LT ro 1862. IN MEMORIAM. John Swett THE PROGRESSIVE PRIMARY ARITHMETIC, FOB PRIMARY CLASSES PUBLIC AND PEIVATE SCHOOLS. BY HORATIO N. ROBINSON, LL. D. AUTHOR OP A FULL COURSE OF MATHEMATICS. NEW YORK: IYISON, PHINNEY & CO., 48 & 50 WALKER ST. CHICAGO : S. C. GRIGGS & CO., 39 & 41 LAKE ST. BOSTON: BROWN, TAOGAKD & CHASE. PHILADELPHIA.: SOWER, BARXKS it, CO., AND J. B. LIPPINOOTT A CO. CINCINNATI: MOOKK. \VILSTACH, KKY8 A CO. SAVANNAH : J. M. COOPKK A CO. ST. LOUIS : KE1TU tt WOODS. KKW ORLKANS: BLOOMFIKLD, STKEL A CO. DETROIT: F. RAYMOND A co. 1862. Entered, according to Act of Congress, in the year 1858, by DANIEL W. FISH, A.M. In the Clerk's Office of the District Court of the United States for Northern New York. < .;- ELECTROTTPED AT THE BOSTON STEREOTYPE FOUNDRY. PEEFACE. THIS primary work is designed for small children, and as an easy introduction to the " Progressive Intel- lectual Arithmetic," for advanced classes. Its object is to lead the young pupil, by brief and simple processes, applied to practical examples of easy gradation, to acquire habits of thought and of reasoning, in their simplest forms, and to draw out and strengthen the mind by a progressive and almost imperceptible gra- dation of thought and expression. The operations of Adding and Subtracting, of Multi- plying and Dividing, are first shown by pictorial objects ; portions of the elementary tables are introduced at the commencement of each lesson, and applied to short ex- amples concerning familiar objects ; promiscuous reviews of the elementary tables, and the more simple and easy Denominate tables have been introduced. Fractions have been treated as far as was thought practicable in a work of this kind. It gives me pleasure to acknowledge my obligations toD. W.Fish. A.M., of Rochester, N. Y., a thorough, prac- tical teacher, and who has, by my request, prepared this little book, which, it is confidently believed, will, by its progressive and systematic arrangement, its simplicity and adaptation to the juvenile mind, insure for it abun- dant success. 54 !?3t ,3, SUGGESTIONS TO TEACHERS. 1. A TEACHER should have a particular time allotted to every exercise, and regular lessons should be assigned, to be recited each day at a specified hour. 2. Sufficient time being given the pupils to learn their lessons, they should not be allowed the use of the book at the time of recitation. 3. The teacher should first ascertain that the table is 4 thoroughly learned by every pupil in the class. 4. Each question should be slowly and distinctly read, and the pupils be called upon promiscuously ; the pupil called upon should stand erect, repeat the question, and then give the solution. This will require close attention. 5. A correct and uniform analysis of each question should be required from every pupil. 6. The class should be encouraged to detect and cor- rect errors in the statement and solution of questions, to be signified by raising the hand. 7. The teacher can extend the questions in each les- son at pleasure, either by repeating those given, or making additional ones. (4) PRIMARY ARITHMETIC. LESSON I. 1. What is the first thing to be taught and learned in Arith- metic? ANS. Counting. 2. What is counting ? ANS. Expressing numbers by words. 3. What is a number r ANS. A unit, or a collection of units. 4. What is a unit ? ANS. A single thing. 5. How may numbers be expressed ? ANS. By words, letters, and figures. 6. Which is the most common method? ANS. By figures. 7. How many figures are used to express numbers ? ANS. Ten. 8. Name them. ANS. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 9. Count the bells on each of the above rows. NOTATION AND NUMERATION. LESSON II. 1. What is No tation? Ans. Writing ^ num- bers. 2. What is Numeration ? Ans. Reading numbers. 3. How many letters are used to express numbers ? Ans. Seven. 4. What are they? Ans. I, V, X, L, C, D, and M. 5. What is this method called ? Ans. The Roman method. 6. Why is it so called? Ans. Because it was first used by the Romans. 7. How many figures or characters are used to express numbers ? Ans. Ten. 8. What are they ? Ans. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 9. What is this method called? Ans. The Arabic method. 10. Why is it so called? Ans. Because it was first used by the Arabs. 11. What may the ten figures used in ex- pressing numbers be called? Ans. The Arithmetical Alphabet. 12. Can all numbers be expressed by these ten figures ? Ans. They can, by repeating and combining them. NOTATION AND NUMERATION. 7 LE SSON III. REMARK. This lesson presents the printed and written figures, and the Roman letters, by which num- bers are commonly expressed. It should be carefully studied by children, until they can read the figures with facility when written on the black-board, or when they meet with them in books. Numbers. Printed Written Figures. Figures. Roman Letters. Naught o One i / I Two 2 2 II Three 3 s III Four 4 4 IV Five 5 5 V Six 6 6 " VI Seven 7 / VII Eight 8 $ VIII Nine 9 9 ^IX Ten 10 40 X Eleven 11 // XI Twelve 12 42 XII Thirteen 13 43 XIII Fourteen 14 44 XIV Fifteen 15 45 XV Sixteen 16 46 XVI Seventeen 17 // XVII Eighteen 18 4$ XVIII Nineteen 19 4 9 XIX Twenty 20 go XX Twenty-one 21 34 XXI 8 NOTATION AND NUMERATION. L ESS ON IV. Numbers. Printed Figures Written Figures. Roman Letters. Twenty-two 22 22 XXII Twenty-three 23 S3 XXIII Twenty-four 24 24 XXIV Twenty-five 25 25 XXV Twenty-six 26 26 XXVI Twenty-seven 27 27 XXVII Twenty-eight 2$ 2$ XXVIII Twenty-nine 29 29 XXIX Thirty 3t 30 XXX Thirty-one 81 Sf XXXI Forty 40 40 XL Forty-one 41 4tf XLI Fifty 50 50 L Fifty-one 51 5f LI Sixty 60 60 LX Sixty-one 61 6S LXI Seventy 70 70 LXX Seventy-one 71 rt LXXI Eighty 89 $0 LXXX Eighty-one 81 $s LXXXI Ninety 9$ 90 XC Ninety-one 91 9* XCI Ninety-two 92 92 XCII One hundred 10d too C Two hundred 200 200 CC Five hundred 500 500 D One thousand 100 4000 M NOTATION AND NUMERATION. LESSON V. REMARK. The children should now be furnished with slates and pencils, and required to read the follow- ing numbers from the book, or when written on the black-board by the teacher, and then to copy them on their slates in straight columns. 1 11 21 31 41 2 12 22 32 42 3 13 23 33 43 4 14 24 34 44 5 15 25 35 45 6 16 26 36 46 7 17 27 37 47 8 18 28 38 48 9 19 29 39 49 10 20 30 40 50 LESSON VI. 51 61 71 81 91 52 62 72 82 92 53 63 73 83 93 54 64 74 84 94 55 65 75 85 95 56 66 76 86 96 57 67 77 87 97 58 68 78 88 98 59 69 79 89 99 60 70 80 90 100 10 ADDITION. LESSON I. Putting two or more numbers or things together into one sum, is called ADDITION : thus, 1. m and m more make ^g. ^ ^g, ^ mug mug mugs. 2. and IS more make tree trees 2 2 3. C^<^ and <^& more make caps caps 6. trees. 