six sheep is writ- ten, 48,036 sheep. Here we write 48 for the word forty-eight ; then put a comma after the 8 for the word thousand ; then 0, as there are no hundreds, and lastly, 36 for the word thirty-six. The unit for the ones' period is 1 sheep. The unit for the thousands' period is 1000 sheep. The unit for the next higher period is a million. A million is 1000 thousands, and is written 1,000,000. The unit of any period is equal to 1000 units of the next lower period. Three hundred million two hundred forty-six thousand five hundred dollars is written $300,246,500. Here we put a comma after the 300 for the word million, and after the 246 for the word thousand. The left-hand period may have one, two, or three figures, but every other period must have three fig- ures, one figure for the hundreds, one for the tens, and one figure for the ones, of that period. LESSON 33. 143 How many millions, thousands, and ones in 50,032,106 ? 41,107,106 ? 500,200,300 ? Read : 32,027,020 316,106,207 100,370,200 70,000,035 275,701,050 170,202,305 75,017,500 28,028,280 57,207,005 202,170,503 10,987,278 111,798,827 65,371,954 210,007,500 87,250,520 120,052,250 54,054,540 540,504,054 95,720,027 905,059,950 Write in figures : Thirty million, twenty-seven thousand, one hun- dred twenty dollars ? Two hundred seven million, seven hundred twenty thousand, three hundred dollars. Ninety-five million, fifty-nine thousand, one hundred sixty-six dollars. Five hundred nine million, five hundred four thousand, five hundred forty dollars. Twenty million, two hundred twenty thousand, three hundred sixty-four dollars. Nineteen million, nineteen thousand, nine hun-- dred nineteen dollars. Thirty-seven million, three hundred thirty-seven thousand, seven hundred dollars. Two hundred twenty million, three hundred thirty thousand, four hundred forty dollars. 144 LESSON 34. THOUSANDTHS AND TEN-THOUSANDTHS. If a unit is divided into ten equal parts, each part is called a tenth of the unit ; if into a hundred equal parts, each part is called a hundredth ; if into a thou- sand equal parts, each part is called a thousandth ; if into ten thousand equal parts, each part is called a ten- thousandth. Note. The Teacher should use the meter stick to show the deci- mal parts of a unit. The decimeters show the tenths, the centimeters the hundredths, and the millimeters the thousandths, of the meter. Tenths occupy one decimal place 0.1 Hundredths occupy two decimal places .... 0.21 Thousandths occupy three decimal places . . . 0.213 Ten-thousandths occupy four decimal places . . 0.2134 The decimal 0.1 is read one tenth ; 0.21 twenty- one hundredths ; 0.213 two hundred thirteen thou- sandths ; 0.2134 twenty-one hundred thirty-four ten-thousandths ; 4.4045 is read four and four thousand forty-five ten-thousandths. Note. In reading a number, part of which is integral and part decimal, pronounce and at the decimal point and omit it in all other places. Read: 1.09; 23.023; 50.107; 7.0017; 7.0209; 5.5055; 2.3785; 15.0015; 6.2567. Write in figures : two and five tenths ; two and five hundredths ; two and five thousandths ; two and five ten-thousandths ; two and twenty-five hun- dredths ; two and twenty-five thousandths ; two and twenty-five ten-thousandths ; two and two hun- dred twenty-five thousandths ; two and two hundred twenty-five ten-thousandths. LESSON 36. 146 ADDITION. To test the correctness of the work in addition, we add in a different order. The results should be the same. Thus, if we have added from the bottom to the top, we add from the top to the bottom. 1. 2. 3. 4. 5. 6. 7. 321 615 522 178 312 124 673 502 143 617 512 723 780 485 279 687 843 296 677 379 289 8. 9. 10. 11. 12. 13. 4321 3214 5423 8372 70.52 58.23 2751 5467 6543 543 53.84 1.92 6284 873 7654 7941 98.72 64.95 863 9124 6785 9078 8.76 8.67 Arrange and add, taking care to have units of the same order stand in the same column. Decimals are easily arranged by taking care to have the decimal points stand in a vertical column. 14. 43,307; 96,812; 60,798; 21,121. 15. 83,654; 34,747; 58,659; 32,321. 16. 59.852; 41.664; 68.054; 90.594. 17. 10.5921; 27.3007; 31.9789; 2.563. 18. $5.86; 1561.75; 128.32; $40.50. 19. 121,016; 167,404; 84,121; m^^Q. 20. 90.0542; 32.8971; 55.674; 348.78. 21. 64.3372; 6.4337; 0.3723; 100.733. 22. 0.415; 70.634; 121.5007; 8.3467. 23. 8.0213; 15.101; 12.0031; 0.2256. 24. 121.0015; 100.37; 148.561; 1121.505. 25. 15.86; $8.78; $11.89; $12.58; $95.37; $59.88. 146 LESSON 37. SLATE EXERCISES. 1. John Dix deposited in the Third National Bank of Boston $ 4321, and a week later $ 13,893. How much did he deposit in all ? 2. The steamer Majestic made on four successive days 503, 504, 505 and 505 miles. How many miles did she make in the four days together ? 3. In 1890 the population of New York was 1,513,501, of Brooklyn 804,377, and of Jersey City 162,317. What was the population of these three cities ? 4. In 1890 St. Louis had 460,357 inhabitants, Boston had 447,720, Baltimore 432,095, and San Francisco 297,990. How many had these four cities together ? 5. In 1890 Chicago had 1,098,576 inhabitants, Milwaukee 206,308, Minneapolis 164,738, St. Paul 133,156. How many had these four cities together ? 6. In 1890 Philadelphia had 1,044,894 inhabi- tants, Pittsburgh 238,473, Alleghany 104,967, Scranton 83,450. What is the population of the four largest cities of Pennsylvania ? 7. In 1890 Cincinnati had 296,309, Cleveland 261,546, Buffalo 255,543, Detroit 205,669. How many had these four cities together ? 8. In 1890 Washington had 228,160, New Orleans 241,995, Louisville 161,005, and Rich- mond 80,838. Find the population of these four cities together. LESSON 38. 147 SUBTRACTION. To test tlie correctness of the work in subtrac- tion, we add the subtraliend and the remainder. The sum shouhl be equal to tlie minuend. Subtract 427 from 736. Beginning on the right, subtract 7 from 1(5, and write 9 below. Afterwards subtract 2, not from 3, but from 2, and write 3^9 below. Then subtract 4 from 7, and write 3 below. 736 427 Subtract 7658 from 9000. 9000 Subtract 8 from 10, and write 2; then subtract 5, not 7658 from 10, but from 9, and write 4 ; again, subtract from 9, TqTq" and write 3 ; then subtract 7 from 8, and write 1. Proof. Add 7658 1342 9000 Proof. Add 427 309 736 Subtract : 1. 873 169 6. 3850 1929 11. 60570 48692 16. 462085 345396 2. 679 298 7. 5435 1567 12. 20729' 17934 17. 701406 243859 3. 700 177 8. 5634 5284 13. 32405 21657 18. 740052 698253 4. 901 475 9. 9005 6476 14. 20604 11847 19. 402701 317485 5. 506 347 10. 3401 2085 15. 60004 28597 20. 400100 375916 148 LESSON 39. SUBTRACTION OF DECIMALS. In the subtraction of decimals, make the number of decimal places in the minuend and subtrahend the same, annexing zeros if necessary. Subtract 25.468 from 62.1253 ; and 2.1789 from 7.2. OPERATION. OPERATION. 52.1253 7.2000 25.4680 2.1789 26.6573 5.0211 Arrange so that the decimal point of the subtra- hend shall be under that of the minuend, and subtract : 1. 0.85 - -0.79. 16. 13.2589-10.06. 2. 1.76 - -0.98. 17. 71.1002-52.387. 3. 2.729- -1.836. 18. 11.2487-5.3579. 4. 5.482- -3.176. 19. 10.9041-9.8765. 5. 2.354- -2.287. 20. 17.3258-16.37. 6. 3.826- -3.719. 21. 2.5-0.025. 7. 5.902- -3.678. 22. 75 -0.7575. 8. 5.77 - -4.888. 23. 1.52-1.0024. 9. 9.62 - -3.765. 24. 129.5-96.349. 10. 8.42 - -5.661. 25. 0.157-0.1547. 11. 7.23 - -6.562. 26. 752.8-4.9732. 12. 9.02 - -7.163. . 27. 819.3-57.687. 13. 4.31 - -3.425. 28. 83.52-64.743. 14. 1.27 - -1.198. 29. 61.98-4.3554. 15. 1.46 - -o.or,", 30. 6.716-0.8725. LESSON 40 149 SLATE EXERCISES. 1. Shakespeare was born in 1564 and died in 1616. How many years did he live ? 2. Milton was born in 1608 and died in 1674. How many years did he live ? 3. Daniel Webster died in 1852 at the age of 70. In what year was he born ? 4. President Washington's first inaugural ad- dress contained 1300 words. His second inaugural address contained 134 words. How many more words did the first contain than the second ? 5. President Lincoln's first inaugural address contained 3500 words. His second inaugural ad- dress contained 580 words. How many more words did the first contain than the second ? 6. The population of Kansas City was 55,585 in 1880, and 132,416 in 1890. Find the increase. 7. The population of Denver was 35,629 in 1880, and 106,670 in 1890. Find the increase. 8. The population of Omaha was 30,518 in 1880, and 139,526 in 1890. Find the increase. 9. The number of silk looms in the United States in 1880 was 8474, and in 1890 the number was 22,569. Find the increase. 10. There are CL Psalms. James has read XCIX. How many more has he to read ? 11. A woman bought groceries to the amount of 1 3.83. She gave a five-dollar bill in payment. How much change should she receive ? 150 LESSON 41. MULTIPLICATION. If a product greater than 9 is obtained in multi- plying, the figure for the ones only is written, and the tens are added to the following product. Thus, in the problem in the margin 4 x 8 = 32, we write the 2 ; then 4x5 tens = 20 tens, and to the 20 tens we add the 3 tens of the last product, obtaining 23 tens or 2 hun- dreds and three tens ; we write the 3 ; then 4x3 hundreds = 12 hundreds, and to the 12 hundreds we add the 2 hundreds of the last product, obtaining 14 hundreds, which we write. The entire product is therefore 1432. 358 4 1432 1. 2x3687. 2. 2x4783. 3. 3x2879. 4. 3x3657. 5. 5x1953. 6. 5x2849. 7. 4x3567. 8. 4x2586. 9. 5x6852. 10. 6x1376. 11. 6x5647. 12. 6x3124. 13. 3x8798. 14. 7x2342. 15. 8x4323. 16. 9x5215. 17. 4x7826. SLATE EXERCISES. 18. 5x8267. 19. 6x6754. 20. 7x7854. 21. 7x9384. 22. 8x4337. 23. 3x9785. 24. 3x8694. 25. 7x2334. 26. 9x1682. 27. 5x9889. 28. 4x8977. 29. 6x9778. 30. 7x3879. 31. 9x3355. 32. 8x6675. 33. 7x8643. 34. 9x6854. 35. 4x29354. 36. 5x70528. 37. 6x56713. 38. 7x31567. 39. 8x37582. 40. 9x56014. 41. 9x34749. 42. 9x36927. 43. 9x73186. 44. 8x25839. 45. 7x98325. 46. 8x63578. 47. 9x67489. 48. 7x38697. 49. 9x48769. 50. 7x57009. 51. 8x99798. LESSON 42. 151 If the multiplier has two or more figures : We 7n.ultiply hy eachfitjure separately, taking care to jyut the first figure of each product directly under the figure of the multiplier used in obtaining it ; and add the products. Thus, Proof. 2046 7235 ' 7235 2046 10230 43410 6138 28940 4092 14470 14322 14802810 14802810 The multiplicand and multiplier are called fac- tors of the product. If either factor is 0, the product is 0. The product of two factors is not changed if the order of the factors is changed. To jjrove multiplication, we change the order of the factors, and multiply again. The products should be the same in both cases. Multiply : 1. 114 by 32. 11. 714 by 48. 21. 3159 by 507. 2. 112 by 76. 12. 578 by 97. 22. 3819 by 206. 3. 365 by 56. 13. 842 by 86. 23. 8769 by 517. 4. 372 by 23. 14. 682 by 69. 24. 5731 by 475. 5. 283 by 64. 15. 792 by 79. 25. 8592 by 486. 6. 564 by 47. 16. 8763 by 407. 26. 7069 by 908. 7. 259 by 57. 17. 8437 by 502. 27. 5604 by 609. 8. 538 by 38. 18. 9872 by 603. 28. 6789 by 789. 9. 467 by 59. 19. 7356 by 805. 29. 4769 by 687. 10. 736 by 94. 20. 5983 by 704. 30. 6897 by 976. 152 LESSON 43. If the multiplier is 10, 100, 1000, etc., we obtain the product by annexing to the multiplicand as many zeros as there are in the multiplier. Thus, 100 times 746 is 74,600. In short, if one or both factors end in zeros, we multiply without regard to the zeros. Then we annex to the product as many zeros as there are at the ends of the factors together. Thus, To multiply 74,200 by 230, we first multiply 742 by 23, and obtain 17,066. To this number we an- nex 3 zeros, and get 17,066,000 for the true result. Multiply : 1. 