dividing the numerator or multiplying the denom inator. Art. 76. RULES.-1. To divide a fraction by an integer, Divide the numerator or multiply the denominator. 2. To divide a mixed number by an integer, Divide the integral part and then the fraction. LESSON XIII. Integers divided by Fractions. 1. How many times is of an apple contained 2. How many times are of a yard contained in 3 yards? SOLUTION.-3 yards = 12 fourths, and 3 fourths are contained in 12 fourths 4 times. 3. If a basket holds of a bushel, how many baskets will hold 4 bushels? 4. How many times is contained in 4?? in 4? in 4? 5. If of a yard of silk will trim a hat, how many hats will 6 yards trim? 6. How many times is contained in 3? # in 6? in 6? in 3? NOTE. Since 14 is reduced to fifths by multiplying it by 5, the process may be shortened by omitting the denominators, 14 × 5 ÷ 3 = 23}. thus: 14 integer by a Art. 77. RULE.-To divide an fraction, Multiply the integer by the denominator of the fraction, and divide the product by the nu merator. LESSON XIV. Fractions divided by Fractions. 1. If of a barrel of flour will supply a family one month, how many months will of a barrel last? 2. How many times is contained in? } in? 3. If of a yard of cloth will make a vest, how many vests will of a yard make? 4. How many times in ? 5. If a pound of butter cost in g? of a dollar, how many pounds can be bought for g of a dollar? SUGGESTION.-Change to eighths. 6. How many times in ? in ? Art. 78. RULE. -To divide a fraction by a fraction, Reduce the fractions to a common denominator, and divide the numerator of the dividend by the numerator of the divisor. NOTE. When pupils are familiar with this method, they may be taught to divide by inverting the terms of the divisor and multiplying. This method is fully explained in the author's Complete Arithmetic. LESSON XV. Numbers Fractional Parts of Other Numbers. 1. 5 is of what number? SOLUTION. If 10 is of a number, of the number is of 10, which is 5; if 5 is of a number, of it will be 3 times 5, which is 15. left: how much money had he at first? 13. A boy gave 24 cents for a slate, which was of his money: how much money did he have? 14. A man pays $25 a month for house-rent, which is of his monthly salary: what is his salary? 5 15. A farmer sold a cow for $45, which was 4 more than he paid for her: what was the cost of the cow? 16. A man sold of a farm for $1500: at this rate, what was the value of the farm? LESSON XVI. Miscellaneous Problems. 1. Reduce 183 to an improper fraction. 5 4. Add,,, and . 5. Add 28%, 40, 633, and 19,3⁄4. 6. From take . From 28 take 163. 7. Multiply by 7. 13 by 3. by 9. 15. 256 by 21ğ. by 12. by . what? - ? ? 10. Divide 2433 by 11. 256 by 51. 11. 급 + 글 12. There are 5280 feet in a mile: how many feet in of a mile? 13. A vessel is worth $6000, and the cargo is worth as much as the vessel: what is the value of the cargo? 14. A man sold of his farm to one neighbor and of it to another: what part of the farm has he left? 15. A man owning of a factory, sold of his share what part of the factory did he sell? What part does he still own? 16. There are 16 feet in a rod: how many feet in 66 rods? 17. There are 5 yards in a rod: how many rods in 66 yards? 18. At $61 a barrel, how many barrels of flour can be bought for $150? 19. If of a ship is worth $12000, what is the whole ship worth? of 20. A man owning of an estate, sells his share for $2400: at this rate, what would be the value of the estate? 5 21. A farmer had two fields of wheat. The first yielded 840 bushels, which was of the amount yielded by the second field. How many bushels did the second field yield? 22. A man owning of a ship, sells of his share for $4400: at this rate, what is the value of the ship? |