4 ADDITION. 11 LESSON II. 1 and 1 are 2 1 and 2 are 3 1 and 3 are 4 1 and 4 are 5 1 and 5 are 6 1 and 6 are 7 1 and 7 are 8 1 and , 8 are 9 1 and 9 are 10 1 and 10 are 11 1. If a slate pencil cost 1 cent, and an or- ange 3 cents, how many cents will both cost ? ANALYSIS. They will both cost as many cents as the sum of 1 cent and 3 cents, which is 4 cents. Therefore if a slate pencil cost 1 cent, and an orange 3 cents, they will both cost 4 cents. 2. Sarah had 4 books, and her mother gave her 1 more ; how many books did she then have I 3. In a garden are 1 plum tree and 6 pear trees ; how many trees in the garden ? 4. A man gave 8 dollars for a coat, and 1 dollar for a hat ; how much did he give for both? 5. In a class are 5 girls and 1 boy ; how many pupils in the class ? 6. A boy gave 1 cent for a sponge, and 10 cents for a spelling book ; what did he give for both? 7. Bought a broom for 1 shilling, and some sugar for 9 shillings ; what did both cost ? 12 ADDITION. LESSON III. 2 and 1 are 3 2 and 2 are 4 2 and 3 are 5 2 and 4 are 6 2 and 5 are 7 2 and 6 are 8 2 and 7 are 9 2 and 8 are 10 2 and 9 are 11 2 and 10 are 12 1. James rode 2 miles in the stage, and 4 miles in the cars; how far did he ride in both? ANALYSIS. He rode as many miles as the sum of 2 miles and 4 miles, which is 6 miles. Therefore, since James rode 2 miles in the stage and 4 miles in the cars, he rode 6 miles in both. 2. If a barrel of cider cost 2 dollars, and a barrel of flour 7 dollars, what will both cost ? 3. A man had 2 sons and 5 daughters to support ; how many children had he ? 4. A lady gave 2 cents for some ribbon, and 10 cents for a comb; what did she pay for both ? 5. A farmer sold a sheep for 2 dollars, and a hog for 9 dollars ; what did he get for both ? 6. John went to the river to fish, and caught 2 trout and 8 perch ; how many fish did he catch ? 7. If a boy spend 2 cents and have 2 left, how many cents had he* at first? ADDITION. 13 LESSON IV, 3 and 1 are 4 3 and 2 are 5 3 and 3 are 6 3 and 4 are 7 3 and 5 are 8 3 and 6 are 9 3 and 7 are 10 3 and 8 are 11 3 and 9 are 12 3 and 10 are 13 1. Frank picked 3 ripe plums from one tree, and 5 from another ; how many did he pick from both ? ANALYSIS. As many plums as the sum of 3 plums and 5 plums, which is 8 plums. Therefore, since Frank picked 3 plums from one tree, and 5 from another, he picked 8 plums both. 2. A grocer sold 3 pounds of sugar to one man, and 4 to another; how many pounds did he sell to both 1 3. Mary bought an inkstand for 7 cents, and some paper for 3 cents ; how much did she pay for both ? 4. A beggar received 6 cents from one lit- tle girl, and 3 from another ; how many cents did he receive from both ? 5. A boy found two hen's nests ; in one were 8 eggs, in the other 3 eggs ; how many eggs were there in both nests ? 6. A knife cost 9 cents, and a top 3 cents ; what did they both cost I 14 ADDITION. LESSON V. 4 and 1 are 5 4 and 2 are 6 4 and 3 are 7 4 and 4 are 8 4 and 5 are 9 4 and 6 are 10 4 and 7 are 11 4 and 8 are 12 4 and 9 are 13 4 and 10 are 14 1. Henry had 4 cents in one hand and 3 cents in the other ; how many cents had he in both ? ANALYSIS. As many cents in both as the sum of 4 cents and 3 cents, which is 7 cents. Therefore, since Henry had 4 cents in one hand, and 3 cents in the other, he had 7 cents in both. 2. If a skein of silk cost 4 cents, and a yard of tape 6 cents, how much do both cost? 3. A farmer has 4 black sheep, and 8 white ones ; how many sheep has he of both kinds ? 4. There are 5 birds on one tree, and 4 on another ; how many birds are there on both trees ? 5. Rollin had 4 books, and his father gave him 4 more ; how many books had he then ? 6. If a lady paid 7 dollars for a dress, and 4 for a bonnet, what did she pay for both 1 7. There are 4 books on one shelf, and 9 on another ; how many books on both shelves 1 ADDITION. 15 LESS< 5 and 1 are 6 5 and 2 are 7 5 and 3 are 8 5 and 4 are 9 5 and 5 are 10 3N VI. 5 and 6 are 11 5 and 7 are 12 5 and 8 are 13 5 and 9 are 14 5 and 10 are 15 1. A miller sold 5 barrels of flour at one time, and 4 barrels at another; how many barrels did he sell in all 1 2. George lost 2 cents, and had 5 cents left ; how many cents had he at first ? 3. Gave 5 cents for a writing book, and 3 cents for a pen holder ; what was the cost of both? 4. A boy had 7 peaches in his basket, and his sister put in 5 more ; how many peaches had he then ? 5. Joseph rode 6 miles, and walked 5 miles ; how far did he go 1 6. Carrie had 5 roses, and Nellie had 8 ; how many roses had both ? 7. A merchant sold 5 yards of calico at one time, and 5 at another ; how many yards did he sell in all I 8. A farmer paid 10 dollars for a plow, and 5 dollars for a harrow ; how much did he pay for both 1 16 ADDITION. LESSON VII. 6 and 1 are 7 6 and 2 are 8 6 and 3 are 9 6 and 4 are 10 6 and 5 are 11 6 and 6 are 12 6 and 7 are 13 6 and 8 are 14 6 and 9 are 15 6 and 10 are 16 1. A boy, after losing 6 marbles, had 4 left ; how many had he at first \ 2. Albert spent 6 cents, and had 5 left ; how many had he at first ? 3. A man paid 3 dollars for a barrel of cider, and 6 dollars for a barrel of flour; what did he pay for both 1 4. A gardener picked 6 peaches from one tree, and 7 from another ; how many peaches did he pick from both ? 5. Dick caught 2 gray squirrels, and 6 red ones ; how many did he catch in all 1 6. A cabinet maker asks 6 dollars for a rocking chair, and 6 dollars for a table ; what is the cost of both ? 7. In the fruit dish are 6 red apples and 9 green ones ; how many apples in the dish \ 8. Edwin is 6 years old, and his sister Martha is 10 years older ; what is the age of .Martha? ADDITION. 17 LESSON VIII. 7 and 1 are 8 7 and 2 are 9 7 and 3 are 10 7 and 4 are 11 7 and 5 are 12 7 and 6 are 13 7 and 7 are 14 7 and 8 are 15 7 and 9 are 16 7 and 10 are 17 1. Bought a ton of hay for 7 dollars, and some oats for 6 dollars ; what was the cost of both 1 2. David gathered 3 quarts of walnuts, and Homer 7 quarts ; how many quarts did both gather ? 3. Howard had 7 rabbits, and Herbert gave him 2 more ; how many had he then ? 4. A farmer picked 5 bushels of apples from one tree, and 7 bushels from another ; how many bushels did he gather from both ? 5. Asa is 8 years old ; how old will he be 7 years from this time ? 6. In a basket are 7 bunches of green grapes and 7 bunches of purple ones ; how many bunches of both ? 7. If a boy earn 7 shillings in one week, and 9 shillings the next, how many shillings will he earn in 2 weeks 1 8. In a shop, 2 men and 7 boys are em- ployed ; how many persons are employed ? 