467 by 10. 9. 56000 by 3480. 2. 312 by 100. 10. 50060 by 7000. 3. 587 by 1000. 11. 50400 by 2080. 4. 6112 by 3000. 12. 47000 by 2070. 5. 7281 by 4000. 13. 504304 by 100. 6. 8127 by 5000. 14. 7120 by 7002. 7. 43070 by 2000. 15. 102039 by 112000. 8. 43200 by 2340. 16. 932600 by 184900. 17. If a man takes 180 steps a minute, how many steps will he take in an hour ? 18. If a man takes 2400 steps a mile, how many steps will he take in walking 20 miles ? 19. A cat has 18 toes. How many toes will 6000 cats have ? 20. At 60 cents a yard, what will be the cost of digging a drain 350 yards long ? LESSON 44. 153 If one or both factors have decimal places : We multiply without regard to the decimal point. Aftenvards we point of in the product as many decimal places as there are decimal places in the two factors together. Thus : Multiply 20.15 by 0.05. 20.15 0.05 1.0075 We multiply 20.15 by 0.05 and obtain 10075. As there are 2 decimal places in the multiplicand and 2 in the multiplier, we point off 4 decimal places in the product and have 1.0075, one and seventy-five ten-thousandths. SLATE EXERCISES. Multiply : 1. 0.541 by 444. 13. 22.74 by 0.525. 2. 0.853 by 232. 14. 3792 by 0.024. 3. 3764 by 0.47. 15. 0.715 by 141.5. 4. 32.12 by 1.73. 16. 466.4 by 45.06. 5. 7860 by 46.8. 17. 3.417 by 1000. 6. 0.623 by 373. 18. 0.955 by 10000. 7. 763.2 by 8.65. 19. 6781 by 1.007. 8. 68.42 by 75.5. 20. 527.1 by 0.103. 9. 8730 by 0.05. 21. 56.95 by 0.45. 10. 2.406 by 0.35. 22. 426.8 by 0.204. 11. 0.048 by 723. 23. 84.49 by 54.49. 12. 0.008 by 2.05. 24. 700.7 by 7.071. 154 LESSON 45. SLATE EXERCISES. 1. A clock that strikes the hours, and 1 for the first quarter, 2 for the second and 3 for the third quarter, of each hour, strikes 300 times a day. How many times will it strike in a common year ? 2. A clock that strikes the hours only, strikes 156 times in a day. How many times will it strike in a leap year ? 3. If corn is $1.12 a bag, how much will 60 bags cost ? 4. If coal is $ 5.75 a ton, how much will 17 tons cost ? 5. If pine wood is $ 3.50 a cord, how much will 19 cords cost ? 6. A farmer has 37 acres of corn worth on the average $27 an acre. What is the total value of his corn crop ? 7. The earth moves in its orbit 19 miles a sec- ond. How many miles does it move in 1 minute ? 8. If a bricklayer earns on the average $ 20.25 a week, how much will he earn in 28 weeks ? 9. The lunar month is 29.53 days. How many days are there in 12 lunar months ? 10. Sound travels at the rate of 1120 feet a second. Find the distance of a thunder-cloud when the thunder is heard 13 seconds after the lightning is seen. 11. A dealer sold 27 bushels of potatoes at 30 cents a peck. How much did he receive ? LESSON 46. 155 Divide 654 by 3. Here 6 -f- 3 = 2, and as 6 is in the place of hundreds, we 3) 654 write 2 in the place of hundreds under the 6. oTc Then 5 4-3 = 1, with remainder 2. ^^^ We write the 1 in the place of tens, under the 5. The remainder 2 is 2 tens or 20 ones, and 20 ones put with the 4 ones make 24 ones. Then 24 -f- 3 = 8, and we write 8 in the place of ones, under the 4. The quotient, therefore, is 2 hundreds, 1 ten, and 8 ones ; that is, 218. Divide 564 by 3. Here 5-^3 = 1, with remainder 2. We write the 1 in g'\ 554 the place of hundreds, under the 6. ^ ^^ The remainder 2 is 2 hundreds, or 20 tens, and 20 tens loo put with 6 tens make 26 tens. Then 26 -4- 3 = 8, with remainder 2. We write the 8 in the place of tens, under the 6. The remainder 2 is 2 tens, or 20 ones, and 20 ones put with 4 ones make 24 ones. Then 24 h- 3 = 8, and we write 8 in the place of ones, under the 4. The quotient, therefore, is 1 hundred, 8 tens, and 8 ones ; that is, 188. Divide 765 by 9. Since 7 will not contain 9, we take for the first par- 9) 765 tial dividend 76. Then 76 -j- 9 = 8 with remainder 4, and ^ — ^ as 6, the last figure of this dividend, is in the place of "^ tens, we write the quotient 8 in the place of the tens under the 6. The remainder 4 is 4 tens or 40 ones, and 40 ones put with the 5 ones make 45 ones. Then 45 - 9 = 5. Tlie quotient, therefore, is 8 tens and 5 ones ; that is, 85. 156 LESSON 47. Divide by 2 : 468 456 372 332 634 972 326 254 214 548 418 908 Divide by 3 : 354 365 624 484 408 798 444 235 651 790 891 976 Divide by 4 : 924 824 956 564 592 918 752 912 734 723 712 513 Divide by 5 : 510 520 640 770 590 745 665 735 560 880 620 825 Divide by 6 : 666 636 732 726 822 924 624 720 744 810 846 933 Divide by 7 : 728 784 812 861 910 945 742 797 805 875 931 952 Divide by 8 : 808 832 912 336 416 256 816 840 920 352 424 264 Divide by 9 : 927 945 405 378 288 135 936 918 396 387 297 225 LESSON 48. 157 SHORT I>IVISIOX. When the divisor is so small that the work can be performed mentally, the process is called short division. Divide 63169 by 7. 7 )63169 9024 with rem. 1. Wording : 7 in 63, 9 ; in 1, ; in 10 2 ; in 29, 4 ; witli rem. 1. ExpLAXATioN : Since 7 is not con- tained in 6, we take two figures 63 for the first partial dividend, and write the quotient 9 under the right-hand figure 3 of this partial dividend. 7 is not contained in 1 , so is written as the second figure of the quotient, and this 1, which is equal to 10 units of the next lower order of units, is joined to the 6, and makes 16 for the next partial dividend. Then 16 is divided by 7 ; the quotient is 2 and the remainder 2 ; the remain- der 2 is equal to 20 of the next lower order of units, and with the 9 makes 29. Then 29 is divided by 7 ; the quotient is 4 and the remain- der 1. Therefore the quotient is 9024, and the remainder is 1. To prove division, we find the product of tlie divisor and quotient, and to this product add the remainder. The result should be equal to the dividend. Proof. 9024 7 63168 1 63169 The product of the divisor and quotient is G3168. To this product add the remainder 1, and the result is 63169, the same as the dividend. Divide $54322 by 19. $9 )854322 6035 with $7 rem. In this example we are required to find the number of times we can take away $9 from .$ 54322. The answer is 6035 times, with $7 over. The complete quotient may be written 6035f Divide $54322 by 9. 9 ) $54322 $6035 with $7 rem. In this example we are required to divide $54322 into nine eqnal parts, and to find the number of dollars in each part. The answer is 6035 dollars, with $ 7 over. The answer may be written .^i 6035|. 158 LESSON 49. The last two examples illustrate the dif ferent mean- ings of division. If the divisor and dividend refer to the same kind of units, the quotient denotes the number of times the divisor must be taken tc > equal 1 :he dividend. If the divisor is an abstract number as 2, i B, 4, etc., the quotient denotes a number of units of the same kind as the units of the dividend. Divide : 1. 434 by 2. 23. 5794 by 2. 45. 95874 by 2. 2. 876 by 3. 24. 5874 by 3. 46. 45873 by 3. 3. 596 by 4. 25. 5696 by 4. 47. 46372 by 4. 4. 432 by 4. 26. 8975 by 5. 48. 78295 by 5. 5. 180 by 5. 27. 3354 by 6. 49. 66372 by 6. 6. 715 by 5. 28. 1176 by 7. 50. 92582 by 7. 7. 875 by 5. 29. 8568 by 8. 51. 87824 by 8. 8. 618 by 6. 30. 2943 by 9. 52. 98172 by 9. 9. 324 by 6. 31. 3711 by 2. 53. 78956 by 7. 10. 819 by 7. 32. 3226 by 3. 54. 65978 by 8. 11. 847 by 7. 33. 8467 by 4. 55. 76598 by 6. 12. 920 by 8. 34. 9573 by 5. 56. 83621 by 3. 13. 904 by 8. 35. 6983 by 6. 57. 86123 by 6. 14. 945 by 9. 36. 8659 by 7. 58. 38612 by 9. 15. 621 by 9. 37. 4329 by 8. 59. 12386 by 7. 16. 513 by 2. 38. 8256 by 9. 60. 50080 by 8. 17. 707 by 3. 39. 5879 by 3. 61. 65387 by 7. 18. 845 by 4. 40. 7361 by 9. 62. 75429 by 5. 19. 901 by 5. 41. 6539 by 8. 63. 31285 by 6. 20. 862 by 6. 42. 5396 by 7. 64. 29514 by 9. 21. 872 by 7. 43. 9751 by 3. 65. 65387 by 8. 22. 907 by 9. 44. 6857 by 7. 66. 57148 by 3. LESSON 50. 159 LONG DIVISION. The process of Long Division is the same as that of Short Division, except that the work is written in full, and the quotient is written over the dividend. Divide 31864 by 87. The beginner will find it convenient to form a table of products of the divisor by the numbers 1, 2, 3, ..., as follows: 1 1 X 87 = 87 4 X 87 = 348 7 X 87 = 009 2 X 87 = 174 6 X 87 =3 435 8 X 87 = 696 3 X 87 = 261 6 X 87 = 522 9 X 87 = 783 As 87 is more than 31, it is necessary to take three figures of the dividend for the first partial dividend. Of the products in the table OPERATION. 366 87)31864 261 576 522 544 522 22 rem. that do not exceed 318, the greatest is 261 ; that is, 3 X 87. Hence the first quotient figure is 3, and is written over the 8, the right, hand figure of the first partial dividend ; then 261 is subtracted from 318. To the remain- der 57, the next figure 6 of the dividend is annexed. Of the products that do not exceed 576, the greatest is 522 ; that is, 6x87. Hence 6 is the next figure of the quotient, and the next remainder is 54, to which the 4 of the dividend is annexed. Of the products that do not ex- ceed 544, the gTcatest is 522 ; that is, 6 x 87. Hence the next figure of the quotient is 6, and the remainder 22. Therefore the quotient is 366, and the remainder 22. After a little practice the operation of division can be performed without the aid of a table of products. If at any step the product is greater than the partial dividend, the number denoted by the quotient-figure is too large and must be diminished ; if the remainder is greater than the divisor, the number denoted by the quotient-figure is too small and must be increased. 160 LESSON 51. Divide 1006078 by 247. The first partial dividend is 1006. We find that 5 x 247 is 1235, OPERATION. which is greater than 1006, and therefore 5 Af\no is too large. We try 4, and find that 4 x 247 ^^LIA is 988. We write the 4 over the 6, the z47}10Ud07o right-hand figure of the partial dividend, 988 and subtract the 988 from 1006. To the 1807 remainder 18 we annex 0, the next figure 1729 of the dividend, and have 180. Since 247 <7QQ is not contained in 180, we write for the rjA-t next figure of the quotient, and annex to — — - 180 the next figure of the dividend, 7. The 4< rem. j^g^t figure of the quotient is not 9, for 9x247=2223, and is not 8, for 8x247 = 1976, and each of these prod- ucts is greater than 1807. We try 7, and find the product to be 1729, which is less than 1807. The remainder obtained by subtracting 1729 from 1807 is 78, to which we annex the 8 of the dividend, and have 788. The next figure of the quotient is 3, and the product of 3 x 247 is 741. Subtracting 741 from 788 we get 47 for the remainder of the division. Hence the quotient is 4073, and the remainder 47. Divide : 1. 5938 by 36. 13. 8757 by 67. 25. 8332 by 71. 2. 5743 by 37. 14. 9212 by 91. 26. 9888 by 93. 3. 9853 by 49. 15. 2786 by 22. 27. 7112 by 43. 4. 7369 by 52. IG. 3764 by 29. 28. 2931 by 19. 5. 9423 by 63. 17. 6753 by 57. 29. 9213 by 29. 6. 6578 by 74. 18. 9362 by 89. 30. 8778 by 55. 7. 6457 by 59. 19. 8579 by 73. 31. 61238 by 101. 8. 3579 by 21. 20. 8957 by 79. 32. 86123 by 201. 9. 7436 by 34. 21. 7319 by 53. 33. 38612 by 302. 10. 4589 by 42. 22. 8609 by 61. 34. 23816 by 205. 11. 5936 by 47. 23. 6891 by 31. 35. 12386 by 502. 12. 8372 by 65. 24. 3954 by 23. 36. 83216 by 603. LESSON 52. 