9. Take a square foot from of an acre. Ans. 1R. 18P. 5yd. 4ft. 10. A man sold 15 of a house to one man, to another, and to another: what part did he still own? 4 11. One man bought of cwt. of iron, another of 41 5 cwt.: how much did one buy more than the other? 5 17. From 8 cwt. take 4lb. Ans. 8cwt. 3qr. 5lb. 12oz. 1518dr. 18. From 3b., Troy weight, take oz. Ans. 19. What is the difference between 14 rods and an inch? 46 take # 42* of Ans. 21ft. 11 in. Ans. Ans. 21. From 3 take 253. MULTIPLICATION OF VULGAR FRACTIONS. 153. John gave must he give for For 5? For 6? of a cent for an apple. How much 2 apples? For 3 apples? For 4? For 7? For 8? For 9? Charles gave of 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. 1. Multiply the fraction by 4. When we propose to multiply a fraction by a whole number, it is required to take the fraction as many times as there are units in the multiplier, which may be done by mul OPERATION. ×4===24; or by dividing the denom- tiplying the numerator (ART. 118), or by dividing the denominator (ART. 121). 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 2 is to take 8, 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 will be half the multiplicand: if the multiplier be 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 unity. 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. 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 5. taken times. That is, is first to be multiplied by 5 and OPERATION. the product divided by 7, a result which is obtained by multiplying the numerators and denominators together. 2. Multiply of by 8. We first reduce the compound fraction to the simple one, and then the mixed number to the equivalent fraction 25; OPERATION. Hence, &x=1=23. 75 25 after which, we multiply Ans. 25. Ans. 14131. 9. Required the product of 32 by 411. 10. Required the product of 5, 3, 4 of 3, and 4. 11. Required the product of 41, 2 of 4, and 18. Ans. 9140 12. Required the product of 14, %, † of 9, and 63. 156. What is the product of one-sixth by one-seventh? Of threefourths 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 $3 per vard? Ans. $51. 2. What will 32 gallons of brandy cost at $1 per gallon? Ans. $36. 3. If 17b. of tea cost $11, what will 617b. cost? 4. What will be the cost of 17 yards of cambric at 2 shillings per yard? Ans. £2 3s. 9d. 5. What will 15 barrels of cider come to at $3 per barrel ? Ans. $45 6. What will 3 boxes of raisins cost at $2 per box? Ans. $8,76. 157. How may you multiply by a mixed number? When is this the best method? 7. What will 15 barrels of sugar cost at 17 dollars per barrel? Ans. 8. What will 33 cords of wood cost at $33 per cord? Ans. $141. of 24 times 8 dollars? Ans. 3. hours if he Ans. buy? 11. How much is goes at the rate of 95 miles an hour? 13. How many miles are of 7 miles, multiplied by Ans. 403 mi. 14. What will 293 tons of gravel cost ton ? 15. I own of a ship, and sell of what part is it of the whole? at 1 dollar a Ans. of my share: Ans. 16. What will 237 pounds of lead cost at dollar a pound? Ans. 1. 17. What will cords of wood cost at 53 dollars a cord ? 18. A merchant sold 37 Ans. $532. hogsheads of vinegar for 17 dollars a hogshead: what did it come to? 19. Sold of 9cwt. of sugar for of 17 dollars a cul.: what did it come to? 20. Sold of of 267b. of rice for cents a pound: what did it come to ? Ans. $78. of 2 of 10 Ans. 831. 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. |