18 ADDITION. LESSON IX, 8 and 1 are 9 8 and 2 are 10 8 and 3 are 11 8 and 4 are 12 8 and 5 are 13 8 and 6 are 14 8 and 7 are 15 8 and 8 are 16 8 and 9 are 17 8 and 10 are 18 1. Henry hoed 8 rows of corn one day, and 5 the next ; how many rows did he hoe in both days ] 2. Andrew had 8 apples and 8 peaches in his basket ; how many had he of both ? 3. There are 3 gentlemen and 8 ladies in a boat ; how many persons in the boat ? 4. A man had 8 dollars, and borrowed 6 more ; how many dollars had he then ? 5. Bought a pound of raisins for 9 cents, and a pound of sugar for 8 cents ; what was the cost of both ? 6. Emily had 7 white roses and 8 red ones; how many roses had she of both kinds? 7. A boy sold 8 boxes of matches to one man, and 4 boxes to another; how many boxes did he sell to both ? 8. There are 10 shade trees now in the park, and 8 have been cut down; how many trees were set out ? ADDITION. 19 LESSON X. 9 and 1 are 10 9 and 2 are 11 9 and 3 are 12 9 and 4 are 13 9 and 6 are 15 9 and 7 are 16 9 and 8 are 17 9 and 9 are 18 9 and 5 are 14 9 and 10 are 19 1. If a firkin of butter is worth dollars, and a cord of wood ' dollars, what are both worth ? 2. A lady bought a muff for 9 dollars, and a hat for 5 dollars; what did she pay for both ? 3. Cora read 10 pages of history, and 9 pages of poetry; how many pages did she read in all ? 4. A traveler paid 9 shillings a day for his board, and 7 shillings a day for his horse; how much did he pay for both 1 5. Annie had 9 pictures, and her brother gave her 2 more ; how many had she then ? 6. If a peck of apples cost 9 cents, and a head of cabbage 4 cents, what will both cost ? 7. In a certain class there are 9 boys and 8 girls; ho/v- many scholars are there in the class I 8. There are 9 geese and 9 ducks swim- ming in a pond ; how many of both I 20 ADDITION. LESSON XI 10 and 1 are 11 10 and 2 are 12 10 and 3 are 13 10 and 4 are 14 10 and 5 are 15 10 and 6 are 16 10 and 7 are 17 10 and 8 are 18 10 and 9 are 19 10 and 10 are 20 1. If a man give 10 dollars for a harness, and 4 dollars for a whip, how much does he give for both ? 2. A farmer has 10 sheep in one lot, and 9 in another ; how many has he in both ] 3. A tailor sold a coat for 10 dollars, and a pair of pantaloons for 6 dollars; how much did he receive for both ? 4. A beggar met two boys ; one gave him 10 cents, and the other 7 cents ; how many cents did they both give him ? 5. There were 8 boys on one bench, and 10 on another; how many boys on both benches ? 6. Alice had 10 cents, and her mother gave her 2 more ; how many had she then ? 7. Bought a pig for 3 dollars, and a calf for 10 dollars ; how much did I pay for both ? 8. Charles picked 10 pears from a tree, and left 10 on it; how many were on the tree at first ? ADDITION. 21 LESSON X I I. PROMISCUOUS REVIEW. 2 and 5 are how many? 7 and 9 are how many ? 6 and 2 are how many ? 6 and 5 are how many ? 2 and 4 are how many? 3 and 6 are how many? 8 and 9 are how many? 4 and 4 are how many ? 9 and 4 are how many? 7 and 8 are how many ? 4 and 7 arc how many? 9 and 3 are how many ? 8 and 6 are how many? 2 and 9 are how many? 6 and 3 are how many? 5 and 4 are how many? 7 and 2 are how many ? 3 and 8 are how many? 3 and 3 are how many? 5 and 6 are how many? 3 and 9 are how many? 5 and 8 are how many? 4 and 5 are how many? 4 and 2 are how many? 9 and 8 are how many? 3 and 7 are how many? 8 and 5 are how many? 6 and 4 are how many? 4 and 9 are how many? 7 and 6 are how many ? 5 and 4 are how many ? 6 and 8 are how many? 2 and 7 are how many? 9 and 5 are how many? 7 and 5 are how many? 8 and 3 are how many? 2 and 3 are how many? 9 and 6 are how many? 5 and 2 are how many? 5 and 7 are how many? 6 and 9 are how many? 4 and G are how many? 7 and 7 are how many? 7 and 3 are how many ? 3 and 4 are how many ? 2 and 8 are how many ? 8 and 7 are how many? 5 and 9 are how many ? 4 and 8 are how many? 8 and 8 are how many ? 9 and 2 are how many? 6 and 7 are how many? 5 and 3 are how many ? 5 and 5 are how many ? 6 and G are how many ? 9 and 7 are how many ? 3 and 5 are how many? 2 and G are how many? 7 and 4 are how many ? 9 and 9 are how many? 22 ADDITION. LESSON XIII. PROMISCUOUS EXAMPLES. 1. Henry paid 6 cents for an inkstand, 4 cents for some pens, and 5 cents for a writing book ; how much did he pay for all I ANALYSIS. He paid as many cents as the sum of 6 cents, 4 cents, and 5 cents ; 6 cents and 4 cents are 10 cents , and 5 cents are 15 cents. Therefore, fyc. 2. A drover bought 4 cows of one man, 3 of another, and 7 of another ; how many cows did he buy in all I 3. Elizabeth gave 10 cents for three spools of thread, b cents for a thimble, and 9 cents for some needles ; how many cents did she give for all ] 4. A lady bought a dress for 8 dollars, a shawl for 9 dollars, and a parasol for 2 dollars ; how many dollars did she pay for them all ? 5. If a man paid 6 dollars for a cord of wood, 5 dollars for a ton of hay, 7 dollars for some pork, and 3 dollars for some beef, how many dollars did he pay for the whole ? 6. A boy traveled 6 miles one day, 8 miles the next day, and 10 miles the next ; how many miles did he travel in three days ? 7. A cabinet maker asked 12 dollars for a bureau, 10 dollars for a table, and 5 dollars for a stand ; what was his price for the whole ? SUBTEACTION. 23 LESSON I. Taking a less number or quantity from a greater, is called SUBTRACTION. leaves flSjL. rabbits, rabbit. 1 3 2 2. H taken from (||) |||| leaves ||J| hat hats, hats. 2 42 3. f^> Q taken from 00 (GO) leaves 06 eggs- 2 tulips 3 glasses 3 birds taken from taken from taken from * leaves I tulips. h CJESjif^Si I rH <*lHtJL Two times four are how many ? 5. If there are 3 owls in each of 3 cages, how many owls in all ? Three times three are how many ? MULTIPLICATION. 37 LESSON II. once 1 is 1 once 2 is 2 once 3 is 3 once 4 is 4 once 5 is 5 once 6 is 6 once 7 is 7 once 8 is 8 once 9 is 9 once 10 is 10 1. At 1 cent each, what will 2 eggs cost ? ANALYSIS. Since 1 egg cost 1 cent, 2 eggs, which are 2 times 1 egg, will cost 2 times 1 cent, which are 2 cents. Therefore, at 1 cent each, 2 eggs will cost 2 cents. 2. If a man earn 1 dollar a day, how much can he earn in 4 days ^ 3. If Rollin reads 1 hour each evening, how many hours will he read in 6 even- ings ] 4. What will 5 bushels of wheat cost, at 1 dollar a bushel ? 5. At 1 cent each, what will 9 steel pens costl 6. If a family eat 1 bushel of corn in a week, how many bushels would they eat in 10 weeks ? 7. If Thomas gets 1 credit mark a day, how many credit marks will he get in 7 days ? 