1. 98245 by 704. 28. 200836 by 897. 2. 59824 by 215. 29. 650734 by 635. 3. 45982 by 316. 30. 573206 by 753. 4. 82459 by 638. 31. 732065 by 537. 5. 93827 by 859. 32. 723540 by 871. 6. 96548 by 789. 33. 680023 by 997. 7. 84596 by 627. 34. 650734 by 736. 8. 23469 by 295. 35. 572036 by 853. 9. 24963 by 468. 36. 704532 by 973. 10. 59376 by 261. 37. 432960 by 187. 11. 56379 by 237. 38. 349062 by 259. 12. 79476 by 732. 39. 802365 by 795. 13. 67532 by 557. 40. 690409 by 389. 14. 70456 by 678. 41. 109370 by 167. 15. 80026 by 709. 42. 963047 by 398. 16. 72345 by 567. 43. 750431 by 578. 17. 90365 by 463. 44. 895047 by 757. 18. 78659 by 741. 45. 938704 by 198. 19. 94158 by 429. 46. 618543 by 4021. 20. 48519 by 229. 47. 816354 by 2008. 21. 67857 by 479. 48. 543168 by 4307. 22. 99321 by 912. 49. 604307 by 4803. 23. 79132 by 811. 50. 729718 by 5184. 24. 83742 by 566. 51. 542385 by 4978. 25. 650734 by 537. 52. 604730 by 4758. 26. 732065 by 631. 53. 817279 by 9814. 27. 704523 by 873. 54. 729718 by 4918. 161 162 LESSON 53. ORAL. EXERCISES. 1. If 3 cords of wood cost $ 9, what will 4 cords cost? Note. Require the pupil to analyze this and similar problems by the unitary method. Thus, if 3 cords cost $9, 1 cord will cost | of $ 9, or $ 3 ; and 4 cords will cost 4 x 1 3, or $ 12. 2. If 4 men can mow a field in 6 days, how many days will it take 3 men to mow the field ? Analysis. If it takes 4 men 6 days to mow a field, it will take 1 man 4x6 days, or 24 days ; if it takes 1 man 24 days to mow a field, it will take 3 men i of 24 days, or 8 days. 3. Find the cost of 7 barrels of flour, if 8 barrels cost $40. 4. Find the cost of 12 oranges, if 5 oranges cost 15 cents. 5. What will 12 lambs cost, if 3 lambs cost |12? 6. If 12 men can dig a certain ditch in 6 days, how many men will be required to dig the ditch in 8 days ? 7. If 8 pounds of sugar cost 40 cents, how many cents will 11 pounds cost? 8. If 3 tons of coal cost $ 21, how much will 8 tons cost? 9. If 4 men can build a wall in 5 days, how many men will be required to build it in 4 days ? 10. If 3 yards of cloth are worth $6, how much are 7 yards worth ? 11. If 2 lamps cost $ 8, what will 5 lamps cost ? 12. If 9 yards of muslin cost 63 cents, what will 8 yards cost ? 13. If 8 men can do a piece of work in 9 days, how many days will it take 6 men to do it ? 14. How many pounds of butter at 20 cents a pound must be given for 2 pounds of tea at 60 cents a pound? Part IV. LESSON 1. DIVISION OF DECIMALS. In Division, if the dividend and divisor are both mul- tiplied or both divided by the same number, the quotient is not changed. Thus, 18-!- 6 = 3, and (when both divi- dend and divisor are multiplied by 2) 36-^12 = 3. Again (when both dividend and divisor are divided by 2), 9-3 = 3. If the divisor is a whole number, and the dividend has decimals : We divide as in ivhole numbers^ hut 2vrite the decimal point in the quotient as soo7i as the decimal point in the dividend is reached. Divide 1.29 by 3. 3)1.29 Since 3 is not contained in 1, we write under the 1 ; A Ao then the decimal point, and afterwards we continue, 3 in 12, 4 ; 3 in 9, 3. The quotient is 43 hwidredths. Divide : 1. 3.27 by 3. 8. 89.6 by 32. 15. 416.64 by 112. 2. 4.64 by 4. 9. 17.92 by 16. 16. 4089.8 by 121. 3. 5.75 by 5. 10. 313.6 by 14. 17. 17.161 by 131. 4. 16.24 by 7. 11. 375.7 by 17. 18. 380.48 by 232. 5. 18.66 by 6. 12. 709.5 by 15. 19. 140.36 by 116. 6. 18.48 by 8. 13. 42.12 by 18. 20. 140.30 by 115. 7. 28.17 by 9. 14. 8.489 by 13. 21. 2702.7 by 117. 163 164 LESSON 2. If the divisor has decimals, and the dividend is a whole number : We annex as many zeros to the dividend as there are decimal places in the divisor, and remove the decimal point from the divisor. Divide 129 by 0.2. 2)1290 Here we add to the 129, making 1290, and divide by nAr 2 ; in other words, we multiply both dividend and divisor by 10. Divide : 1. 129 by 0.3. 8. 132 by 0.33. 15. 121 by 0.11. 2. 122 by 0.4. 9. 625 by 2.5. 16. 132 by 0.12. 3. 136 by 0.5. 10. 603 by 1.5. 17. 169 by 0.13. 4. 174 by 0.6. 11. 165 by 3.3. 18. 196 by 1.4. 5. 161 by 0.7. 12. 282 by 4.7. 19. 256 by 0.16. 6. 128 by 0.8. 13. 318 by 5.3. 20. 324 by 1.8. 7. 117 by 0.9. 14. 648 by 7.2. 21. 585 by Q.b, li both the divisor and dividend have decimals : We remove the decimal point from the divisor, and move the decimal point in the dividend to the right as many places as there are decimals in the divisor. Divide 1.29 by 0.3. 3)12.9 Here we carry the decimal point in the dividend one 7~o place to the right, and remove it from the divisor. In other words, we multiply both dividend and divisor by 10. Divide : 22. 12.9 by 0.3. 28. 3.24 by 0.9. 34. 0.96 by 0.2. 23. 12.4 by 0.4. 29. 13.2 by 0.3. 35. 0.33 by 0.3. 24. 13.5 by 0.5. 30. 2.01 by 0.5. 36. 1.98 by 0.9. 25. 1.86 by 0.6. 31. 1.28 by 0.4. 37. 17.6 by 0.8. 26. 1.61 by 0.7. 32. 17.4 by 0.6. 38. 15.5 by 0.05. 27. 12.8 by 0.8. 33. 1.82 by 0.7. 39. 12.6 by 0.09. LESSON 3. 165 Divide 28.3696 by 1.49. OPERATION. 19.04 149)2836.96 149 1346 1341 596 596 Here the decimal point is removed from the divisor, and is moved two places to the right in the dividend ; in other words, both dividend and divisor are multiplied by 100. Find the quotients of 1. 80.24^8. 17. 300 -^ 0.015. 2. 12.5664-1-4. 18. 32-0.064. 3. 1301.4-241. 19. 2.88 -^ 0.0024. 4. 2647.08^324. 20. 6.2-0.0025. 5. 9.215^0.08. 21. 65.1021-3.207. 6. 664.56-0.18. 22. 7704.256-928. 7. 132.6-425. 23. 506.016^753. 8. 7.48^0.085. 24. 1.9248-^-0.008. 9. 0.748^44. 25. 62825^1.75. 10. 2878.2-369. 26. 700727 -J- 0.029. 11. 2.3328-0.36. 27. 276.766-- 37.1. 12. 52.5-0.025. 28. 0.1024-2.56. 13. 1521-11.7. 29. 1024--25.6. 14. 7236-^1.44. 30. 1292 --3.23. 15. 67288^64.7. 31. 906.5^0.185. 16. 73807-^0.023. 32. 0.4496 -^ 11.24. 166 LESSON 4. SLATE EXERCISES. 1. A box contains 1416 eggs. How many dozen eggs are there in the box? 2. If 13 yards of velvet cost 197.50, what is the price of one yard ? 3. If '138,057 are divided into 19 equal parts, how many dollars will there be in each part? 4. How many times is the sum of $17 contained in 12890? 5. There are 320 rods in a mile. How many miles are there in 9280 rods ? 6. At $16.50 a ton, how many tons of hay can be bought for 1 280.50? 7. At $5.75 a ton, how many tons of coal can be bought for $103.50? 8. At 24 cents a dozen, how many dozen eggs can be bought for 1 61.44? 9. I bought 96 shares of railroad stock for $12,000. How much did the stock cost a share ? 10. If a field produces 4905 bushels of corn, produc- ing on the average 45 bushels to the acre, how many acres does the field contain ? 11. At $ 10.50 a ton, how many tons of plaster can be bought for $65,625? 12. A man bought a barrel of sugar, weighing 232 pounds, for $12.76. How many cents a pound did he pay for the sugar ? 13. When the price of Messina oranges is $2.75 a box, how many boxes can be bought for $77 ? 14. In how many hours will a cistern holding 4200 gallons be filled by a pipe that discharges into it 175 gallons an hour ? LESSON 5. 167 Tf the divisor is not contained in the dividend with- out a remainder, zeros may be annexed to the dividend, and the division continued. Divide 0.39842 by 3.7164 to four decimal places. OPERATION. 0.1072 37164) 3984.2 3716 4 267800 260148 76520 74328 2192 If the divisor is a whole number, and ends in zeros. We cut off the zeros fro7n the divisor^ and move the decimal pomt in the dividend as many places to the left (^prefixing zeros if necessary)^ as there are zeros cut off. Divide 42.08 by 8000. Ol'EKATION. 8 ) 0.04208 0.00526 Here the three zeros are cut off from the divisor, and the decimal point in the dividend is moved three places to the left. In other words, both divisor and dividend are divided by 1000. SLATE EXERCISES. Divide to four decimal places : 1. 5.8 by 4.79. 6. 8.6 by 3000. 2. 7.34 by 2.3. . 7. 95 by 7000. 3. 16.28 by 0.67. 8. 89 by 6700. 4. 54.87 by 0.39. 9. 0.32 by 410. 5. 2.86 by 349. 10. 0.51 by 3700. 168 LESSON 6. SLATE EXERCISES. 1. The production of pig-iron in the United States for the census year of 1890 was 9,579,779 tons, and 3,781,- 021 tons for the census year of 1880. Find the increase. 2. In 1880 Alabama produced 62,336 tons of pig-iron, and 890,432 tons in 1890. How many times the pro- duction of 1880 is the production of 1890 ? 3. The production of steel rails in the United States in 1880 was 741,475 tons, and 2,036,654 tons in 1890. Find the increase. 4. The value of wool manufactures in the United States for the census year of 1890 was 1337,768,524; of cotton manufactures $267,981,724 ; of silk manufactures 187,298,454. Find the total value of the products of these three industries. 5. Find the difference in value between the wool and the cotton manufactures of the United States in 1890. 6. The total area devoted to the cultivation of cereals in the New England States in 1889 was 580,297 acres, and in 1879 the total area was 746,128 acres. Find the decrease. 7. In 1889 New Hampshire raised 988,806 bushels of Indian corn from 23,746 acres. Find to two places of decimals the average number of bushels per acre. 8. In 1889 Iowa raised 313,130,782 bushels of Indian com from 7,585,522 acres. Find to the nearest bushel the average number of bushels per acre. 9. In 1889 the United States raised 468,321,424 bushels of wheat from 33,575,898 acres. Find to the nearest bushel the average number of bushels per acre. LESSON 7. 169 COMPOUND QUANTITIES. A quantity expressed in a single unit is called a sim- ple quantity ; but a quantity expressed in different units is called a compound quantity. Thus, 20 1 pounds is a simple quantity, but 20 pounds 4 ounces is a compound quantity. A unit of greater value or measure than another is said to be of a higher denomination than the other. Thus, the dollar is of a higher denomination than the cent, the pound than the ounce, the yard than the inch, the hour than the minute. The process of changing the denomination in which a quantity is expressed, without changing the value of the quantity is called reduction. If the change is from a higher denomination to a lower, it is called reduction descending ; if from a lower to a higher, it is called reduction ascending. Thus, 1 yard = 36 inches is an example of reduction descending ; and 24 inches = 2 feet is an example of reduction ascending. OQUID MEASURE. Liquid Measure is used in measuring liquids, as water, milk, etc. Table. 4 gills (gi.) = 1 pint (pt.). 2 pints = 1 quart (qt.). 4 quarts = 1 gallon (gal.). . Hence, 1 gal. = 4 qts.= 8 pts. = 32 gi. 31^ gals. = 1 barrel (bbl.). 63 gals. = 1 hogshead. Note. Casks holding from 28 gals, to 43 gals, are called barrels, and casks holding from 54 gals, to 63 gals, are called hogsheads. If we say, however, that a cistern holds 100 barrels, we mean barrels of 31 1 gals, each ; or if we say that a cistern holds 100 hogsheads, we mean hogsheads of 63 gals. each. 170 LESSON 8. Reduce 10 gallons 3 quarts 1 pint to i)ints. gals. qts. pts. 10 3 1 4 10 gals. = 10 X 4 qts. = 40 qts. , and 40 qts. with the — — 3 qts. added are 43 qts. ^^ 43 qts. = 43 X 2 pts. = 86 pts., and 86 pts. with the ^ 1 pt. added are 87 pts. 8T 87 pts. Ans. Hence in reduction descending : We 7nultiply the given number of highest units hy the number of the next lower units required to 7nake one of this higher ; and add to the product the given number of this lotver unit. We proceed in this wag with each successive result^ until the required unit is reached. Reduce : 1. 