: 9. Take } a square foot from ii of an acre. Ans. 1R. 18P. 5yd. 4ft. 10. A man sold is of a house to one man, 34 to another, and 1, to another: what part did he still own ? 11. One man bought 1 of cwt. of iron, another of 57 41 cwt.: how much did one buy more than the other ? 5} Ans. 313.) drams. 12. From of 12, take 14 of 1. Ans. 13. From of l} of 7, take off. Ans. 4.32. 14. From 7575, take } of 34. Ans. 15. From 1} of a £ take of a shilling. Ans. £1 9s. 3d. 16. From 14oz. take pwt. Ans. 17. From 86cut. take 4 lb. Ans. 8cwt. 3qr. 5lb. 12oz. 153 dr. 18. From 3116., Troy weight, take oz. Ans. . 19. What is the difference between l} rods and of Ans. 21ft. 11 in. 2 1 1 20. From take Ans. 43 21. From 3 take 313. Ans. an inch ? 46 49 37 MULTIPLICATION OF VULGAR FRACTIONS. a 15. John gave of a cent for an apple. How much must he give for 2 apples ? For 3 apples ? For 4 ? For 5 ? For 6 ? For 7 ? For 8 ? For 9 ? Charles gave şof a cent for a peach. How much must he give for 2 peaches ? For 3? For 4 ? For 5? For 6? CASE I. 154. To multiply a fraction by a whole number. Multiply the numerator, or divide the denominator by the whole number. 154. How do you multiply a fraction by a whole number? EXAMPLES ILLUSTRATING PRINCIPLES. 47 49 17 5 47 157 47 1. Multiply the fraction by 4. When we propose to OPERATION. multiply a fraction by a ģx4===21; whole number, it is re or by dividing the denom. quired to take the fraction inator by 4, we have as many times as there are units in the multiplier, Š x 4=v==21 which may be done by mul. tiplying the numerator (Art. 118), or by dividing the denominator (Art. 121). 2. Multiply 17 by 12. Ans. 37 3. Multiply A7 by 7. Ans. 6. 4. Multiply 44 by 9. Ans. . 5. Multiply 27 by 5. Ans. 6. Multiply if by 49. Ans. 124143 155. When we multiply by a fraction it is required to take the multiplicand as many times as there are units in the fraction. For example, to multiply 8 by is to take 8, i times; that is, to take of 8, which is 6. Hence, when the multiplier is less than 1 we do not take the whole of the multiplicand, but only such a part of it as the fraction is of unity. For example, if the multiplier be one-half of unity, the product wiil be half the multiplicand: if the multiplier be į of unity, the product will be one-third of the multiplicand. Hence, to multiply by a proper fraction does not imply increase, as in the multiplication of whole numbers. The product will always be such a part of the multiplicand as the multiplier is of unily. 3 6 9 155. What is required when we multiply by a fraction? What is the product of 8 multiplied by one-half? By one-fourth ? By oneeighth? By three-halves? By six-halves? What is the product of 9 multiplied by one-half? By one-third ? By one-sixth? By one-ninth ? When the multiplier is less than 1, how much of the multiplicand is taken? Does the multiplicand by a proper fraction imply increase? What part of the multiplicand is the product ? CASE II. OPERATION. 156. To multiply one fraction by another. Reduce all the mixed numbers to improper fractions, and all compound fractions to simple ones : then multiply the numerators together for a numerator, and the denominators together for a denominator. EXAMPLES ILLUSTRATING PRINCIPLES. 1. Multiply by In this example i is to be taken times. That is, is **=*x5x1=1 first to be multiplied by 5 and the product divided by 7, a result which is obtained by multiplying the numerators and denominators together. 2. Multiply į of by 83. We first reduce the compound fraction to the * of ris, simple one is, and then 81=: the mixed number to the Hence, iaxx=1=45. equivalent fraction ; after which, we multiply Ans. the numerators and denominators together. 3. Multiply 54 by. Ans. 41=ž. 4. Multiply 12 by of 9. Ans. 810 5. Multiply of 3 of į by 15. 6. Multiply by of Ans. 7. Required the product of 6 by of 5. Ans. 20. 8. Required the product of of by á of 34. OPERATION. 7 5 Ans. 13 . Ans. 9. Required the product of 34 by 43. Ans. 14131. 10. Required the product of 5, , of, and 44. 11. Required the product of 41, of ļ, and 18%. Ans. 9 12. Required the product of 14, 6 of 9, and 69. 156. What is the product of one-sixth by one-seventh? Of three. fourths by one-half? Of six-ninths by three-fifths? Give the general rule for the multiplication of fractions. 157. In multiplying by a mixed number, we may first multiply by the integer, then multiply by the fraction, and then add the two products together. This is the best method when the numerator of the fraction is 1. 1. What will 7 yards of cloth cost at $ per yard? Ans. $51 2. What will 32 gallons of brandy cost at $14 per gallon? Ans. $36. 3. If ilb. of tea cost $14, what will 641b. cost ? 4. What will be the cost of 174 yards of cambric at 21 shillings per yard? Ans. £2 38. 9d. 5. What will 151 barrels of cider come to at $3 per barrel ? Ans. $45% 6. What will 37 boxes of raisins cost at $2 per box ? Ans. $816. 157. How may you multiply by a mixed number? When is this the best method ? 9 buy? 7. What will 151 barrels of sugar cost at 174 dollars per barrel ? Ans, 8. What will 3 cords of wood cost at $3% per cord ? Åns. $1416 9. Multiply bushels by of 7. Ans. 3}}bu. 10. A man bought i of of a ship: what part did he Ans. 25 11. How much is of 21 times 8 dollars ? Ans. 3). 12. How far will a man travel in 17 i hours if he goes at the rate of 95 miles an hour ? Ans. 13. How many miles are of 7 miles, multiplied by 15 of 87 11 ? Ans. 403 mi. 14. What will 294 tons of gravel cost at 1} dollar a Ans. 15. I own of a ship, and sell } of of my share: what part is it of the whole ? 16. What will 233 pounds of lead cost at a dollar a pound ? Ans. 1806 17. What will {.cords of wood cost at 5 dollars a cord ? $ 18. A merchant sold 371} hogsheads of vinegar for 175 dollars a hogshead: what did it come to ? 19. Sold of 94cwt. of sugar for of 17 dollars a cut.: 을 what did it come to ? Ans. $785. 20. Sold of of 26116. of rice for 4 of 2 of 10 cents a pound: what did it come to ? Ans. 8316 ton ? Ans. Ans. $535. DIVISION OF VULGAR FRACTIONS. 158. We have seen that division of entire numbers explains the manner of finding how many times a less number is contained in a greater. In division of fractions the divisor may be larger than the dividend, in which case the quotient will be less than 1. For example, divide 1 apple into 4 equal parts. Here it is plain that each part will be ; or that the dividend will contain the divisor but times. |