8. If Henry write 1 page a day, how many pages will he write in 8 days I 38 MULTIPLICATION. LESSON III, 2 times 1 are 2 2 times 2 are 4 2 times 3 are 6 2 times 4 are 8 2 times 5 are 10 2 times 6 are 12 2 times 7 are 14 2 times 8 are 16 2 times 9 are 18 2 times 10 are 20 1. What will 2 pounds of rice cost, at 6 cents a pound I ANALYSIS. Since 1 pound costs 6 cents, 2 pounds, which are 2 times 1 pound, will cost 2 ta'?ftes 6 cew&, which are 12 m^s. T/ierefore 2 pounds of rice will cost 12 cerate, a 6 cents a pound. 2. Sarah gave 2 girls 3 apples apiece; how many did she give them both ? 3. If on one rose bush there are 4 roses, how many on 2 bushes 1 4. Almira bought 2 yards of ribbon at 5 cents a yard ; how much did she pay for the whole ? 5. At 7 cents a pound, what will 2 pounds of sugar cost ? 6. What will 2 tons of hay cost, at 9 dol- lars a ton ? 7. At 5 shillings a bushel, what will be the cost of 2 bushels of corn ? 8. At 2 cents apiece, what will 2 pears cost] MULTIPLICATION. 39 LESSON IV. 3 times 1 are 3 3 times 2 are 6 3 times 3 are 9 3 times 4 are 12 3 times 5 are 15 3 times 6 are 18 3 times 7 are 21 3 times 8 are 24 3 times 9 are 27 3 times 10 are 30 1. If a man earn 9 dollars in one week, how many dollars will he earn in 3 weeks 1 ANALYSIS. If a man t earn 9 dollars in 1 week, in 3 weeks, which are 3 times 1 week, he will earn 3 times 9 dollars, which are 27 dollars. Therefore, if a man earn 9 dollars in 1 week, he will earn 27 dollars in 3 2. If a farmer give 4 bushels of corn for one yard of cloth, how many bushels must he give for 3 yards ? 3. At 8 shillings a yard, what will 3 yards of silk cost ? 4. In one cent are 10 mills; how many mills in 3 cents'? 5. When sugar is worth 7 cents a pound, what will 3 pounds cost 1 6. A drover paid 3 dollars a head for sheep ; how much did he pay for 3 sheep 1 7. Egbert gave three of his classmates 5 apples apiece ; how many apples did he give them all ? 40 MULTIPLICATION. LESSON V. 4 times 1 are 4 4 times 2 are 8 4 times 3 are 12 4 times 4 are 16 4 times 5 are 20 4 times 6 are 24 4 times 7 are 28 4 times 8 are 32 4 times 9 are 36 4 times 10 are 40 1. What will 4 yards of ribbon cost, at 4 cents a yard ? ANALYSIS. Since 1 yard of ribbon costs 4 cents, 4 yards, which are 4 times 1 yard, will cost 4 ft'mes 4 ce/zte, wfo'cA are 1 6 cents. Therefore, 4 yards of ribbon, at 4 ceftte a yara 7 , mY/ eos 1 6 cents. 2. If a horse eat 8 quarts of oats a day, how many quarts will he eat in 4 days ? 3. At 9 shillings a day, what will 4 days' work come to ] 4. If one bench will seat 6 pupils, how many pupils will 4 benches seat ] 5. Martha's dress contains 7 yards of mus- lin, at 4 shillings a yard ; what was the cost of the dress ? 6. If Joseph walk 3 miles in an hour, how far will he walk in 4 hours ] 7. A butcher bought 4 calves at 5 dollars apiece ; what did they cost 1 8. At 2 shillings a quart, what will 4 quarts of molasses cost I MULTIPLICATION. 41 LESSON VI. 5 times 1 are 5 5 times 2 are 10 5 times 3 are 15 5 times 4 are 20 5 times 5 are 25 5 times 6 are 30 5 times 7 are 35 5 times 8 are 40 5 times 9 are 45 5 times 10 are 50 1. There are 7 days in 1 week ; how many days in 5 weeks 1 2. How far will a boat sail in 5 hours, at at the rate of 9 miles an hour ? 3. What will 5 barrels of flour cost, at 5 dollars a barrel 1 4. How many yards are there in 5 pieces of cloth, if there are 10 yards in each piece ? 5. If an orange is worth 4 apples, how many apples are 5 oranges worth 1 6. If a pupil work 6 problems a day, how many problems will he work in 5 days ? 7. Carlos gave 5 beggars 5 cents apiece ; how many cents did he give them all I 8. If a horse travel 8 miles an hour, how far can he travel in 5 hours I 9. Which is greater, 5 times 8, or 4 times 10? 10. Which is greater, 4 times 6, or 3 times 815 times 6, or 3 times 101,5 times 8, or 4 times 9 1 42 MULTIPLICATION. LESSON VII. 6 times 1 are 6 6 times 2 are 12 6 times 3 are 18 6 times 4 are 24 6 times 5 are 30 6 times 6 are 36 6 times 7 are 42 6 times 8 are 48 6 times 9 are 54 6 times 10 are 60 1. A farmer bought a plow for 5 dollars ; what would 6 plows cost at the same rate ? 2. At 2 dollars a day, how many dollars would a man earn in 6 days ? 3. What cost 6 tons of hay, at 7 dollars a ton! 4. George bought 6 lemons at 4 cents apiece ; what did they all cost I 5. There are 8 quarts in 1 peck; how many quarts in 6 pecks I 6. What will 6 pounds of honey cost, at 10 cents a pound] 7. What will 6 pounds of ginger cost at 6 cents a pound] 8. In a garden are 6 apple trees, and 4 bushels of apples on each tree ; how many bushels on all the trees ? 9. Which is greater, 6 times 1, or times 61 10. Which is greater, 6 times 5, or 3 times 10 I MULTIPLICATION. 43 LESSON VIII. 7 times 1 are 7 7 times 2 are 14 7 times 3 are 21 7 times 4 are 28 7 times 5 are 35 7 times 6 are 42 7 times 7 are 49 7 times 8 are 56 7 times 9 are 63 7 times 10 are 70 1. If a mill grind 5 bushels of wheat an hour, how many bushels will it grind in 7 hours ? 2. When wheat is worth 2 dollars a bushel, what will 7 bushels cost ? 3. In New England, 6 shillings make a dollar ; how many shillings in 7 dollars ? 4. If you write 8 lines in a day, how many lines will you write in 7 days ? 5. At 10 dollars a month, how many dol- lars will a man earn in 7 months ] 6. What will be the cost of 7 barrels of flour, at 7 dollars a barrel ] 7. What are 7 quarts of cherries worth, at 4 cents a quart I 8. At 9 shillings a bushel, what will 7 bushels of peaches cost ? 9. If there are 3 sheets of paper in one writing book, how many sheets in 7 books ? 10. Which is greater, 7 times 6, or 6 times 7 I 44 MULTIPLICATION. LESSON IX, 8 times 1 are 8 8 times 2 are 16 8 times 3 are 24 8 times 4 are 32 8 times 5 are 40 8 times 6 are 48 8 times 7 are 56 8 times 8 are 64 8 times 9 are 72 8 times 10 are 80 1. If a ton of hay cost 7 dollars, what will 8 tons cost ? 2. In New York, 8 shillings make a dol- lar ; how many shillings in 5 dollars ? 3. When coffee is worth 10 cents a pound, what will be the cost of 8 pounds I 4. At 4 cents a pound, what will 8 pounds of rice cost ? 5. What will 8 hats cost, at 3 dollars apiece ? 6. In one square yard are 9 square feet ; how many square feet in 8 square yards ? 7. What will 8 bushels of potatoes cost, at 6 dimes a bushel ? 8. At 6 dollars a barrel, what will 8 bar- rels of flour cost ? 9. What is the difference between 8 times 7, and 7 times 8 ? 10. At 8 cents a pound, what will 8 pounds of soda cost ? 11. What cost 2 slates, at 8 cents apiece? MULTIPLICATION. 45 LESSON X. 9 times 1 are 9 9 times 2 are 18 9 times 3 are 27 9 times 4 are 36 9 times 5 are 45 9 times 6 are 54 9 times 7 are 63 9 times 8 are 72 9 times 9 are 81 9 times 10 are 90 1. If a man travel by stage 5 miles an hour, how far will he travel in 9 hours I 2. What cost 9 lambs, at 6 shillings a head ? 