5 qts. 3 pts. to pints. 5. 8 gals. 1 pt. to pints. 2. 3 qts. 1 pt. to pints. 6. 11 gals. 1 qt. to pints. 3. 7 gals. 1 pt. to pints. 7. 2 bbls. to quarts. 4. 1 gal. 1 pt. to gills. 8. 3 hhds. to pints. Reduce 129 pints to higher units. 2 129 pts. 129 pts. = 1-1^ qts. = 64 qts. and 1 pt. over. 4 64 qts. ... 1 pt. 64 qts. =-\* gals. = 16 gals, and no qts. over. 16 gals. . . qts. 16 gals. qts. 1 pt. Ans. Hence in reduction ascending : We divide by the given number of units required to make one of the 7iext higher. We divide this quotient^ and each successive quotient in like manner^ until the required unit is reached. The last quotient and the several reiyiainders arranged in order is the answer sought. Reduce to higher units : 9. 229 pints. 11. 365 pints. 13. 1052 pints. 10. 51 pints. 12. 442 pints. 14. 1727 gills. gals. qts. l)t8. 4 3 1 11 1 3 1 25 2 1 LESSON 9. 171 Add 4 gals. 3 qts. 1 pt. ; 11 gals. 1 qt. ; 3 qts. 1 pt. ; and 25 gals. 2 qts. 1 pt. Write the quantities so that units of the same name shall be in the same column. The sum of the pints is S. Divide the 3 pts. by 2 (2 pts. = 1 qt.). The result is 1 qt. and 1 pt. Write the 1 pt. under the column of pints. The sum of the quarts, including 1 qt. from the 3 pts. , ■^2 2 1 is 10. Divide the 10 qts. by 4 (4 qts. = 1 gal.). The result is 2 gals, and 2 qts. Write the 2 qts. under the column of quarts, and add the 2 gals, to the gallons in the coluuni of gallons. 42 gals. 2 qts. 1 pt. Ans. From 4 gals. 2 qts. 1 pt. take 2 gals. 3 qts. 1 pt. gals. qts. pts. Since 1 pt. — 1 pt. is pt. , write under the column 4 2 1 of pints. 2 3 1 Since 3 qts. are more than 2 qts., take 1 gal. from ~ ~ ~ the 4 gals., reduce it to quarts, and add them to the 1 ^ ^ 2 qts., making 6 qts. Then, 6 qts. - 3 qts. = 3 qts. Write 3 under the column of quarts. Then 3 gals. — 2 gals. = 1 gal. 1 gal. 3 qts. Ans. Add: 1. 2. 3. gals. qts. pts. gals. qts. pts. gals. qts. pts. 3 11 21 3 n 43 1 1 7 3 1 18 2 1} 27 3 1 8 3 1 7 2 1 31 3 11 Find the difference ) between: 4. 5. 6. gals. qts. pts. gals. qts. pts. gals. qts. pts. 21 2 1 18 2 27 2 1^ 7 3 1 7 2 1 17 3 r 7. From a barrel that held just 40 gals, and 2 qts. of vinegar there were drawn 19 gals, and 1 pt. How much vinegar was left in the barrel ? 172 LESSON 10. Multiply 27 gals. 3 qts. 1 pt. by 5. gals. qts. ptB. 5 X 1 pt. = 5 pts. = 2 qts. 1 pt. Write the 1 pt. 27 3 1 under the pints, and reserve the 2 qts. to be added to 5 the product of 5 x 3 qts. -joq ^ 7 5x3 qts. = 15 qts., and 15 qts. + 2 qts. = 17 qts. = 4 gals, 1 qt. Write the 1 qt. under the quarts and add the 4 gals, to 5 x 27 gals. 139 gals. 1 qt. 1 pt. Ans. Divide 113 gals. 2 qts. by 4. gals. qts. pts. The quotient from dividing 113 gals, by 4 is 4)113 2 28 gals., and the remainder is 1 gal. 28 1 1 Keduce the 1 gal. to quarts, and add them to the 2 qts. The sum is 6 qts. The quotient from dividing 6 qts. by 4 is 1 qt., and the remainder is 2 qts. Reduce the 2 qts. to pints, and we have 4 pts. Then 4 pts. -f- 4 = 1 pt. 28 gals. 1 qt. 1 pt. An%. Divide 12 gals. 1 qt. by 3 qts. 1 pt. 12 gals. 1 qt. = 49 qts. = 98 pts. 3 qts. 1 pt. =7 pts. and 98 H- 7 = 14. Ans. Multiply : 1. 7 gals. 3 qts. 1 pt. by 9. 2. 31 gals. 2 qts. by 7. 3. 3 qts. 1 pt. 3 gi. by 8. Divide : 4. 126 gals. 3 qts. 1 pt. by 6. 5. 110 gals. 1 qt. by 7. 6. 131 gals, by 8. Note. Methods precisely similar to the preceding are employed for the reduction, addition, subtraction, multiplication, and division of all compound quantities. LESSON 11. 173 DRY MEASURE. Dry Measure is used in measuring dry articles, as grain, seeds, fruit, vegetables. Table. 2 pints (pt.) = 1 quart (qt.). 8 quarts = 1 peck (pk.). 4 pecks = 1 bushel (bu.). Hence 1 bu. = 4 pks. = 32 qts. NoTK 1. The gallon of liquid measure contains 231 cubic inches. Therefore the quart of liquid measure contains 57 1 cu. in. The bushel of dry measure contains 2150.42 cubic inches. Therefore, the quart of dry measure contains 67 i cu. in. Note 2. In measuring grain, seeds, and small fruits, the measure must be even full. In measuring apples, potatoes, and other large articles, the measure must be heaping full. 1. Reduce 5 bu. 3 pks. 4 qts. to quarts. 2. Reduce 4056 pts. to higher denominations. 3. Multiply 7 bu. 2 pks. 7 qts. by 9. 4. Divide 25 bu. 3 pks. 2 qts. by 7. 5. How many 4-quart measures will 2 bu. 2 pks. 4 qts. mi? 6. Divide 20 bu. 2 pks. by 8. Add: 7. 8. 9. bu. pks. qts. 5 13 3 3 3 7 2 7 bu. pks. 8 3 9 3 9 3 qts. 1 7 6 bu. pks. 121 1 156 3 132 3 qts. 7 6 5 Subtract : 10. 11. 12. bu. pks. qts. 5 2 2 3 17 bu. pks. 8 1 4 3 qts. 2 3 bu. pks. 150 2 136 3 qts. 5 7 174 LESSON 12. AVOIRDUPOIS WEIGHT. Avoirdupois Weight is used in weighing all articles except gold, silver, and precious stones. Tablk. 16 ounces (oz.) = 1 pound (lb.). 2000 pounds = 1 ton (t.) . The long ton is used in the United States Custom Houses and in wholesale transactions in iron and coal. 112 pounds Avoirdupois = 1 long hundredweight (cwt). 2240 pounds Avoirdupois — 1 long ton. 1 pound Avoirdupois = 7000 gi-ains. Note. Many articles are sold by weight, as follows : 1 bu. of wheat or beans = 60 lbs, 1 bu. of corn or rye = 56 lbs. 1 bu. of corn or rye 1 ^ 5Q ^^^ meal or cr'ked corn / 1 bu. of oats = 82 lbs. 1 bu. of barley = 48 lbs. 1 bu. of timothy seed = 45 lbs. 1 bu. of potatoes = 60 lbs. 1 barrel of flour = 196 lbs. 1 barrel of beef or pork = 200 lbs. 1 cask of lime = 240 lbs. 1 quintal of fish = 100 lbs. 1 stone of iron or lead = 14 lbs. 1 pig of iron or lead = 300 lbs. 1. Reduce 3 long tons 12 cwt. 110 lbs. to pounds. 2. Reduce 87,956 lbs. of coal to long tons. 3. Multiply 3 t. 1200 lbs. of hay by 5. 4. Divide 8 t. 1500 lbs. of hay by 7. 5. Add 1 t. 1326 lbs., 1 1. 1560 lbs., 1 t. 1728 lbs. 6. From 2 t. 1015 lbs. take 1 t. 515 lbs. 7. From a firkin of butter containing 42 lbs. there were sold 13 lbs. 10 oz. How much was left ? 8. At 23 cents a pound, what will 3.5 lbs. of steak cost? 9. At 115 a ton, what will 3.75 tons of hay cost? LESSON 13. 175 TROY WEIGHT. Troy Weight is used in weighing gold, silver, and precious stones. Tablk. 24 grains (grs.) = 1 pennyweight (dwt.). 20 pennyweights = 1 ounce (oz.) . 12 ounces* = 1 pound (lb.). The pound Troy contains 6760 grs. 1. How many more grains does a pound Avoirdupois contain than a pound Troy ? 2. Reduce 8 oz. 12 dwt. to pennyweights. 3. Reduce 1760 dwt. to higher denominations. 4. How many grains are there in an ounce of silver ? 5. From 1 lb. Troy take 5 oz. 5 dwt. 6. If 1 dwt. of silver is worth 4 cents, find the value of an ounce. 7. How many spoons weighing 1 oz. 5 dwt. each can be made from 30 oz. of silver? 8. How many table-spoons weighing 2 oz. 17 dwt. each can be made from 310 oz. 13 dwt. of silver ? 9. Divide 373 oz. 2 dwt. by 7. 10. Multiply 27 oz. 13 dwt. by 6. 11. Add 11 oz. 11 dwt. 15 grs. ; 7 oz. 12 dwt. 19 grs. ; 10 oz. 13 dwt. 17 grs. 12. From 7 oz. 19 dwt. take 3 oz. 19 dwt. Note. Apothecaries, in compounding medicines, use the following : Apothecaries' Measure. 60 minims (TT\,) z= 1 dram (VCl Ix.). 8 drams = 1 ounce (fl. drm. viij.). 16 ounces = 1 pint (fl. oz. xvj.). 176 LESSON 14. TIME MEASURE. Time Measure is used in measuring duration. Table. 60 seconds (sec.) = 1 minute (min.). 60 minutes = 1 hour (hr.). 24 hours = 1 day (dy.). 7 days = 1 week fwk.). 365 days (or 52 wks. 1 dy.) = 1 common year (yr.). 366 days = 1 leap-year. 100 years = 1 century. 1. Reduce 3 dys. 11 hrs. 32 min. to minutes. 2. Reduce 7 hrs. 30 min. 50 sec. to seconds. 3. Reduce 20,400 min. to higher denominations. 4. Reduce 481,200 sec. to higher denominations. 5. From 3 yrs. 15 dys. take 2 yrs. 12 dys. 23 hrs. 6. Divide 10 wks. 5 dys. 9 hrs. by 9. 7. Multiply 2 dys. 7 hrs. 15 min. by 8. 8. From 6 dys. 5 hrs. 48 min. 43 sec. take 13 hrs. 30 min. 40 sec. 9. Divide 31 dys. 2 hrs. 54 min. by 7. COUNTING. Paper. Various. 24 sheets = 1 quire. 12 things = 1 dozen. 20 quires = 1 ream. 12 dozen = 1 gross. 2 reams = 1 bundle. 12 gross = 1 great gross. 5 bundles = 1 bale. 20 things = 1 score. How many sheets make a ream ? How many pens make a gross ? How many buttons make a great gross ? How many years are 3 score and ten ? LESSON 15. 177 LONG MEASURE. Long Measure is used in measuring lines or distances. Table, 12 inches (in.) = 1 foot (ft.). 3 feet = 1 yard (yd.). 5 J yards, or 16| feet = 1 rod (rd.). 320 rods = 1 mile (mi.). 1 mi. = 320 rds. = 1760 yds. = 5280 ft. Note. A line = y^ in. ; a barleycorn = J in. ; a hand (used in meas- uring the height of horses) = 4 in. ; a palm = 3 in, ; a span = 9 in. ; a cubit = 18 in. ; a military pace = 2^ ft. ; a chain = 4 rds. ; a link = j^-Q chain ; a furlong = ^ mi. ; a knot (used in navigation) = 0086 ft.; a league = 3 knots ; a fathom (used in measuring depths at sea) = 6 ft. ; a cable length = 120 fathoms. Note. Lengths measured by yards are generally expressed in yards and fractions of a yard ; and distances of 100 rds. and 80 rds. are called half-miles and quarter-miles respectively. Reduce 283 inches to higher denominations. 12 283 3 23. ..7 7. ..2 5i 11 7 yds. 2 ft. 7 in. Ans. Reduce 328 yards to rods. Since it takes 5^ yards, or 11 half- yards, to make a rod, reduce the 328 yards to half-yards and divide by 11. The quotient is 69 rods, and the re- mainder is 7 half-yards. The 7 half- yards are equal to Sh yards. 59 rds. 3^ yds. Ans. 328 9 656 half -yards. 59. . . 7 half-yards. What part of a yard ,Tri ..^ . .^ . „...i 160 rds. ? 80 rds.*? are 9 in.? 18 in. vv 11511 part ui ct yitra a-re What part of a mile are xj^,„ ^ — , yards in 2 rds.? in 3 rds.? in 4 rds feet in 2 rds How many yards How many in 2 rds.? '^ ^^ 4 rds. ? in 6 rds. ? m 178 LESSON 16. 1. Change 5 yds. 2 ft. 7 in. to inches. 2. Change 2 yds. 2 ft. 4 in. to inches. 3. Change 2 mi. 268 rds. to rods. 4. Change 16 mi. 181 rds. to rods. 5. Change 15,840 ft. to miles. 6. Change 935 yds. to rods. 7. Change 720 rds. to miles. 8. Change 19,360 yds. to miles. Add: yds. 9. ft. 10. yds. ft. 13 1 5 28 2 7 5 2 11 27 14 14 4 1 3 2 3 2 12. mi. ids. ft. 13 35 15 11 57 11 10 85 13 5 96 8 13. mi. rds. ft. 7 140 10 5 230 12 3 275 5 1 255 11 Find the difference between : 15. 16. yds. ft. in. yds. ft. in. 14 1 4 22 3 15 3 2 6 18. mi. rds. ft. 17 125 1 8 257 14 19. mi. Ids. yds. 7 3 255 1 21. Multiply 15 yds. 1 ft. 9 in. by 11. 22. Multiply 21 rds. 4 yds. 2 ft. by 13. 11. rai. rds. yds. 15 25 3 27 12 36 14. rds. ft. in. 170 8 9 115 11 11 130 14 8 175 13 7 17. mi. rds. ft. 23 76 1 16 238 15 20. mi. rds. yds. 13 33 2 4 H LESSON 17. 179 BECT ANGLE. PERIMETERS. The Perimeter of any surface bounded by straight lines is the sum of the lengths of the bounding lines. Draw rectangles of the following dimensions and meas- ure their perimeters : 2 in. by 3 in. 2 in. by 4 in. 3 in. by 3 in. 8 in. by 5 in. 3 in. by 4 in. 4 in. by 6 in. Find the perimeter of 1. A rectangular floor 15 ft. by 15 ft. 2. A rectangular ceiling 22 ft. by 20 ft. 3. A rectangular room 16 ft. by 18 ft. 4. A rectangular room 24 ft. by 21 ft. 5. Find the cost of fencing a rectangular field 30 rds. by 20 rds., at $1.20 a rod. The length of the circumference of a circle is found by multiplying the length of the diameter by 22 and dividing the result by 7. Find the length of the circum- ference of a circle : 6. If the length of the diameter is 21 in. ; 28 in. ; 7 ft. The length of the diameter of a circle is found by multiplying the length of the circumference by 7 and dividing the result by 22. Find the length of the diameter of a circle : 7. If the length of the circumference is 11 in. 8. If the length of the circumference is 2 ft. 9 in. 180 LESSON 18. SQUARE MEASURE. Square Measure is used in measuring surfaces. The units of square measure are squares having units of length for the lengths of their sides. Table. 