7. Mary gave 3 pears to Lucy, which was 1 half of all she had; how many had she? 8. Three girls divided some roses equally among themselves; what part of the roses did each girl have? If each girl had 2 roses, how many had all the girls? 9. 2 is 1 third of what number? 10. 7 is 1 third of what number? 11. How many thirds of a number equal the whole number? 12. When 1 third of a number is given, how do you find the whole number? 13. Sarah spent 6 cents for candy, which was 1 third of all the money she had; how many cents had she? 14. Four boys divided some books equally among themselves; what part of the books did each boy have? If each boy had 2 books, how many books did all the boys have? 15. 2 is 1 fourth of what number? 16. 9 is 1 fourth of what number? 17. How many fourths of a number equal the whole number? 18. When 1 fourth of a number is given, how do you find the whole number? 19. Felix missed 6 words in spelling, which was 1 fourth of all the words missed by the whole school; how many words were missed by the whole school? 20. Agnes is 3 years old, which is 1 fifth of the age of her brother; what is the age of her brother? 21. How many fifths of a number equal the whole number? 22. Mr. Gray is hired to gather apples for Mr. Frost, and is to keep 1 bushel of apples for every 6 bushels gathered; what part of the apples gathered does Mr. Gray keep? If Mr. Gray keeps 4 bushels, how many bushels are gathered? 23. How many sixths of a number equal the whole number? 24. Mr. Jones pays $3 for a vest, which is 1 seventh as much as he pays for a coat; how much does he pay for a coat? 25. How many sevenths of a number equal the whole number? 26. Mr. Tyler is an auctioneer who sells goods and keeps 1 eighth of the money received, to pay him for selling; if he keeps $5, how many dollars' worth are sold? 27. How many eighths of a number equal the whole number? 28. Alvin gave 6 cents for a pencil, which was 1 ninth as much as he gave for a book; how many cents did he give for the book? 29. How many ninths of a number equal the whole number? 30. How many tenths of a number equal the whole number? how many elevenths? how many twelfths? 31. Edith has spent 2 weeks at a boarding-school, which is 1 eleventh of the term; how many weeks are there in the term? 32. After travelling 11 miles, Mr. Ives finds he has performed 1 tenth of his journey; how many miles had he to travel? 33. Sarah has learned 8 pages of her Arithmetic, which is 1 twelfth of the whole book; how many pages are there in the whole book? 34. 11 is 1 sixth of what number? 35. 10 is 1 twelfth of what number? For Slate Exercises, perform examples on pages 171 and 172, changing the left hand figure of each divisor to a figure denoting one more. Section XX. GENERAL REVIEW. 45. 1. What is a unit? 4. Give an example in addition. 6. Give an example in subtraction. 7. What is multiplication? 8. Give an example in multiplication. 9. What is division? 10. Give an example in division. 11. Loring found 17 pears under a tree, and gave 2 to Mary, 3 to John, and 7 to his mother; how many did he give away? How many had he left? 12. What number must be put with 18 to make 30? 13. What number must be taken out of 75 to leave 62? 14. The sum of two numbers is 48, and one of the numbers is 16; what is the other number? 15. The sum of three numbers is 50: two of the numbers are 12 and 13; what is the third number? 16. Clarence is 3 years younger than Arthur, and 4 years older than George: if Clarence is 12 years old, how old is Arthur? How old is George? 17. I bought at a confectioner's some candy for 15 cents, some oranges for 25 cents, some nuts for 18 cents, and some raisins for 20 cents, and gave $1 in payment; what change should I receive? 18. A man bought 5 calves at $8 apiece, and gave in payment 3 barrels of mackerel at $12 a barrel, and paid the balance in money; how many dollars in money did he pay? 19. A merchant bought 8 sheep at $6 apiece, and paid as much of the cost as possible in 10-dollar bills, as much of the balance as possible in 5-dollar bills, and the rest in 1-dollar bills; how many bills of each sort did he pay? 20. Mr. Williams had 2 boxes of hats, with 10 hats in each box, and 4 hats besides; Mr. Frank had 3 boxes of hats, with 11 hats in each box, and 9 hats besides; how many more hats had Mr. Frank than Mr. Williams? 21. A man exchanged 7 pounds of butter for cheese, at the rate of 10 pounds of butter for 30 pounds of cheese; how many pounds of cheese did he receive? 22. If 1 man can build a cistern in 12 days, how many men will be required to build it in 1 day? 23. If it costs $48 for bricks to build a cistern, when bricks are worth $8 a thousand, what will it cost for bricks to build it when bricks are worth $10 a thousand? 24. When apples are worth $5 a barrel, and coal $10 a ton, how many barrels of apples will pay for 6 tons of coal? 25. If a number of 5-cent loaves weigh 10 pounds, what will the same number of 12-cent loaves weigh? 26. A man raised 36 bushels of potatoes, which was 12 times as many as he planted; how many bushels did he plant? 27. Ezra had 48 plums; if he gave 1 sixth of them to his sister, and 3 eighths to his brother, how many plums had he left? 28. A man paid $4 for a week's board, which was 1 sixth of what he earned; how much did he earn? 29. Take 5, multiply it by 4, add 5, divide by 5, subtract 1, subtract 2, multiply by 12, add 3, take 1 ninth of that number, divide by 3, and subtract 1; what number have you? For Slate Exercises, see page 173. Section XXI. MULTIPLES AND FACTORS. 46. 1. Name some of the multiples of 2; of 3. The multiples of 2 are . . 2, 4, 6, 8, 10, 12, etc. The multiples of 3 are.. 3 6, 9, 12, etc. NOTE. 6 and 12 are multiples of both 2 and 3; hence 6 and 12 are Common Multiples of 2 and 3; and 6 is the Least Common Multiple of 2 and 3. 2. What numbers from 3 to 24 are multiples of 3? of 4? of both 3 and 4? 3. What is the least common multiple of 3 and 4? of 4 and 6? of 9 and 6? of 5 and 6? of 12 and 9? 4. What is a multiple of a number? Ans. Any number which will contain it without a remainder. 5. What is a common multiple of two or more numbers? the least common multiple? 47. 1. Of what numbers is 6 a multiple? Ans. 6 is a multiple of 2 and 3. NOTE. 2 and 3 are called the Factors of 6. Ans. 3 with 6; 2 with 9; 2 with 3 with 3. of 7? 3. What are the factors of 20? 4. What are the factors of 2? have no factors besides themselves and 1. Numbers which have no factors besides themselves and 1 are called Prime numbers. Numbers which have other factors besides themselves and 1 are called Composite numbers. 5. Is 3 a composite number? is 4? is 5? is 6? |