3. What will 9 pounds of sugar cost, at 9 cents a pound ? 4. If Maria write 4 lines a day, how many lines will she write in 9 days ? 5. There are 10 dollars in one eagle; how many dollars in 4 eagles I 6. At 3 cents a skein, w r hat will be the cost of 9 skeins of silk ? 7. If a man consume 8 pounds of meat in | a week, how much will he consume in 9 weeks ] 8. If it take 7 yards of calico to make one dress, how many yards will it take to make 9 dresses ] 9. What cost 9 hats at 3 dollars apiece ? 10. What cost 9 pounds of nails, at 6 cents a pound ? 46 MULTIPLICATION. LESSON XI. 10 times 1 are 10 10 times 2 are 20 10 times 3 are 30 10 times 4 are 40 10 times 5 are 50 10 times 6 are 60 10 times 7 are 70 10 times 8 are 80 10 times 9 are 90 10 times 10 are 100 1. If a barrel of apples is worth 9 shil- lings, what are 10 barrels worth ? 2. At 5 dollars a yard, what are 10 yards of broadcloth worth ? 3. What will be the cost of 10 cords of wood, at 3 dollars a cord ? 4. What will be the cost of 10 yards of calico, at 10 cents a yard? 5. If a man earn 8 shillings a day, how much will he earn in 10 days? 6. If Margaret earn 7 shillings a week, how much will she earn in 10 weeks ? 7. In an orchard are 10 rows of trees, and 6 trees in each row; how many trees in the orchard ] 8. Ellen paid 4 shillings a yard for 10 yards of delaine ; what did the whole cost ] 9. What cost 10 bushels of potatoes, at 2 shillings a bushel ? 10. What cost 10 pounds of sugar at 10 cents a pound ] MULTIPLICATION. 47 LESSC PROMISCUO1 2 times 8 are how many? 3 times 9 are how many? 4 times 8 are how many? 7 times 5 are how many? 9 times 4 are how many? 6 times 3 are how many? 4 times 9 are how many? 3 times 4 are how many? 5 times 9 are how many? 7 times 6 are how many? >N XII. US REVIEW. 2 times 9 are how many? 8 times 2 are how many? 6 times 5 are how many? 4 times 7 are how many? 9 times 3 are how many? 5 times 7 are how many? 5 times 8 are how many? 9 times 5 are how many ? 6 times 4 are how many? 8 times 3 are how many? 3 times 7 are how many? 8 times 9 are how many? 6 times 8 are how many? 5 times 6 are how many? 7 times 3 are how many? 6 times 6 are how many? 9 times 7 are how many? 3 times 8 are how many? 4 times 6 are how many? 7 times 4 are how many? 5 times 2 are how many? 7 times 7 are how many? ( 4 times 2 are how many? 9 times 9 are how many? 4 times 3 are how many? 6 times 9 are how many ? 2 times 6 are how many? 8 times 5 are how many? 4 times 4 are how many? 9 times 8 are how many? 8 times 7 are how many? 5 times 4 are how many? 3 times 5 are how many? 3 times 4 are how many? 2 times 5 are how many ? 8 times 6 are how many? 7 times 8 are how many? 5 times 3 are how many? 3 times 6 are how many? 8 times 8 are how many? 7 times are how many? 2 times 4 are how many ? 5 times 9 are how many ? 9 times 8 are how many? 3 times 3 are how many ? 2 times 3 are how many ? 7 times 4 are how many? times 8 are how many? 3 times 6 are how many? 6 times 10 are how many ? 48 MULTIPLICATION. LESSON XIII. PROMISCUOUS EXAMPLES. 1. If one ream of paper cost 5 dollars, what will 9 reams cost I ANALYSIS. If 1 ream of paper cost 5- dollars, 9 reams, which are 9 times 1 ream, will cost 9 times 5 dol- lars, which are 45 dollars. Therefore, fyc. 2. At 4 dollars apiece, what is the value of 3 satin vests 1 of 6 ? of 8 ] of 7 ? 3. A man bought 5 brooms, at 2 shillings apiece, and 2 gallons of molasses at 4 shil- lings a gallon ; what was the cost of the whole I 4. At 9 dollars a month, how much will a man earn in 4 months I in 6 months I in 7 months 1 in 9 months ? 5. Bought 5 cords- of wood at 3 dollars a cord, and 2 tons of hay at 7 dollars a ton ; which cost the most, and how much ? 6. How much is 6 times 9 less 4 ? 8 times 7 less 6 1 4 times 7 less 8 1 7 times 7 less 9 1 7. Which is less, 6 times 8, or 5 times 914: times 10, or 5 times 813 times 9, or 5 times 6 ? 8. Peter sold his knife for 30 cents, and received in payment 3 quarts of chestnuts at 8 cents a quart, and the remainder in money ; how much money did he receive ? DIVISION. 49 LESSON I. DIVISION is finding how many times one number or quantity is contained in another : thus, 1. How many churches will three bells supply, if each church has one bell ? One is contained in three how many times ? 2. If one man can make 2 axes in one day, how many days will it take him to make 4 axes ? Two is contained in four how many times ? 3. A lady gave 6 dolls to some children, giving them 2 apiece ; to how many children did she give the dolls ? Two is contained in six how many times ? 4. If a chair-maker can make 3 chairs in a day, how many days will it take him to make 9 chairs ? Three is contained in nine how many times? 5. James gave 8 bunches of grapes to his sisters, giv- ing them 4 bunches each ; how many sisters had he ? Four is contained in eight how many times ? 50 DIVISION. LESSON II. 1 in 1, 1 time 1 in 6, 6 times 1 in 2, 2 times 1 in 7, 7 times 1 in 3, 3 times 1 in 8, 8 times 1 in 4, 4 times 1 in 9, 9 times 1 in 5, 5 times 1 in 10, 10 times 2 in 2, 1 time 2 in 12, 6 times 2 in 4, 2 times 2 in 14, 7 times 2 in 6, 3 times 2 in 16, 8 times 2 in 8, 4 times 2 in 18, 9 times 2 in 10, 5 times 2 in 20, 10 times 1. At 2 cents apiece, how many peaches can be bought for 6 cents ? ANALYSIS. Since 2 cents will buy 1 peachy 6 cents will buy as many peaches as 2 cents, the price of 1 peachy is contained times in 6 cents, which are 3 times. There- fore) at 2 cents apiece, 3 peaches can be bought for 6 cents. 2. At 2 cents apiece, how many oranges can you buy for 8 cents ? for 16 cents ] 3. If a man walk 2 miles an hour, how long will it take him to walk 14 miles'? 4. At 2 shillings a bushel, how many bushels of apples can be bought for 18 shil- lings ] 5. At 1 dollar a yard, how many yards of cloth can be bought for 9 dollars ? DIVISION. 51 LESSON III. 3 in 3, 1 time 3 in 18, 6 times 3 in 6, 2 times 3 in 21, 7 times 3 in 9, 3 times 3 in 24, 8 times 3 in 12, 4 times 3 in 27, 9 times 3 in 15, 5 times 3 in 30, 10 times 1. At 3 dollars a cord, how many cords of wood can be bought for 12 dollars ? ANALYSIS. Since 3 dollars will buy 1 cord, 12 dol- lars will buy as many cords as 3 dollars, the price of 1 cord, is contained times in 12 dollars, which are 4 times. Therefore, at 3 dollars a cord, 4 cords of wood can be bought for 12 dollars. 2. For 21 cents, how many yards of rib- bon can you buy, at 3 cents a yard ? 3. If the cars run a mile in 3 minutes, how many miles will they run in 30 min- utes ] 4. A father divided 24 marbles among his 3 boys ; how many did he give to each ? 