144 square inches (sq. in.)= 1 square foot (sq. ft.). 9 square feet = 1 square yard (sq. yd.). 30| square yards, or | ^ ^ ^^^ 272^ square feet J ^ 160 square rods, or | 10 square chains / 640 acres = 1 square mile (sq. mi.). 1 acre (A.) 1 square mi Hence, 1 A. = 160 sq. rds. = 4840 sq. yds. = 43,560 sq. ft, A square of flooring or roofing = 100 sq. ft. A section of land = 1 mile square. A township = 36 sq. mi. The units of square measure are obtained by squaring the units of long measure. Thus, 144 = 122 ; 9 = 3-2 . 301 =(5^)2 ; 272^ = (16^)2. 122 ig read the square of 12 and means 12 x 12. 1. Reduce 507 sq. yds. 7 sq. ft. to square feet. 2. Reduce 50 sq. chains to acres. 3. Reduce 3 A. 90 sq. rds. to square rods. 4. Reduce 44,996 sq. in. to square feet. 5. Reduce 67,760 sq. yds. to acres. 6. Reduce 85,316 sq. rds. to acres. 7. Add: 3 A. 116 sq. rds. ; 2 A. 120 sq. rds.; 5 A. 119 sq. rds. ; 1 A. 40 sq. rds. 8. From 13 sq. yds. 7 sq. ft. 12 sq. in. take 3 sq. yds. 8 sq. ft. 136 sq. in. 9. Multiply 2 A. 20 sq. rds. by 9. LESSON 19. 181 AREAS. The area of any surface is the number of units of area the given surface contains. The unit of area is a square, the side of which is some given unit of length. Find the area of a rectangle 2 ft. 3 in. by 1 ft. 8 in. : 2 ft. 3 in. = 24 in. + 3 in. = 27 in. 1 ft. 8 in. = 12 in. + 8 in. = 20 in. Therefore the area required is 20 x 27 = 640 sq. in. Hence, in finding the area of a rectangle : We express the length and breadth in units of the same denomination., and multiply the number of units in the length by the number of units in the breadth ; this product ivill be the number of square units of that denomination. Find the area of a rectangle : 1. 8 in. by 5 in. 4. 11 in. by 10 in. 7. 3 ft. by 2 ft. 2. 9 in. by 6 in. 5. 15 in. by 6 in. 8. 4 ft. by 2 ft. 3. 8 in. by 7 in. 6. 16 in. by 4 in. 9. 8 ft. by 2 ft. 10. How many square feet in a floor 21 ft. by 20 ft. ? 11. How many square feet in a floor 18 ft. by 15 ft. ? 12. How many square feet in a blackboard 12 ft. long, and 3 ft. wide ? 13. How many square yards in a roll of wall-paper I yd. wide and 8 yds. long? 14. Find the number of square yards in a house-lot 87 ft. front and 102 ft. deep. 15. Find the number of square rods in a house-lot 8 rods front and 10 rods deep. 16. Find the total area of the four ivalls of a room 18 ft. long, 15 ft. wide, and 9 ft. high. 182 LESSON 20. 1. Find the total area of the four walls and the ceiling of a room 16 ft. long, 15 ft. wide, and 10 ft. high. 2. Find the total area in square yards of the ceiling of a room 18 ft. long, and 15 ft. wide. 3. Find the area in square yards of the four walls of a room 19 ft. long, 17 ft. wide, and 9 ft. high. 4. Find the number of acres in a field 40 rds. square. 5. Find the number of square yards in a flower bed that is 12 ft. square. 6. Find the number of square yards in a poppy bed that is 24 ft. long, and 12 ft. wide. 7. Find the number of square inches in the surface of a slate 8 in. by 14 in. 8. Find the number of square inches in the surface of a crayon-box 7 in. by 4 in. by 3 in. 9. Find the number of square feet in the surface of a cube 3 ft. by 3 ft. by 3 ft. The area of a circle is found by multiplying the area of the square on its radius by 22 and dividing the result by 7. Find the area of a circle : 10. If the length of the radius is 10 in. ; 16 in. ; 20 in. 11. If the length of the radius is 1 ft. 4 in. ; 1 ft. 6 in. 12. If the length of the diameter is 1 ft. 10 in. ; 2 ft. 4 in. 13. If the length of the diameter is 2 ft. 6 in. ; 3 ft. 4 in.; 3 ft. 8 in.; 3 ft. 10 in. 14. If the length of the diameter is 4 ft. 2 in. LESSON 21. 183 CARPETING FLOORS. In carpeting floors, decide whether the strips shall run lengthwise of the room or across it, and find the number of strips required by dividing the width of the room by the width of the carpet, if the strips are to run lengthwise of the room ; and the length of the room by the width of the carpet, if the strips are to run across it. A fraction of a width of carpeting required is reckoned a full width, and enough is turned under to make the carpet fit the room. The number of yarda in the length of the strip required multiplied hy the number of strips will give the number of yards of carpeting required. In determining the length of the strip, allowance must be 7nadefor matching the patterns. Ex. Find the number of strips of carpeting 27 in. wide required for a rooni 18 ft. by 17 ft., if the strips run lengthwise. Solution. 17 ft. =17 X 12 in. = 204 in. 204 in. - 27 in. = 7|f. Therefore 8 strips are required. 1. Find the number of strips of carpeting 1 yd. wide required for a room 17 ft. by 15 ft., if the strips run lengthwise. 2. Find the number of strips of carpeting 27 in. wide required for a room 20 ft. by 22 ft. 6 in., if the strips run across the room. 3. Find the number of yards of carpeting 1 yd. wide required for a room 17 ft. 6 in. by 17 ft., if the strips run lengthwise. What width will be turned under ? 184 LESSON 22. PAPERING ROOMS. Wall-paper is made in strips 18 in. wide. Single rolls are 8 yds. long, and double rolls are 16 yds. long. To find the number of rolls required to paper a room of common height : We find the number of feet in the perimeter of the room^ omitting the width of the doors and windows ; mid allow a double roll^ or two single rolls, for every 7 feet of the perimeter. Find the number of rolls required for a room of ordi- nary height, 17 ft. by 15 ft., having 1 door and 3 windows each 4 ft. wide. Perimeter of the room = 2 x 17 ft. + 2 x 15 ft. = 64 ft. Width of door and windows = 16 ft. Deducting, we have 48 ft. 48 - 7 = 6f Ans. 7 double rolls. 1. How many double rolls of paper will be required for a room 20 ft. by 18 ft., with 2 doors and 3 windows, each 4 ft. wide? 2. Find the cost of paper at 50 cents a single roll for a room 21 ft. by 19 ft., with 2 doors and 4 windows, each 4 ft. 2 in. wide. 3. Find the cost of paper at 30 cents a single roll for a room 16 ft. by 15 ft., with 1 door and 2 windows, each 4 ft. wide. 4. How many double rolls of paper will be required for a room the perimeter of which is 68 ft., after allow- ance is made for doors and windows ? 5. How many double rolls of paper will be required for a room the perimeter of which is 60 ft., after allow- ance is made for doors and windows ? LESSON 23. 185 CUBIC MEASURE. Cubic Measure is used in measuring solids. The units of cubic measure are cubes having units of length for the lengths of their edges. Table. 1728 cubic inches (cu. iii.)= 1 cubic foot (cu. ft.). 27 cubic feet = 1 cubic yard (cu. yd.). The units of cubic measure are cubes of the units of long measure. Thus, 1728=128; 27 = S^. 12^ is read the cube of 12 and means 12 x 12 x 12. WOOD MEASURE. Table. 16 cubic feet = 1 cord foot (cd. ft.). 8 cord feet = 1 cord (cd.). Therefore, 128 cubic feet = I cord. 1. Reduce 13 cu. yds. 21 cu. ft. to cubic feet. 2. Reduce 600 cu. ft. to cubic yards. 3. From 58 cu. yds. 24 cu. ft. take 34 cu. yds. 26 cu. ft. 4. Multiply 13 cu. yds. 13 cu. ft. by 13. 5. Divide 17 cu. yds. 14 cu. ft. by 11. 6. Add : 34 cu. yds. 11 cu. ft. ; 13 cu. yds. 10 cu. ft. ; 17 cu. yds. 4 cu. ft. 7. How many cords of wood in 1280 cu. ft. ? 8. How many cords of wood in a pile 42 ft. long, 8 ft. wide, and 6 ft. high ? Note. Divide the product of the numbers! expressing the length, width, and height by 128. 9. How many cubic yards in a cord of wood ? 10. At $4 a cord, find the value of a pile of wood 18 ft. long, 4 ft. wide, and 4 ft. high. 186 LESSON 24. VOLUMES. The volume of any solid is the number of units of volume the given solid contains. The unit of volume is a cube, the edge of Avhich is some given unit of length. In finding the volume of a rectangular solid : We express the lengthy breadth^ and thickness in units of the same denomination ; then ive multiply the number of units in the length by the number of units in the breadth^ and this product by the number of units in the thickness ; the result ivill be the yiumber of cubic units of that denomination. Find the volume of a rectangular solid: 1. 8 in. X 4 in. x 3 in. 4. 7 in. x 3 in. x 4 in. 2. 4 in. X 4 in. X 3 in. 5. 10 in. x 8 in. x 4 in. 3. 4 in. X 4 in. x 4 in. 6. 3 in. x 3 in. x 3 in. 7. Find the number of cubic feet in a stick of square timber 30 ft. long, 1 ft. square at the end. 8. Find the number of cubic yards in an excavation for a cellar 42 ft. by 33 ft. by 9 ft. 9. Find the number of cubic yards in an excavation for a cellar 33 ft. by 24 ft. by 9 ft. LESSON 25. COMMON FRACTIONS. 187 If a circle is divided into 2 equal parts, What part of the whole circle is each of these parts ? What part of the whole circle are 2 of these parts ? If a circle is divided into 3 equal parts, What part of the whole circle is each of these parts ? What part of the whole circle are 2 of these parts ? What part of the whole circle are 3 of these parts ? If a circle is divided into 4 equal parts. What part of the whole circle is each of these parts ? What part of the whole circle are 2 of these parts ? What part of the whole circle are 3 of these parts ? What part of the whole circle are 4 of these parts ? How many halves of a unit make the whole unit ? How many thirds of a unit make the whole unit? How many fourths of a unit make the whole unit ? What is the 7iame of one of the parts of a unit, When the unit is divided into two equal parts ? When the unit is divided into three equal parts ? When the unit is divided into four equal parts? Which is larger |^ of a circle or ^ of the circle ? Which is larger |- of a circle or \ of the circle ? Which is larger ^ of a circle or ^ of the circle ? 188 LESSON 26. /XVs «. X / «\ / >/s \ Us/ Vs y^ If a circle is divided into 5 equal parts, What part of the circle is each of these parts ? What part of the circle are 2 of these parts? 3 of these parts ? 4 of these parts ? 5 of these parts ? If a circle is divided into 6 equal parts, What part of the circle is each of these parts ? What part of the circle are 2 of these parts ? 3 of these parts ? 4 of these parts ? 5 of these parts ? 6 of these parts ? If a circle is divided into 8 equal parts, What part of the circle is each of these parts ? What part of the circle are 2 of these parts ? 4 of these parts ? 6 of these parts ? 7 of these parts ? 8 of these parts? How many Jifths of a unit make the whole unit ? How many sixths f how many sevenths ? how many eighths? how many tenths? how many twelfths? how many sixteenths? What is the name of one of the parts of a unit, when the unit is divided into 5 equal parts ? into 6 equal parts ? into 8 equal parts ? into 10 equal parts ? into 12 equal parts ? Which is larger -I- of a unit or J of the unit ? | of a unit or J of the unit ylg- of a unit or '^:^ of the unit. LESSON 27. 189 Any standard used in counting or in measuring is called a unit. In 3 quarters of a yard the unit is a quarter of a yard. But a quarter of a yard is ii fractional part of the whole unit, a yard. A unit which is a fractional part of another unit is called a fractional unit, and the unit of which it is a part is called its whole unit. Numbers that count whole units are called whole numbers. Numbers that count fractional units are called fractional numbers, or fractions. Note. The Teacher must explain tliat the words ichole and frac- tional^ though applied to numbers, refer only to the units counted by the numbers. Name the fractional unit and the integral unit in : 3 quarters of an inch. 1 half of an hour. 4 fifths of a pound. 6 sevenths of a week. 2 thirds of a yard. 5 twelfths of a foot. 3 eighths of a bushel. 3 sixteenths of a ton. 9 tenths of a dollar. 5 sixths of an acre. Express: J of a yard in inches. \ of a pound in ounces. I of a yard in inches. f of a pound in ounces. I of a yard in inches. | of a pound in ounces. I of a yard in inches. | of a pound in ounces. Every common fraction is written in figures by means of two whole numbers, which are called the terms of the fraction. One of these gives the name of the parts, and is called the denominator ; and the other gives the number of the parts taken, and is called the numerator. 190 LESSON 28. To write a common fraction, write the denominator under the numerator with a line between them. To write 5 sevPMths, for example, we write the numerator 5, draw a line under it, and under the line we write the denominator 7 ; thus, f. To read a common fraction, read the numerator and then the denominator. Thus, I, i, f, I, y\, are read two-thirds, one-half, three-fifths, seven-eighths, nine- elevenths, f is read three-fourths or three-quarters. seven twentieths, thirteen twenty-fifths, five sevenths, nine thirteenths, eleven twelfths, four twenty-firsts, seventeen eighteenths, thirty thirty-seconds. thirteen twenty-fourths, fifteen nineteenths. Write in figures : one third, one quarter, two fifths, five sixths, five eighths, seven twelfths, three sixteenths, nine fourteenths, nine twentieths, four twenty-fifths. RpflH • 3 5 411_9 3 4 121911 iteaa. g, ^g, g, 2t^ 22' yy 19' 23' 25' 27- If tlie numerator is smaller than the denominator, the fraction is called a proper fraction ; as ^. If the numerator is equal to the denominator, or greater than the denominator, the fraction is called an improper fraction; as |, i^-. A mixed number is a whole number and a fraction ; as 5|, read five and two-sevenths. Every whole number may be regarded as a fraction having 1 for the denominator. Thus, 8 may be written f . LESSON 29. 191 How many halves of an apple in 2 apples? in 3 apples ? in 5 apples ? in 6 apples ? in 8 apples ? How many halves of an apple in 2J apples ? in 3 J apples ? in 4J apples ? in b^ apples ? How many quarters of a dollar in f 2? in 13? in 14? in|2i? in.f3i? in|4|? Change to improper fractions : 2=j 2=j 2=, 2=r 2 = 5 8=. 3=j 3 = 5 3=ir 3 = 5 4 = 1 4 = 5 4 = T 4=^ 4 = 5 5 = 2 5 = 5 5 = 5 5=1. 5 = 5 6 = 2- 6 = 5 6=5 6 = r 6 = 5 7=j 7 = 5 7 = , 7 = T 7 = 5 8 = ,- 8 = 5 8 = 5 8 = T 8 = 5 9=2 9 = 5 9 = 5 9=5 9 = 5 2=5 2=1. 2 = TT 2 = TJ 2 = T5 3 = 5 8=8 3= IT 3 = T. 3 = T5 4 = 5 4 = 5 4 = w 4 = TJ 4 = T5 6=5 5=9 5=„ 5 = T^ 5=15 6 = 5 6=9 6 = TTr 6 = T2 6=15 7 = 5 7 = 9 7 = w 7=TJ 7 = T5 8 = 5 8=9 8 = TT 8 = T^ 8 = T6 9 = 5 9=^ 9=w 9 = T^ 9 = T5 2i = j H=5 2f = e 3i = 5 1A = T^ 4i = f 3i = 5 3* = j 5^ = 5 2t^ = TJ 6i = j 2i = T 6f=T 2i=» 1A = T5 71 = 2 5i = T 34 = ^ 21 = 9 HHt5 192 LESSON 30. To change an improper fraction to a whole or mixed number : We divide the numerator by the denominator. The quotient will be a whole number or a mixed number. If a mixed number, the fractional part will have for numerator the re- mainder of the division, and for denominator the divisor. Change to whole or mixed numbers the following : 1. ¥• 7. ¥■ 13. ¥• 19. !§• 2. ¥• 8. -¥- 14. ¥• 20. U- 3. H- 9. ¥• 15. ¥• 21. H- 4. ¥• 10. ¥- 16. ¥• 22. fl- 5. ¥• U. V- 17. ¥• 23. it- 6. ¥• 12. !!• 18. -tl- 24. H- To reduce a fraction to lower terms : We divide both terms by any number that will divide each term without a remainder. Thus by dividing both terms of -f-^ by 2 we get Note. The Teacher must illustrate this example, and other exam- ples until the pupils understand fully that the reduction of a fraction to lower terms does not alter its value. Reduce to lowest terms : 1. «• 7. If 13. H- 19. If. 2. if 8- A- 14. If 20. If. 3. w 9. IJ. 15. it- 21. §f 4. H- 10. If. 16. ,'h- 22. ff. 5. A- 11- U- 17. -h%- 23. fl- 6. A- 12. it. 18. i^- 24. ||. LESSON 31. 193 MULTIPLICATION OF FRACTIONS. If we take |- of ^ of an apple, we have J of an apple, and if we take | of | of an apple, we have | of an apple. Note. The Teacher should illustrate this by actually dividing an apple into quarters and then each quarter into halves. That is, -^ of ^= g, and ^ of | = |. Hence, To multiply one fraction by another : We fake the product of the mimeratoris for the required numerator^ and of the denominators for the denominator. Mixed numbers and ivhole numbers may be written as improper fractions, and thus brought under the rule. The work of multiplying fractions may be much shortened by cancellation ; that is, by first dividing out every number that is contained in the numemtor and denominator without remainder. Find the product of f , 2|, and 3. Now 2i = Y", ^^^ ^ iT^^y ^6 written f. 2 Hence the product is ^-li-^ = 3 6 = 71 J X 5 X 1 ' Cancel the 7 from the denominator and from the 14 in the numera- tor, and then multiply ; we have ^^^, or 7i. 1. I- of f = 7. 7. I of 1 = ,. 13. fof f = ,. 2. lof 1 = 5. 8. iofi| = ^3. 14. I of i = ^. 3. |ofii = „- 9. i of 14 = ,-^. 15. fof-i/=-j. 4. iof f = ^. 10. iofi^ = „. 16. fof 1 = 5. 5. i of ^ = „. 11. i of if = „. 17. 1^ of H = 5. 6-Jofi|=Te. 12. ioff2 = j^. 18. fof^=^. 194 LESSON 32. To multiply a mixed number by a whole number : We multiply the fraction firsts and then the integral part of the mixed number^ and add the results. Find the products of : 1. 2x2-1. 8. 4x21. 15. 5x21 2. 2x31-. 9. 4x3J. 16. 5x2|. 3. 2x3J. 10. 4x2J. 17. 5x3f. 4. 3x31. 11. 4x31. 18. 5x4|. 5. 3x21. 12. 4x41. 19. 5xl|. 6. 3x51. 13. 4x4f 20. 5x2i. 7. 3x31. 14. 4x3i. 21. 5x To multiply a whole number by a mixed number : We multiply the ivhole number hy the fraction firsts and then hy the integral part of the mixed number^ and add the results. Multiply 8 by 21 8 21 Here we multiply 8 by i and get 2|. "^ Then we multiply 8 by 2 and get 16. 2|^ By adding the 2f and the 16 we obtain 18f . 16 Find the products : 1. 21x6. 6. 21x12. 11. 71x21. 2. 2^x6. 7. 2|x8. 12. 8|x22. 3. 3^x6. 8. 2f x9. 13. 2ix6f 4. 3Jx6. 9. 3|^x20. 14. 3Jx8f 5. 41x6. 10. 3|xl2. 15. 3ix6f LESSON 33. 195 niVISION OF FRACTIONS. To divide | of a dollar by ^ of a dollar is to find the number of quarters of a dollar it is necessary to take in order to have half a dollar. It is obvious the number is 2. Hence, hH But 1x4 :2. 2. Therefore, to divide by \ gives the same result as to multiply by \. Now f is J inverted. Therefore, To divide by a fraction : We invert the fraction and multiply. Mixed numbers and whole numbers may be ivritten as improper fractions., and thus brought under the rule. Find the quotients : 2. 1^1 3 4 8. 6-1 9. 1^6. 9 • 3 3 • 9 13. 2 H-2J. 14. 2 -3J. 15. %\-^2. 16. 31-3. 17. 2^-3. 18. 51^7. 19. 2|-4. 25. ^^^. 26. ^-^^. 27. 2^-41. 28. ^^^. 29. 81^41. 30. 41 ^ 31. 81 ^1|. 20. 4 ^31 32. b\ 10. #H- li- 11. I^f. 12. I 21. 6 -^ll. 22. 4 -2f 23. 4 -11 24. 8 -2-|. 33. 4|h-31 34. 5J^2f. 35. 2|-5J. 36. 71^ If If- 196 LESSON 34. SIMIL.AK FKACTIONS. If both terms of a fraction are multiplied by the same number, the value of the fraction is not altered. By this operation the number of parts is increased, and the size of the parts is decreased, at the same rate. Fractions that have a common denominator are called similar fractions. Reduce |-, |, |- to similar fractions, having 12 for their common denominator. We find the required numerators by dividing 12 by the denom- inator of the first fraction and multiplying the result by the numerator of the first fraction ; and so proceed with each of the given fractions. Thus, 12 - 2 = 6, and 1 x(S = Q. Therefore \ = j% 12 -- 3 = 4, and 2 X 4 = 8. Therefore | = y^. 12 - 4 = 3, and 3x3 = 9. Therefore | = j%. Hence the required fractions are j%, j%, j%. Therefore, To reduce fractions to similar fractions with a given common denominator : We divide the given common denominator hy the denoin- inator of the first fraction^ and multiply the quotient hy its numerator^ and this will he the required numerator of the first fraction. In the same way we find the numerator of each of the other fractions. Reduce to similar fractions having for denominator the number given in parenthesis for each problem : 1- h f- 1 (12). 6. f, I, A (24). 11. f, f, A (24). 2. i, 1 Vj (12). 7. 1-, f, Jj (14). 12. f, W, f (28). 3. i, 1, 1 (18). 8. i, f ^T (21). 13- A' A- 1 (36). 4- h f' f (8)- 9- h h ^z (15)- 14. f, {^, ^j (42). 5. J, f, Jj (18). 10. ^, f, ^ (42). 15. !, 1^, A (75). LESSON 35. 197 ADDITION OF FRACTIONS. Add 1, J, f . These fractious changed to similar fractions with denominator 12 become ^^, ^^, j%, and ^^ + /j + j% = if. But }f = f = 1^. Therefore, To add fractions : We change the fractions to similar fractions (if they are not similar)^ and write the sum of the nujnerators of the similar fractions over the commo7i denojninator. We reduce the resulting fraction to its lowest terms ; and if it is an improper fraction^ ive reduce it to a whole or mixed number. * Change to similar fractions and add : i+\=i i+ \ = = 12 i + 1 6 = 1^ i + i=TJ Hi=i H i= = 2^ i + i = ^ i + A = l^ |- + i=c H i = '6 i + iV = 2^ i + i=.T i + i=6- HtV= = 12 i + tV = 12 i + 4=Tf f+Hw i+ i= = 20 i + 1^ = T6 i + i=j? 1=6 i=8 2 = 10 2=r2 "2 = 12 i=6 i = ^ i = TO Ht5 i = TJ J = ^ i = ^ tV = to tV = T2" lV = T2 i = W i = T2 i = 12" i=i8- i = TJ i = T6 i = T2 6=T2 6 = l¥ i = TJ tV = T6 T2=T2 '12=J2_ i = T8 Ht. 2 = 12 i = T2 2 = 2T 6=2T 6=^ i = T2 i = T2 4=2T i = 2¥ 9 = ¥6 9=12 6=12 i=2¥ tV=2¥ ¥=36 198 LESSON 36. SUBTKACTION OF FRACTIONS. Subtract ^ from |. These fractions changed to similar fractions having 12 for a denominator become y\, j% ; and j% - ^^ =j\. Hence, To subtract one fraction from another : We change the fractio7is to shnilar fractions (if they are not similar^ ; then subtract the numerator of the subtrahend from that of the miyiuend^ and write the reynainder over the common denominator. We reduce the resulting fraction to its lowest terms. Change to similar fractions and subtract : 2~J 2~8 2~6 2~6 3~6 1=-^ 1—- 1—-. 1 — „ 1_ i J 8~8 6~6 3~"6 6 ""6 i—^ 3— T2 i— T^ i— 12 | — ¥ 1__ 1 — 1__ _1 _ _ 1_ 9~9 4~]2 5~15 12~~12 2~¥ 2. j5 3 4 4 3~6 8~"^ 5 "10 5—10 5 — 20 1— _ 1 — _ _1_ 1— 3_ _ 2"~6 2"~¥ 2~10 2~]0 4"~20 *= TJ i= ■TJ 1= ^¥ i= 'S 1= ITS A= To A= I7f 1= 10 i= 16 ■ts = '16 3_ ^_ 4 — 20 5—10 2—10 "5—10 5 — 2"0 To" ^10" 5^10" T0"^TO iV— 10 /o — 10 16 — 16 16 — 11 10" 5— 1"0 ^~16 4— Ti 1_ 1_ 3__ 5___ It ~ 16 2 ~ 1 6 ? — 1 2 6 ~" 1 2 1% = T6 T6 — 16 T2— T5^ ?— 12 i= T^ 1 _ '5 — 15 3_ 5~ TO -h= TO 1 = TO 2_ 5 — TO il = T6 1- T6 1 = T2 ^^2 = 12 tV= TO 2 _ 5 ~ 10 3_ 4 — T2 1 = T2 i= 12 «= 12 LESSON 37. 