5. How many lemons, at 3 cents apiece, can be bought for 18 cents ] 6. At 3 cents a quart, how many quarts of milk can be bought for 27 cents ] 7. Harriet paid 3 cents a spool for some thread ; how many spools could she buy for 15 cents I 52 DIVISION. LESSON IV. 4 in 4, 1 time 4 in 8, 2 times 4 in 12, 3 times 4 in 16, 4 times 4 in 20, 5 times 4 in 24, 6 times 4 in 28, 7 times 4 in 32, 8 times 4 in 36, 9 times 4 in 40, 10 times 1. If 4 boys can sit on one seat, how many seats will accommodate 20 boys ? 2. If a class of 4 boys answer 28 ques- tions, how many will each answer ? 3. Clinton earned 40 cents in 4 days ; how many cents did he earn in one day ? 4. If bonnets are 4 dollars apiece, how many can be bought for 20 dollars ? 5. Mary gave 36 cents for 4 yards of rib- bon ; how much was it a yard ? 6. If 4 benches will accommodate 24 pupils, how many must sit on each bench ? 7. If you put 32 sheep into 4 pens, how many must you put into each pen ? 8. Helen paid 4 shillings a yard for lace ; how many yards could she buy for 16 shil- lings ? 9. At 4 dimes apiece, how many books can be bought for 24 dimes ] 10. Carrie gave 12 cents for 4 skeins of silk ; how much was it a skein ? DIVISION. 53 LESSON V. 5 in 5, 1 time 5 in 10, 2 times 5 in 15, 3 times 5 in 20, 4 times 5 in 25, 5 times 5 in 30, 6 times 5 in 35, 7 times 5 in 40, 8 times 5 in 45, 9 times 5 in 50, 10 times 1. A man has 30 dollars, which he wishes to lay out in flour at 5 dollars a barrel ; how many barreK can he buy I 2. If I pay 10 cents for riding 5 miles in the cars, how much is that a mile I 3. George wishes to divide 15 apples among 5 boys ; how many must he give to each 1 4. In a school of 35 pupils, there were 5 classes ; how many pupils in a class ? 5. How many tons of coal, at 5 dollars a ton, can a blacksmith purchase for 40 dol- lars ] 6. How long will it take a man to drive 50 miles, with a horse and carriage, if he drive 5 miles an hour 1 7. How many pounds of tea, at 5 shillings a pound, can be bought for 20 shillings 1 8. Henry gave 45 cents to 5 poor chil- dren ; how many cents did he give to each child I 54 DIVISION. LESSON VI. 6 in 6, 1 time 6 in 12, 2 times 6 in 18, 3 times 6 in 24, 4 times 6 in 30, 5 times 6 in 36, 6 times 6 in 42, 7 times 6 in 48, 6 in 54, 8 times 9 times 6 in 60, 10 times 1. If a man can dig 48 rods of ditch in 6 days, how many rods can he dig in one day? 2. In New England, 6 shillings make one dollar ; how many dollars in 30 shillings 1 3. At 6 cents a pound, how many pounds of lard can be bought for 54 cents 1 4. Burton sold 6 quarts of cherries for 36 cents ; how much did he get a quart 1 5. If a man build 42 rods of fence in 6 days, how many rods can he build in one day I 6. How long will it take you to read 60 pages, if you read 6 pages a day 1 7. If 6 bushels of rye cost 6 dollars, how much is that a bushel ? 8. If a steamboat run 6 miles an hour, how long will it take her to run 24 miles ? 9. When crackers are 6 cents a pound, how many pounds can be bought for 18 cents ] DIVISION. 55 LESSON VII. 7 in 7, 1 time 7 in 14, 2 times 7 in 21, 3 times 7 in 28, 4 times 7 in 35, 5 times 7 in 42, 6 times 7 in 49, 7 times 7 in 56, 8 times 7 in 63, 9 times 7 in 70, 10 times 1. How many yards of cloth, at 7 shillings a yard, can be bought for 42 shillings ? 2. A farmer sold 7 sheep for 14 dollars ; how much did he receive apiece ? 3. Seth sold his sled for 35 cents; how many slates, at 7 cents apiece, can he buy for the money I 4. If 7 yards of calico will make a dress, | how many dresses can be made from a piece j containing 28 yards 1 5. In one week there are 7 days; how many weeks in 21 days? in 28 days'? in 56 days ? in 70 days? 6. Levi paid 7 cents for 7 slate pencils ; how much did he pay apiece ] 7. If a man can build 49 rods of stone wall in 7 days, how much can he build in 1 day] 8. When hops are 7 centa a pound, how many pounds can be bought for 70 cents ? 9. How many times 7 in 63 ? 56 DIVISION. LESSON VIII. Sin 8, 8 in 16, 8 in 24, 8 in 32, 1 time 2 times 3 times 4 times 8 in 80, 10 times 8 in 48, 8 in 56, 8 in 64, 8 in 72, 6 times 7 times 8 times 9 times 8 in 40, 5 times 1. Giles can buy a hoop for 8 cents; how many hoops can he buy for 40 cents ? 2. A man paid 72 cents for 8 pounds of sugar ; what was the price of one pound ? 3. How many bins will be required to hold 56 bushels of oats, if each bin hold 8 bushels 1 4. At 8 dollars a ton, how many tons of hay can be bought for 64 dollars ? 5. A farmer sold 8 barrels of apples for 24 dollars ; how much did he receive for one barrel 1 6. If there are 8 trees in each row, how many rows are there in an orchard contain- ing 80 trees ? 7. How many spelling books, at 8 cents apiece, can you buy for 48 cents ? 8. A laborer received 16 dollars for 8 days' work ; how much was that a day ? 9. James bought 8 lemons for 32 cents ; what was the cost of one lemon ? DIVISION. 57 LESSON IX. 9 in 9, 1 time 9 in 54, 6 times 9 in 18, 2 times 9 in 63, 7 times 9 in 27, 3 times 9 in 72, 8 times 9 in 36, 4 times 9 in 81, 9 times 9 in 45, 5 times 9 in 90, 10 times 1. How many classes, of 9 pupils each, can be formed of 45 pupils \ 2. When eggs are 9 cents a dozen, how many dozen can be bought for 63 cents ? 3. A class of 9 pupils present their teacher with a book which cost 90 cents ; how many cents must each pay towards the book] 4. If you travel 9 miles an hour, how long will it take you to travel 81 miles ? 5. A farmer distributed 9 bushels of pota- toes equally among 9 poor families; how many did he give to each \ 6. If a man spend 9 cents a day for cigars, how long will 54 cents last him ? 7. For 72 shillings, how many yards of silk can a lady buy at 9 shillings a yard I 8. William sold 9 quarts of cherries for 36 cents ; how much did he receive a quart ? 9. How many tons of hay, at 9 dollars a ton, can be bought for 18 dollars \ 58 DIVISION. LESSON X. 10 in 60, 6 times 10 in 70, 7 times 10 in 80, 8 times 10 in 90, 9 times 10 in 10, 1 time 10 in 20, 2 times 10 in 30, 3 times 10 in 40, 4 times 10 in 50, 5 times 10 in 100, 10 times 1. When butter is 10 cents a pound, how many pounds can I buy for 80 cents ? 2. At 10 dollars an acre, how many acres of land can be bought for 100 dollars I 3. How long will it take a boy to earn 90 cents, if he earn 10 cents a day? 4. In one dime are 10 cents; how many dimes in 30 cents ? 5. At 10 shillings apiece, how many glass lamps can be bought for 50 shillings ? 6. How long will it take you to read 70 pages, if you read 10 pages a day ? 7. When shawls are 10 dollars apiece, how many can be bought for 60 dollars ? 8. How long will it take you to earn 40 dollars, if you earn 10 dollars a month'? 9. If one man can build 10 rods of fence in one day, how many men will it take to build 20 rods in the same time 1 10. At 10 cents apiece, how many melons can be bought for 40 cents ? DIVISION. 59 LESS( PROMISCUOl 6 in 36, how many times ? 7 in 42, how many times ? 6 in 18, how many times ? 9 in 81, how many times ? 5 in 35, how many times ? 8 in 72, how many times ? 9 in 27, how many times ? 4 in 20, how many times ? 3 in 18, how many times ? 6 in 54, how many times ? 3N XI. US REVIEW. 3 in 15, how many times? 5 in 25, how many times? 9 in 63, how many times ? 6 in 12, how many times? 7 in 28, how many times? 4 in 16, how many times? 7 in 49, how many times ? 4 in 36, how many times? 8 in 64, how many times ? 8 in 40, how many times ? 8 in 24, how many times ? 5 in 45, how many times ? 6 in 42, how many times? 8 in 56, how many times? 9 in 18, how many times? 5 in 40, how many times ? 7 in 63, how many times ? 3 in 27, how many times ? 7 in 21, how many times? 8 in 16, how many times ? 3 in 12, how many times ? 4 in 28, how many times ? 8 in 32, how many times ? 6 in 48, how many times ? 2 in 14, how many times? 9 in 45, how many times ? 8 in 48, how many times ? 7 in 56, how many times ? 3 in 21, how many times ? 6 in 54, how many times ? 8 in 8, how many times? 4 in 12, how many times? 7 in 35, how many times? 5 in 10, how many times? 7 in 14, how many times? 2 in 6, how many times? 4 in 24, how many times? 5 in 30, how many times? 9 in 36, how many times? 6 in 30, how many times? 3 in 24, how many times? 2 in 16, how many times? 4 in 32, how many times? 6 in 24, how many times? 9 in 72, how many times? 5 in 10, how many times? 4 in 8, how many times ? 5 in 20, how many times? 2 in 10, how many times? 7 in 7, how many times? 60 DIVISION. LE S S ON. XI I. PROMISCUOUS EXAMPLES. 1. When flour is 7 dollars a barrel, how many barrels can be bought for 63 dollars ? ANALYSIS. Since 7 dollars will buy 1 barrel, G3 dollars will buy as many barrels as 7 dollars, the price of 1 barrel, is contained times in 63 dollars, which are 9 times. Therefore, fyc. 2. If it take 81 bushels of apples to make 9 barrels of cider, how many bushels will make one barrel "? 3. How long will it take 5 men to do a job of work that one man can do in 30 days I 4. How long will 12 dollars pay for my board, at the rate of 6 dollars a week I 5. If 54 pounds of provision last one man 9 days, how many pounds would last him one day ? 6. Marcus read 100 pages in 10 days; how many pages did he read each day 1 7. A cabinet maker received 45 dollars for some chairs at 5 dollars apiece ; how many chairs did he sell 1 8. Jf one man can mow a field of grass in 18 days, in what time would 6 men mow the same I 9. A farmer sold some hay for 30 dollars, and took 10 sheep for payment; what was the cost of each sheep ? PKOMISCUOUS REVIEW. 61 LESSON XIII. 1. How many tons of hay, at 6 dollars a ton, will pay for 8 yards of broadcloth, at 3 dollars a yard ? ANALYSTS. As many tons of hay at 6 dollars a ton, as 6 dollars, the price of a ton, is contained times in 8 times 3 dollars, or 24 dollars, the cost of the broad- cloth, which are 4 times. Therefore 4 tons of hay, at 6 dollars a ton, will pay for 8 yards of broadcloth, at 3 dollars a yard. 2. How many dozen of eggs, at 9 cents a dozen, will pay for 6 yards of calico, at 6 cents a yard I 3. Charles sold 6 quarts of beech nuts, at 4 cents a quart, and took his pay in oranges, at 3 cents apiece ; how many oranges did he receive ] 4. At 6 dollars a barrel, how many bar- rels of flour will pay for 3 barrels of pork, at 10 dollars a barrel ? 5. If 5 men can hoe a field of corn in 6 days, how long will it take one man ? 6. If 8 men can build a shed in 10 days, how many men must be employed to build it in one day ? 7. If 4 men can do a piece of work in 7 days, how long will it take one man to do it I 8. How many days' labor, at 8 shillings a day, will pay for 10 bushels of potatoes at 4 shillings a bushel ? 62 PROMISCUOUS REVIEW. LESSON XIV. 1. If 7 oranges cost 28 cents, what will 3 oranges cost ] ANALYSIS. If 7 oranges cost 28 cents, 1 orange will cost as mang cents as 7 is contained times in 28, which is 4 times ; 3 oranges, which are 3 times 1 orange, will cost 3 times 4 cents, or 12 cents. Therefore, if 7 oranges cost 28 cents, 3 oranges will cost 12 cents. 2. If 6 pounds of sugar cost 60 cents, what will 9 pounds cost ? 3. A farmer sells 8 sheep for 24 dollars ; how much does he receive for 5 sheep ? 4. If a man can earn 72 dollars in 8 weeks, how much can he earn in 10 weeks ? 5. Jane bought 5 steel pens for 15 cents ; what would be the cost of 10 pens at the same rate ? 6. A grocer sold 10 pounds of tea for 40 shillings; what would be the cost of 8 pounds at the same rate ? 7. If a man can chop 16 cords of wood in 8 days, how much can he chop in 3 days 1 in 5 days'? in 7 days? in 10 days'? in 12 days ? 8. If 7 yards of calico cost 63 cents, what will 3 yards cost? 5 yards'? 6 yards'? 9 yards] 10 yards ? 9. When 4 cords of wood are worth 20 dollars, what will 9 cords be worth *? PROMISCUOUS REVIEW. 63 LESSON XV. 1. Isabel had 15 pinks, and gave 6 to Clara, and 4 to Herbert ; how many did she keep for herself? ANALYSIS. She kept as many pinks as the difference between 15 pinks and the sum of 6 pinks and 4 pinks ; 6 and 4 are 10, and 10 from 15 leaves 5. Therefore, if Isabel had 15 pinks, and gave away 10, she had 5 left. 2. Lucian, having 20 marbles, gave 9 to Henry, and 6 to John ; how many had he left? 3. From a piece of cloth containing 12 yards, 5 yards were cut for a coat, 3 yards for a pair of pantaloons, and 1 yard for a vest ; how many yards were left ? 4. If 2 men start from the same place and travel in opposite directions, one at the rate of 4 miles an hour, and the other at the rate of 5 miles an hour, how far apart will they be at the end of 1 hour ? At the end of 2 hours I 5 hours'? 6 hours'? 8 hours'? 10 hours'? 5. A grocer sold 2 pounds of rice at 6 cents a pound, a pound of soda for 8 cents, and a bar of soap for 7 cents, and was paid in eggs at 9 cents a dozen; how many dozen of eggs did he receive ? 6. If a man travel 36 miles in 9 hours, how far will he travel in 5 hours'? in 6 hours 1 in 7 hours 1 64 FRACTIONS. LESSOR I. When a unit or whole thing is divided into two or more equal parts, those parts are called FRACTIONS. 1. If a yard measure be divided into two equal parts, one of the parts is called one half. How many halves make a whole thing ? Ans. Two. 2. If a yard measure be divided into three equal parts, one of the parts is called one third, How many thirds make a whole thing ? Ans. Three. 