199 CONVERSION OF FRACTIONS. A decimal fraction is a common fraction whose de- nominator is one of the numbers 10, 100, 1000, etc. Thus, 0.4 is the same as y^j. To convert a decimal fraction to a common fraction : We take for the numerator the entire number obtained after removing the decimal poirit^ and for the denominator^ 1 followed by as ma7iy zeros as there are decimal places in the original fraction ; and reduce the resulting fraction to its loivest terms. Thus, 3.25 = fe = ¥ = 31- To convert a common fraction to a decimal fraction : We divide the numerator by the denominator. Thus, ^ = i-|ftft = 0.125. 4 ^ ^oM. = 0.571f . 1=2.00 =o.()66f. Note. If the division does not terminate at the third decimal place, three decimal places will be sufficiently accurate for most problems. If the number at the fourth decimal place is gi-eater than 5, we add 1 to the third decimal figure; if it is equal to 5, we cany the decimal to four places. Thus, f = 0.571, | = 0.667, and ^ = 0.4376. Change to common fractions : 1. 0.08. 4. 0.375. 7. 0.425. 10. 3.125. 2. 0.625. 5. 0.004. 8. 0.015. 11. 1.725. 3. 0.032. 6. 0.256. 9. 7.075. 12. 7.875. Change to decimal fractions : 13. -h^ 14. A. 15. iV 16. ^V- 19. 17. 2%- 20. 18. ^,. 21. 17f 5|. 22. 23. 24. 200 LESSON 38. ORAL EXERCISES. 1. How many inches in f of a yard ? 2. How many ounces in | of a pound ? 3. How many pounds in J of a ton ? 4. How many cubic feet in | of a cubic yai'd? 5. How many square rods in |^ of an acre ? 6. How many cord feet in |^ of a cord ? 7. How mau}^ pints in y^g of a gallon? 8. How many hours in J of a day ? 9. How many minutes in |^ of an hour ? 10. How many quarters of a pound in 2 pounds? 11. How many quarters of a dollar in f 6|? in $7^7 12. How many halves of an apple in 4 J apples ? 13. I have a string 2| yards long. Into how many pieces, each ^ yard long, can I cut it ? 14. How many gallons will 10 bottles hold if each bottle holds |- of a gallon? 15. Find the price of 2^ dozen of eggs at 16 cents a dozen. 16. Find the price of 3J pounds of sugar at 6 cents a pound. 17. How many miles will a man walk in 2 hours at the rate of S^ miles an hour ? 18. How many miles will a man walk in 2| hours at the rate of 3 miles an hour ? 19. How many miles will a man walk in 3 hours at the rate of 3 J miles an hour ? 20. Express 2 ft. 6 in. as the fraction of a yard. 21. At $7 a ton what is the cost of |^ of a ton of coal ? 22. At 16 a cord what is the cost of |^ of a cord of wood ? 23. At 80 cents a bushel what is the cost of 2| bushels of Baldwin apples ? LESSON 39. 201. SLATE EXEKCISES. Find the cost, reckoning every fraction of a cent as a cent : 1. 3| doz. of eggs at 24 cents a dozen. 2. 3J lbs. of steak at 23 cents a pound. 3. 2J lbs. of tea at Q5 cents a pound. 4. 17| yds. of muslin at 10 cents a yard. 5. 50 cans of tomatoes at $1.25 a dozen. 6. 2| bu. of potatoes at 18 cents a peck. 7. 16 bu. of oats at 37J cents a bushel. 8. 24 bags of corn at f 1.12i- a bag. 9. 36 bu. of wheat at S1^ cents a bushel. 10. 4 lbs. and 12 oz. of butter at 20 cents a pound. 11. 8 lbs. and 10 oz. of mutton at 12 cents a pound. 12. 6 qts. of molasses at 56 cents a gallon. 13. 43^ yds. of cotton cloth at 7 cents a yard. 14. 14 lbs. 6 oz. of ham at 14 cents a pound. 15. 6 bu. and 3 pks. of wheat at 92 cents a bushel. 16. 2680 lbs. of hay at 122 a ton. 17. 2 t. 8 cwt. of coal at 15.60 a ton. 18. 31 bbls. of flour at 15.50 a barrel. 19. 2| bu. of cranberries at 7 cents a quart. 20. 3 pks. and 4 qts. of cranberries at $ 2.56 a bushel. 21. 2 cds. and 6 cu. ft. of wood at $3.50 a cord. 22. A pile of wood 26 ft. long, 4 ft. wide, and 5 ft. high at $3.84 a cord. 23. 4 doz. and 8 eggs at 30 cents a dozen. 24. 75000 bricks at $6.75 a thousand. 25. 9 shares of stock at $ 98^ a share. 202 LESSON 40. BILLS. A Bill of Goods is a written statement of g^oods sold, and of payments, if any, received for them. A Bill of Services is a written statement of ser- vices rendered, or of labor performed. A Statement of Account is a statement of the sum due according to the accounts already rendered. Thus, Tliv. Jcyn^, To BROWN & CO., Dr. June, 1 To Account rendered The Creditor is the person who sells the goods, or who performs the labor. The Debtor is the person who buys the goods, or who pays for the services rendered. The Debit Side of the Account consists of the items due to the person who renders the account. The Credit Side consists of the amounts received by the person who renders the account. The Balance of an Account is the difference be- tween the amounts of the Debit and Credit Sides. Note. When a bill is paid, it should be receipted by writing at the bottom of the bill the date of payment and the words Beceived pay- ment, and under these words the creditor should sign his name and deliver the receipt to the debtor. If a clerk has authority to sign his employer's name, he should write under his employer's name his own name preceded by the word by or per. LESSON 41. 203 RECEIPTED BILLS OF GOODS. Boston^ June i, 1893. nil. f^alytit ^Axyymaru, Bought of CHARLES EDMONDS. 1893 May 15 10 lbs. Coffee @35^ 1 $3 50 50 lbs. Sugar @ 5^ 1 ^ 50 2 lbs. Tea @65^ 1 30 28 lbs. Butter @32^ 8 16 96 26 June 1, 1893. Received payment, JdTyib^ ycyiA, Exeter., June 1, 1893. To KELLY & GARDNER. Dr. 1893 Mar. 8 To 2 gals. Molasses @ 55^ $1 10 $ To 2 bbls. of Flour @ $5.75 11 50 12 60 Apr. 5 To 15 lbs. Rice @ 9^ 1 35 To 25 lbs. Butter @ 33^ 8 25 9 60 22 20 Cr. Mar. 8 By 2 cords Birches @ $4.50<^ 9 00 By 3 bu. Potatoes @ 65^ Balance due 1 95 10 95 11 25 June 1, 1893. Received payment, 204 LESSON 42. Make out bills, and receipt for them the first day of the month that follows the purchase : Bought of JOHN THOMPSON & CO. 1893 Feb. 7 'is 9 lbs. Ham 18 " Steak 15 " Mutton 11 " Veal @15P @25p @16^ 2. jci7ybt'3i. ^(yffimy, To HOWARD MANSUR, Dr 1898 May 8 25 lbs. Codfish @ 9^ ii 10 30 " Bacon @ 10 i( 18 10 " Coffee @ 85^ " 25 2 bbls. Flour @ $5.75 I. fa/b'Tb '/Tldv^AycM, To ROBERT STUART, Dr. 1898 Mar. 8 12 doz. Eggs 17 lbs. Butter @26^ ®32^ a 15 34 '' Cheese 16 bu. Potatoes @ 8p @85fi 1898 Apr. 5 27 bags Whole Com 80 " Meal @ $1.12 (S 1^00 (( 12 60 " Oats 7 tons Hay @ 0.65 @ 17.00 (( 19 Cr. By Cash $200 LESSON 43. 205 PERCENTAGE. A percentage of a number is the result obtained by taking a stated number of hundredths of it. One hundredth of a number is called one per cent of it ; two hundredths, two per cent ; three hundredths, three per cent ; and so on. This sign % stands for the words per cent. Thus, 5 % of 300 means 0.05 of 300. 15^ % of 300 means 0.15i of 300. \ % of 300 means 0.00^ of 300. When the per cent can be expressed a.s a common fraction in small terms^ it is better to write it as a common fraction. 50 1 50 % of a number is or - the number. ^° 100 2 25 1 25 % of a number is — or - the number. '" 100 4 75 % of a number is — ^ or - the number. '" 100 4 12.^ 1 12 il % of a number is — 2 or - the number. - '" 100 8 gi 1 8i% of a number is -^ or — tlie number. ^ ^" 100 12 16|%of anumber is 100 - the number. 33i%of anumber is 100 - the number. 3 66f % of a number is 100 2 - the number, 3 20 % of a number is 2« or 100 -,the number. 5 125 % of a number is 125 or 100 - the number. 4 Express as per cent : i i -h i 5 6 f A i i i 1- i f iV 206 LESSON 44. Find 161% of 336. 336 0.16J 112 2016 336 54.88 16i% = 0.16^. Find 16|% of 336. 16|% = i I of 336 = 56. ^Q. Ans. Hence, 54.88. A71S. To find a per cent of a number : We multiply the number by the given per cent. Find : 1. 6% of 175. 6. 331% of 1840. 2. 25% of 300. 7. 50% of 1216 oz. 3. 16|% of 480 men. 8. 66f % of 1518 lbs 4. 51% of 675 sheep. 9. 75% of 2040 ft. 5. 10% of 1560dys. 10. 121% of 1648 mi. To find the per cent one given number is of another. What per cent of 9 is 3 ? Since 1 is i of 9, 3 is 3 x i 1 = 1; and i = 3)1.00 0.331 ^ 3310/^. The same result is obtained if we divide 3 by 9. 9 )3.00 0.333 331%. Hence, To find the per cent one number is of another : We divide the number which represents the percentage by the other number^ carrying the division to hundredths. What per cent of 1. 90 is 30? 2. 960 is 24? 3. 30 is 90? 4. 24 is 960? 5. 4108.5 is 821.7? 6. 2740 mi. are 548 mi. ? 7. 36 in. are 27 in. ? 8. 12.75 are 10.35? 9. 2240 lbs. are 2000 lbs. ? 10. 7000 grs. are 5760 grs. ? LESSON 45. 207 INTEREST. Money paid for the use of money is called Interest. The money at interest is called the Principal. The sum of the interest and principal is called the Amount. To find interest for a given number of months at 6% : We put the decimal point two places to the left in the principal, and multiply by one-half the number of months. Find the interest on $630 for 4 mos. at 6% : S6 30 Q Here we put the decimal point tico places to the left in — — — - the principal, and multiply by 2 ; that is, by \ of 4. If we wished to find the interest at 4J%, we should divide the $12.60 by 6, and multiply the quotient by ^^. Find the interest on : 1. $1220.40for 3 mos. at 6%. 2. $2612.80for 4mos. at5%. 3. $2084.20 for 1 mo. at ^%. 4. $4500.60 for 5 mos. at 5|%. 5. $7508.50 for 6 mos. at 31%. 6. $8501.20 for 3 mos. at 5%. 7. $9056.75 for 7 mos. at 6%. To find the amount : We find the interest and add it to the principal. Find the amount of : 8. $1000 for 4 mos. at 6%. 9. $1500 for 6 mos. at 4%. 10. $75.50 for 4 mos. at 5%. 208 LESSON 46. To find interest for a given number of days at 6% : We put the decimal point three places to the left in the principal^ and multiply hy one-sixth of the number of days. Find the interest on 17260 for 90 dys. at 6%. $ 7.260 Here we i)ut the decimal point three places to the 15 left in the principal, and multiply by 15 ; that is, by \ 1108.900 ^f ^0. To find the interest for any other rate than 6 per cent : We find the interest at Q %^ divide the result hy 6, a^id multiply the quotient hy the given rate. If the time is given in months and days ; or in years, months, and days ; reduce the time to days, reckoning 30 days for a month, and 360 days for a year. Find the interest on : 1. 13600 for 30 dys. at 6%. 2. $4500 for 33 dys. at 6%. 3. $8000 for 93 dys. at 6%. 4. $9875 for 60 dys. at 5%. 5. $2525 for 63 dys. at ^%. 6. $3750 for 90 dys. at 31%. 7. $15.80 for 63 dys. at 4%. 8. $256.40for 45 dys. at5i%. 9. $645.25for 123 dys. at 3%. 10. $950.50 for 2 yrs. 4 mos. 6 dys. at 6%. 11. $20,000 for 1 yr. 7 mos. at 4%. 12. $515.25 for 1 yr. 9 mos. 8 dys. at ^%. 13. $1000 for 2 yrs. 1 mo. 19 dys. at 5%. 14. $216.75 for 2 yrs. 2 mos. 21 dys. at 5i%. 15. $927.35for lyr. 8 mos. 28dys. at3%. ANSWERS. Lesson 36. Page 145. 1. 1102. 7. 1447. 13. 133.77. 19. 438,997. 2. 1445. 8. 14,219. 14. 222,038. 20. 527.4053. 3. 1982. 9. 18,078. 15. 209,381. 21. 171.8762. 4. 986. 10. 26,405. 16. 260.164. 22. 200.8964. 5. 1712. 11. 25,934. 17. 72.4347. 23. 85.351. 6. 1283. 12. 231.84. 18. $636.43. Lesson 37. Page 146. 24. 1491.4375. 25. $194.36. 1. $18,214. 3. 2,480,195. 5. 1,602,778. 7. 1,019,007. 2. 2017. 4. 1,638,162. 6. 1,471,784. Lesson 38. Page 147. 8. 711,998. 1. 704. 6. 1921. 11. 11,878. 16. 116,689. 2. 381. 7. 3868. 12. 2795. 17. 457,547. 3. 523. 8. 350. 13. 10,748. 18. 41,799. 4. 42(3. 9. 2529. 14. 8757. 19. 85,216. 5. 159. 10. 1310. 15. 31,407. Lesson 39. Page 148. 20. 24,184. 1. 0.06. 9. 5.855. 17. 18.7132. 24. 33.151. 2. 0.78. 10. 2.759. 18. 5.8908. 25. 0.0023. 3. 0.893. 11. 0.668. 19. 1.0276. 26. 747.8268. 4. 2.306. 12. 1.857. 20. 0.9558. 27. 761.613. 5. 0.067. 13. 0.885. 21. 2.475. 28. 18.777. 6. 0.107. 14. 0.072. 22. 74.2425. 29. 57.6246. 7. 2.224. 15. 0.505. 23. 0.5176. 30. 5.8435. 8. 0.882. 16. 3.1989. Lesson 40. Page 149. 1. 52. 4. 1106. 7. 71,041. 10. 51. 2. m. 5. 2920. 8. 109,008. 11. $1.17. 3. 1782. 