3. If a yard measure be divided into four equal parts, one of the parts is called one fourth, two of the parts two fourths, three of the parts three fourths. D N E FOU R TH . I iO'NE F..O U R.T H ON E FO RT H How many fourths make a whole thing? Ans. Four. 4. If a yard measure be divided into five equal parts, one of the parts is called one fifth, two of the parts two fifths, three of the parts three fifths, four of the parts four fifths. How many fifths make a whole thing? Ans. Five. 5. If a yard measure be divided into six equal parts, one of the parts is called one sixth, two of the parts two sixths, and so on. OHE/SIXTRJ :ONE,S!XTH ONES1XTH ONE SIXTH How many sixths make a whole thing ? Ans. Six. FRACTIONS. 65 LESSON II. 1. If any number or whole thing be divided into seven equal parts, one of the parts is called one seventh, two of the parts two sevenths, and so on. How many sevenths make a whole thing ? Ans. Seven sevenths. 2. If any number or thing be divided into eight equal parts, one of the parts is called one eighth, five of the parts Jive eighths, and so on. How many eighths make a whole thing ? Ans. Eight eighths. 3. If any number or thing be divided into nine equal parts, one of the parts is called one ninth, seven of the parts seven ninths, and so on. How many ninths make a whole thing? How many tenths make a whole thing? The following is the method of expressing fractions by figures : i, one half. I, one third, i, one fourth. I, one fifth. 4, one sixth. I, one seventh. \ , one eighth, i , one ninth. T\T, one tenth. NOTE. In any fraction, as , (two thirds,), the num- ber below the line is called the Denominator, and it shows into how many equal parts the whole number or thing is divided. The number above the line is called the Numerator, and it shows the number of parts that are used, or that are expressed by the fraction. 66 FRACTIONS. LESSON III. 1. What do you understand by i of any number or thing ? Ans. One of the two equal parts into which the number or thing is divided. 2. What do you understand by I of any number or thing] Ans. One of the three equal parts into which the number or thing is divided. 3. What do you understand by % of any number or thing] Ans. Two of the three equal parts into which the number or thing is divided. 4. How do you find of any number? Ans. Divide the given number by 2. 5. How do you find i of any number? Ans. Divide the given number by 3. 6. How, then, will you find i of any num- ber ? how i ? how I ? how I ? how ? how 7. What do you understand by i of any number or thing ? by f ? by f ? by f ? by i ? byf? byj? byil'byt? byt? byH by*? byH 9. What is i of 4? of 6? of 8? of 10? of 16? of 20? 10. What is i of 8? of 12? of 16? of 20? of 28? 11. What is i of 12? of 24? of 36? FRACTIONS. 67 LESSON IV. 1. In 1 orange, how many halves? 2. In 3 oranges, how many halves ? ANALYSIS. Since in 1 orange there are 2 halves, in 3 oranges there are 3 times 2 halves, which are 6 halves. Therefore, in 3 oranges there are 6 halves. 3. How do you find how many halves there are in any number or thing ? Ans. Multiply the whole number by 2. 4. How do you find how many thirds there are in any number or thing ? Ans. Multiply the whole number by 3. 5. How many halves are there in 4 pears ? in 4 pears and 1 half ? in 5 pears ? 6. In 6 bushels and 1 half, how many halves ? 7. In 3 apples, how many thirds ? 8. In 4 apples and 1 third, how many thirds are there ? in 4 and 2 thirds ? in 5 ? in 5 and 1 third ? 9. How many halves in 7 ? in 7 and 1 half? in 8? in 9 and 1 half? in 10? 10. How many thirds in 5 ? in 5 and 1 third ? in 5 and 2 thirds ? in 6 ? in 7 and 1 third? in 7 and 2 thirds? 11. In 8 dollars, how many halves? how many thirds ? 12. How many half miles, in 7 miles and 1 half? 68 FRACTIONS. LESSON V. 1. In 5 bushels, how many fourths ? ANALYSIS. Since in 1 bushel there are 4 fourths, in 5 bushels there are 5 times 4 fourths, which are 20 fourths. Therefore, in 5 bushels there are 20 fourths. 2. How many fourths in 6 ? in 6 and 1 fourth? in 6 and 3 fourths? in 7 and 1 fourth 1 in 8 and 3 fourths ? in 9 ? 3. How many fifths in 2 ? in 3 ? in 4 and 1 fifth ? in 5 and 2 fifths ? in 7 and 3 fifths ? 4. How many sixths in 1 ? in 2 ? in 4 ? in 4 and 1 sixth? in 7 and 2 sixths? in 7 and 5 sixths ? 5. In 3, how many sevenths ? in 3 and 5 sevenths ? in 4 and 1 seventh ? in 4 and 4 sevenths ? 6. In 7, how many sevenths ? in 7 and 6 sevenths ? 7. How many eighths in 2 ? in 3 ? in 5 and 1 eighth ? in 5 and 7 eighths ? 8. In 1, how many ninths ? in 2 1 in 5 ? in 6 ? in 4 and 3 ninths ? in 7 and 5 ninths ? in 8? 9. How many tenths in 1 ? in 2 ? in 3 ? in 4 and 5 tenths ? in 6 and 3 tenths ? in 9 and 9 tenths ? 10. In 6, how many fifths ? how many sixths? how many sevenths? how many eighths ? how many ninths ? FRACTIONS. 69 LESSON VI. 1. In 6 halves of a mile, how many miles ? ANALYSIS. Since there are 2 halves in 1 mile, in 6 halves of a mile there are as many miles as 2 halves are contained times in 6 halves, which are 3 times. Therefore, in 6 halves of a mile are 3 miles. 2. How many bushels in 14 halves of a bushel ? 3. In 12 halves, how many units or whole ones? 4. How many units in 15 thirds? in 18 thirds? in 21 thirds? 5. How many units in 16 fourths? in 17 fourths? in 18 fourths? in 20 fourths? in 23 fourths ? 6. In 7 fifths, how many whole ones ? in 10 fifths? in 25 fifths ? in 26 fifths? in 28 fifths? 7. How many times 1 in 18 sixths ? in 19 sixths ? in 24 sixths ? in 30 sixths ? in 32 sixths ? 8. In f how many times 1 ? in -V 1 ? in V- 9. How many times 1 in I ? in Y ? in -^ ? in *8- ? in V- ? in % 4 ? in - 3 /- ? 10. How many units in ? in -V -? in -^? inV-?in^? in% 7 -? 11. In -B, how many times 1 ? in f*? in f*? inH? in^? intt? ii 70 FRACTIONS. LESSON VII. 1. George had f of a dollar, and his father gave him t of a dollar more ; what part of a dollar had he then 1 ANALYSIS. He had the sum of f of a dollar and f of a dollar ; f and f make f of a dollar. Therefore, since George had of a dollar, and his father gave him g of a dollar more, he then had % of a dollar. 2. A lady gave f of an orange to Mary, f to Sarah, and ? to Julia ; how many oranges did she give away ? 3. John bought i of a pound of raisins, and Joseph f of a pound ; how many pounds did they both buy I 4. A blacksmith bought at one time f of a ton of coal, at another time f of a ton, at another time t of a ton, and at another time i of a ton ; how many tons did he buy in all 1 5. Samuel paid T% of a dollar for a slate, A of a dollar for an arithmetic, -TV for a reader, and T 9 L 50 ELEMENTARY ASTRONOMY, 7? UNIVERSITY ASTRONOMY, - - - - CONCISE MATHEMATICAL OPERATIONS, - KEY TO GEOMETRY & TRIGONOMETRY, CONIC SECTIONS & ANALYTICAL GEOMETRY, - 1 00 T/ie most liberal terms for first supplies, for intr- nen copies, for exhumation. Descriptive Catalogu