6. 76,831. 9. 14,095. Lesson 41. Page 160. 1. 7374. 5. 9765. 9. 34,260. 13. 26,394. 2. 9566. 6. 14,245. 10. 8256. 14. 16,394. 3. 8637. 7. 14,268. 11. 33,882. 15. 34,584. 4. 10,971. 8. 10,344. 12. 18,744. 209 16. 46,935. 210 ANSWERS. 17. 31,304. 26. 15,138. 35. 117,416. 44. 206,712. 18. 41,335. 27. 49,445. 36. 352,640. 45, , 688,275. 19. 40,524. 28. 35,908. 37. 340,278. 46. 508,624. 20. 54,978. 29. 58,668. 38. 220,969. 47. 607,401. 21. 65,688. 30. 27,153. 39. 300,656. 48. , 270,879. 22. 34,696. 31. 30,195. 40. 504,126. 49. 438,921. 23. 29,355. 32. 53,400. 41. 312,741. 50. 399,063. 24. 26,082. 33. 60,501. 42. 332,343. 51. 798,384. 25. 16,338. 34. 61,686. Lesson 42 43. 658,674. . Page 151. 1. 3648. 9. 27,553. 17. 4,235,374. 25. 4,175,712. 2. 8512. 10. 69,184. 18. 5,952,816. 26. 0,418,652. 3. 20,440. 11. 34,272. 19. 5,921,580. 27. 3,412,836. 4. 8556. 12. 56,066. 20. 4,212,032. 28. 5,356,521. 5. 18,112. 13. 72,412. 21. 1,601,613. 29. 3,276,303. 6. 26,508. 14. 47,058. 22. 786,714. 30. 6,731,472. 7. 14,763. 15. 62,568. 23. 4,533,573. 8. 20,444. 16. 3,566,541. 24. 2,722,225. Lesson 43, , Page 152. » 1. 4670. 8. 101,088,000. 15. 11,428,368,000. 2. 31,200. 9. 194,880,000. 16. 172,437,740,000. 3. 587,000. 10. 350,420,000. 17. 10,800. 4. 18,-336,000. 11. 104,832,000. 18. 48,000. 5. 29,124,000. 12. 97,290,000. 19. 108,000. 6. 40,635,000. 13. 50,430,400. 20. $210, 7. 86,140,000. 14. 49,854,240. Lesson 44 . Page 153. 1. 240.204. 7. 6601.68. 13. 11.9385. 19. 6828.467. 2. 197.896. 8. 5165.71. 14. 91.008. 20. 54.2913. 3. 1769.08. 9. 436.5. 15. 101.1725. 21. 25.6275. 4. 55.5676. 10. 0.8421. 16. 21015.984. 22. 87.0672. 5. 367,848. 11. 34.704. 17. 3417. 23. 4603.8601. 6. 232.379. 12. 0.0164. Lesson 45, 18. 9550. Page 154. 24. 4954.6497. 1. 109,500. 4. $97.75. 7. 1140. 10. 14,560 ft. 2. 57,096. 5. .$66.50. 8. $567. 11. $32.40. 3. .$67.20. 6. .$999. Lesson 49, £. 354.36. Page 158. 1. 217. 5. 36. 9. 54. 13. 113. 2. 292. 6. 143. 10. 117. 14. 105. 3. 149. 7. 175. 11. 121. 15. 69. 4. 108. 8. 103. 12. 115. 16. 256-1. ANSWERS. S 17. 235-2. 30. 327. 43. 3250-3. 56. 27,873-2. 18. 211-1. 31. 1855-1. 44. 979-4. 57. 14,353-5. 19. 180-1. 32. 1075-1. 45. 47,937. 58. 4290-2. 20. 143-4. 33. 2116-3. 46. 15,291. 59. 1769-3. 21. 124-4. 34. 1914-3. 47. 11,693. 60. 6260. 22. 100-7. 35. 1163-5. 48. 15,659. 61. 9341. 23. 2897. 36. 1237. 49. 11,062. 62. 15,085-4. 24. 1958. 37. 541-1. 50. 13,226. 63. 5214-1. 25. 1424. 38. 917-3. 51. 10,978. 64. , 3279-3. 26. 1795. 39. 1959-2. 52. 10,908. 65. , 8173-3. 27. 559. 40. 817-8. 53. 11,279-3. 66. , 19,049-1. 28. 168. 41. 817-3. 54. 8247-2. 29. 1071. 42. 770-6. 55. 12,766-2. Lesson 51 . Page 160. 1. 164-34. 10. 109-11. 19. 117-:38. 28. 154-5. 2. 155-8. 11. 126-14. 20. 113-30. 29. 317-20. 3. 201-4. 12. 128-52. 21. 138-5. 30. 159-33. 4. 141-37. 13. 130-47. 22. 141-8. 31. 606-32. 5. 149-36. 14. 101-21. 23. 222-9. 32. 428-95. 6. 88-66. 15. 126-14. 24. 171-21. 33. 127-258. 7. 109-26. 16. 129-23. 25. 117-25. 34. 116-36. 8. 170-9. 17. 118-27. 26. 106-30. 35. 24-338. 9. 218-24. 18. 105-17. 27. 165-17. 36. 138-2. Lesson 52 . Page 161. 1. 139-389. 15. 112-618. 29. 1024^94. 43. 1298-187. 2. 278-54. 16. 127-336. 30. 761-173. 44. 1182-273. 3. 145-162. 17. 195-80. 31. 1363-134. 45. 4740-184. 4. 129-157. 18. 106-113. 32. 830-610. 46. 153-3330. 5. 109-196. 19. 219-207. 33. 682-69. 47. 406-1106. 6. 122-290. 20. 211-200. 34. 884-110. 48. 126-486. 7. 134-578. 21. 141-318. 35. 670-526. 49. 125-3932. 8. 79-164. 22. 108-825. 36. 724-80. 50. 140-3958. 9. 53-159. 23. 97-465. 37. 2315-55. 51. 108-4761. 10. 227-129. 24. 147-540. 38. 1347-189. 52. 127-464. 11. 237-210. 25. 1211-427. 39. 1009-210. 53. 83-2717. 12. 108-420. 26. 1160-105. 40. 1774-323. 54. 148-1854. 13. 121-135. 27. 807-12. 41. 654-1.52. 14. 103-622. 28. 223-805. 42. 2419-285. Lesson 53 . Page 162. 1. $12. 4. 36 cts. 8. $56. 12. 56 cts. 2. 8dys. 5. $48. 9. 5. 13. 12 dys. 3. §35. 6. 9. 10. $14. 14. 6 lbs. 7. 55 cts. 11. $20. 211 n2 ANSWERS. Lesson 1. Page 163. 1. 1.09. 6. 2.31. 11. 22.1. 16. 33.8. 2. 1.16. 7. 3.13. 12. 47.3. 17. 0.131. 3. 1.15. 8. 2.8. 13. 2.34. 18. 1.64. 4. 2.32. 9. 1.12. 14. 0.653. 19. 1.21. 5. :].ll. 10. 22.4. 15. 3.72. 20. 1.22. Lesson 2. Page 164. 21. 23.1. 1. 430. 11. 50. 21. 90. 31. 3.2. 2. 305. 12. 60. 22. 43. 32. 29. 3. 272. 13. 60. 23. 31. 33. 2.6. 4. 290. 14. 90. 24. 27. 34. 4.8. 5. 230. 15. 1100. 25. 3.1. 35. 1.1. 6. 160. 16. 1100. 26. 2.3. 36. 2.2. 7. 130. 17. 1300. 27. 16. 37. 22. 8. 400. 18. 140. 28. 3.6. 38. 310. 9. 250. 19. 1600. 29. 44. 39. 140. 10. 402. 20. 180. 30. 4.02. Lesson 3. Page 165. 1. 10.03. 9. 0.017. 17. 20,000. 25. 35,900. 2. 3.1416. 10. 7.8. 18. 500. 26. 24,163,000. 3. 5.4. 11. 6.48. 19. 1200. 27. 7.46. 4. 8.17. 12. 2100. 20. 2480. 28. 0.04. 5. 115.1875. 13. 130. 21. 20.3. 29. 40. 6. 3692. 14. 5025. 22. 8.302. 30. 400. 7. 0.312. 15. 1040. 23. 0.672. 31. 4900. 8. 88. 16. 3,209,000. Lesson 4. 24. 240.6. Page 166. 32. 0.04. 1. 118. 4. 170. 8. 256. 12. 5.5 ets. 2. 37.50. 5. 29. 9. $125. 13. 28. 3. $2003. 6. 7. 17. 18. 10. 109. 11. 6.25. 14. 24. Lesson 5 . Page 167. 1. 1.2109. 3. 24.2985 6. 0.0029. 9. 0.0008. 2. 3.iai3. 4. 140.6923. 7. 0.0136. 10. 0.0001. 5. 0.0082. 8. 0.0133. Lesson 6. Page 168. 1. 5,798,758 tons. 4. $693,048,702. 7. 41.64 bu. 2. 14.28 times. 5. $69,786,800. 8. 41 bu. 3. 1,295,179 tons. 6. 165,831 acres. 9. 14 bu. Lesson 8. Page 170. 1. 13pts. 3. 57 pts. 5. 65 pts. 7. : 252 qts. 2. 7 pts. 4. 36 gi. 6. 90 pts. 8. 1512 pts. ANSWERS. 213 9. 28 gals. 2 qts. 1 pt. 11. 45 gals. 2 qts. 1 pt. 13. 131 gals. 2 qts. 10. 6 gals. 1 qt. 1 pt. 12. 55 gals. 1 qt. 14. 53 gals. 3 qts. 1 pt. 3 gi. Lesson 9. Page 171. 1. 20 gals. qt. 1 pt. 3. 103 gals. 1| pts. 5. 10 gals. 3 qts. 1 pt. 2. 48 gals. 1 qt. 4. 13 gals. 3 qts. 6. 9 gals. 3 qts. I pt. 7. 21 gals. 1 qt. 1 pt. Lesson 10. Page 172. 1. 70 gals. 3 qts. 1 pt. 3. 31 qts. 5. 16 gals. 3 qts. 2. 220 gals. 2 qts. 4. 21 gals. 1| pts. 6. 16 gals. 1 qt. 1 pt. Lesson 11. Page 173. 1. 188 qts. 5. 21. 9. 411 bu. 1 pk. 2 qts. 2. 63 bu. 1 pk. 4 qts. 6. 2 bu. 2 pks. 2 qts. 10. 2 bu. 3 qts. 3. 69 bu. 1 pk. 7 qts. 7. 16 bu. 3 pks. 5 qts. 11. 3 bu. 1 pk. 7 qts. 4. 3 bu. 2 pks. 6 qts. 8. 28 bu. 2 pks. 6 qts. 12. 13 bu. 2 pks. 6 qts. Lesson 12. Page 174. 1. 2. 8174 lbs. 39 t. 596 lbs 3. 18 t. 5. 5 t. 614 lbs. 7. 28 lbs. 6 oz. . 4. 1 t. 600 lbs. 6. 1 t. 500 lbs. 8. 81 cts. 9. §56.26. Lesson 13. Page 175. 1. 2. 3. 4. 1240. 172 dwt. 7 lbs. 4 oz. 480. 5. oz. 15 dwt. 9. 53 oz. 6 dwt. 6. 80 cts. 10. 165 oz. 18 dwt. 7. 24. 11. 29oz. 18dwt.3grs. 8. 109. 12. 4 oz. dwt. Lesson 14. Page 176. 1. 2. 3. 5012 min. 4. 5 dys. 13 hrs. 40 min. 7. 18 dys. 10 hrs. 27,060 sec. 5. 1 yr. 2 dys. 1 hr. 8. 6 dys. 16 hrs. 18 min. 14 dys. 4 hrs. 6. 1 wk. 1 dy. 9 hrs. 3 sec. 9. 4 dys. 10 hrs. 42 min. Lesson 16. Page 178. 1. 2. 3. 4. 5. 6. 7. 211 in. 100 in. 908 rds. 6301 rds. 3 mi. 170 rds. 2 mi. 80 rds. 8. 11 mi. 15. 10 yds. 2 ft. 11 in. 9. 48 yds. 11 in. 16. 18 yds. 6 in. 10. 68 yds. 1 ft. 5 in. 17. 6 mi. 157 rds. 2^ ft. 11. 30 mi. 89 rds. 4i yds. 18. 8 mi. 187 rds. 31 ft. 12. 39 mi. 275 rds. 14 ft. 19. 3 mi. 64 rds. 4ryds. 13. 18 mi. 262 rds. 5 ft. 20. 9 mi. 32 rds. 4 yds. 14. 1 mi. 272 rds. 15 ft. 11 in. 21. 171 yds. 1 ft. 3 in. 22. 283 rds. 5 yds. 2 ft. Lesson 17. Page 179. 1. 2. 60 ft. 84 ft. 3. 68 ft. 5. $120. 7. 3.5 in. 4. 90 ft. 6. 66 in.: 88 in.; 22 ft. 8. 10.5 in. 214 ANSWERS. Lesson 18. Page 180. 1. 4570 sq. ft. 4. 312 sq. ft. 68 sq. in. 7. 13 A. 75 sq. rds. 2. 5 A. 5. 14 A, 8. 9 sq. yds. 7 sq. ft. 20 sq. in. 3. 570 sq. rds. 6. 533 A. 36 sq. rds. 9. 19 A. 20 sq. rds. Lesson 19. Page 181. 1. 40 sq. in. 5. 90 sq. in. 9. 16 sq.ft. 13. 4 sq. yds. 2. 54 sq. in. 6. 64 sq. in. 10. 420 sq. ft. 14. 986 sq, yds. 3. 56 sq. in. 7.6 sq. ft. 11. 270 sq. in. 15. 80 sq. rds. 4. 110 sq. in. 8. 8 sq. ft. 12. 36 sq. ft. 16. 594 sq. ft. Lesson 20. Page 182. 1. 860 sq. ft. 3. 72 sq. yds. 5. 16 sq. yds. 7. 112 sq. in. 2. 30 sq. yds. 4. 10 A. 6. 32 sq. yds. 8. 122 sq. in. 10. 314 sq. in. ; 805 sq. in. ; 1257 sq. in. 9. 54 sq. ft. 11. 805 sq. in. ; 1018 sq. in. 12. 380 sq. in. ; 616 sq. in. 13. 707 sq. in. ; 1257 sq. in. ; 1521 sq. in. ; 1663 sq. in. 14. 1964 sq. in. Lesson 21. Page 183. 1. 5 strips. 2. 10 strips. 3. 35 yds. ; ^ yd. Lesson 22. Page 184. 1. 8. 2. 38.00. 3. 34.50. 4. 10. 5. 9. Lesson 23, , Page 185. 1. 372 cu. ft. 4. 175 cu, . yds. 7 cu ..ft . 7. lOcds. 2. 22 cu. yds. 6 cu. ft. 5. 1 cu. yd. 16 cu. ft. 8. 15 cds. 96 cd. ft. 3. 23 cu. yds. 25. cu. ft. 6. 64 cu.; j^ds. 25cu . ft . 9. 4cu. 10. $9. yds. 20 cu. ft. Lesson 24. Page 186. 1. 96 cu. in. 4. 84 cu. in. 7. 30 cu. ft. 2. 48 cu. in. 5. 320 cu . in. 8, 462 cu. yds. 3. 64 cu. in. 6. 27 cu. 1 ft. or 1 cu, yd 9. 264 cu. yds. Lesson 30 . Page 192. 1. 3. 5. 7. 9. 3f 13. 171, 17. 6|. 21. 3,V 2. 6. 6. 9. 10. 6|. 14. 3|. 18. 31. 22. 3-fV 3. 2. 7. 3i 11. 61. 15. 31 19, 4|. 23. 2,V. 4. 6. 8. 9f. 12. 5tV 16. 4f. 20. SI. 24. 5H. 1. f. 5. f- 9. f. 13. I 17. h 21. f. 2. I 6. h 10. f. 14. f. 18. f. 22. f. 3. i- 7. h 11. f. 15. i- 19. f. 23. 4. 4. h 8. I 12. f 16. I. 20. f. 24. i. ANSWERS. 215 1. f. 2. f 3. A. 1. 5. 2. 7. 3. 6?. 4. f 5. A. 6. ^. 4. 10. 5. 6^. 6. 15i Lesson 31. Page 193. 7. t- 10. tV 13. i 16. i. 8. T^j. 11. ^. 14. i. 17. f 9. ^,. 12. /r- 15. f 18. :>f. Lesson 32. Page 194. 7. 91. 10. 8^. 13. 16|. 16. 12. 8. 9|. 11. 14. 14. 12|. 17. 18. 9. 13. 12. 16i. 15. 11. 18. 24. 19. 5|. 20. 105, 21. 16. 15. 3. 20. 5. 25. 7. 22. 9. 70. 11. 150^. 13. 17. 15. 22. 14. 4. 21. 6. 30. 8. 24. 10. 46. 12. 184|. 14. 27^. 2. Lesson 33. Page 195. 7. 2^. 8. 15. 10. 1^. 11. H. 12. f 13. i. 14. f 15. 1|. 16. H. 17. |. 18. |. Lesson 34. Page 196. 19. i 20. 1^. 21. 4. 22. 1|. 23. 3. 24. 3. 25. II 26. 2. 27. i 28. f. 29. 2. 30. 1. 31. 5. 32. 3. 33. 1^. 34. 2. 35. \. 36. 5. 4 9 10 TJ' TJ' T2' TJ' T2' T2- TJ» rV tI- h h f- f- 3 27 in. 10 oz. 1000 lbs. 24 cu. ft. 5 6 10 7 . TJi T8' T5- 6. hh /t. /f 7. 1^5, il, t\. 8. 9. T5> T^7» T5- 10. it, ft, ||. 11- H, I?, ^. 10 21 11 8 ±Al. OS. IfS, TfTT. 13. 14. 15. Ih ii» T2' tV H, 'rh H' 2T' 2T- Lesson 37. Page 199. 7. H- 9. 7^3^. 10. 34. 11. Iff. 12. 7|. 13. 0.06. 14. 0.15. 15. 0.025. 16. 0.04. 17. 0.135. 18. 0.032. 19. 0.004. 20. 17.875. Lesson 38. Page 200. 6. 112cd. ft. 11. 27qrs.;29 15. 36 cts. 7. li^ pts. qrs. 16. 21 cts. 8. 16 hrs. 12. 9 halves. 17. 7 mi. 9. 45min. 13. 11. 18. 7| mi. 120 sq. rds. 10. 8 qrs. 14. 2 gals. 19. lOimi. Lesson 39. Page 201. $0.90 $0.81 $1.63 $1.78 $5.21 6. $1.98. 7. $6.00. 8. $27.00. 9. $31.50. 10. $0.95. 11. $1.04. 12. $0.84. 13. $3.05. 14. $2.02. 15. $6.21. 16. $29.48. 17. $13.44. 18. $19.25. 19. $6.16. 20. $2.24. 21. 5.375. 22. 7.075. 23. 1.9375. 24. 5.0625. 20. I yd. 21. $5i. 22. $5\. 23. $1.80. 21. $7.16. 22. $15.60. 23. $1.40. 24. $506.25. 25. $884.25. 216 ANSWERS. Lesson 42. Page 204. 1. $9.46. 2. $21.45. 3. $24.88. 4. $18.24. Lesson 44. Page 206. 1. 10.5. 3. 80 men. 5. 156 dys. 7. 608 oz. 9. 1530 ft. 2.75. 4. 36 sheep. 6. $280. 8. 1012 lbs. 10. 206 mi. 1. 33i%. 3. 3000/0. 5. 20%. 7. 75 o/,. 9. 89^%. 2. 2^%. 4. 4000%. 6. 20%. 8. 12/^%. 10. 82f %. Lesson 45. Page 207. 1. $18.31. 3. $7.82. 6. $106,265. 9. $1530. 2. $41.88. 4. $103.14. 7. $316.99. 10. $76.76. 5. $131.40. 8. $1020. Lesson 46. Page 208. 1. $18. 4. $82.29. 7. $0.11. 10. $134.02. 13. $106,805. 2. $24.75. 5. $19.88. 8. $1.76. 11. $1266.67. 14. $26.52. 3. $124. 6. $31.25. 9. $6.61. 12. $41.09. 15. $48.53. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. 6N0VM8JI8 DUE LD 21-100m-9,'47(A5702sl6)476 r b I / 44 / UNIVERSITY OF CALIFORNIA UBRARY