cancelling. The operation of the following questions may be abridged by Ans. Ans.. 12. Multiply by 18. 13. Multiply by 38. 14. Multiply by 11. 15. Multiply by 100. CASE II. To multiply a whole number by a fraction, or a fraction by a whole number. 1. If a man earn of a dollar in one day, how much will he earn in 9 days? OPERATION. To analyze this question, we say, 7 × == $77 Ans. if he earn 7 eighths of a dollar in 1 day, in 9 days he will earn 9 times as much, and 9 times 7 eighths are 63 eighths3=$77 Ans. RULE. Multiply the whole number by the numerator of the fraction, and divide the product by the denominator, and the quotient is the answer required. NOTE. If any of the fractions are compound, they must be reduced to simple fractions by Case VI., Sect. XVI.* 16. At ğ of a dollar per foot, what cost 7 cords of wood? CASE III. Ans. $35. To multiply a mixed number by a whole number, or a whole number by a mixed number. 1. Multiply 7 by 9. 7 OPERATION. In performing this question, we say 9 times b eighths are 45 eighths, and 45 eighths are equal to 5ğ. We write down the and carry the 5 to the product of 9 times 7 : 9 685 68. RULE. Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction, and as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, let it be a numerator and the divisor a denominator to a frac tion to be affixed to the product. 11. What will 237 pounds of lead cost, at 8 cents a pound? 12. What will 15 pound? 13. What will 29 Ans. $1.91. pounds of sugar cost, at 12 cents a Ans. $1.881. cwt. of hay.cost, at $ 1.12 per cwt. ? Ans. $32.943. 14. What will 97 yards of broadcloth cost, at $8 per yard? 6 Ans. $79.00. 15. What will 17 tons of potash cost, at $97 per ton? Ans. $1703.561. 16. What will 3 tons of plaster of Paris cost, at $12.75 per ton? Ans. $40.185. 59 17. What will 17 dozen candles cost, at 16 cents a dozen ? pound? 18. What will 273 19. What will 29 dozen ? pounds of bar soap Ans. $2.783. cost, at 7 cents a Ans. $1.91. dozen of axes cost, at $11.62 per Ans. $343.75%. 20. Bought 28 bales of cotton cloth, each bale containing 313 yards; what will be the cost, at 16 cents per yard? NOTE Ans. $140.56. - If both numbers be mixed, or either of them be a complex fraction, they must first be reduced to simple ones. 30. Multiply 12 by §. 31. Multiply 15 by f. 32. A merchant owns of a ship, he sells A. What part is that of the whole ship? 33. Multiply 37 by 104. 34. Multiply of 74 by 7 of 11. 81 Ans. 84. of his share to Ans. 263. Ans. 25. Ans. 299. Ans. 39. What cost 73 barrels of flour, at $5 per barrel? 380 Ans. $39. 40. What cost 9 acres of land, at $273 per acre? Ans. $25694. 41. What cost 83 bushels of apples, at $14 per bushel ? Ans. $11. 42. Bought 117 bushels of corn, at $13 per bushel, and sold of it for $1 per bushel, and the remainder at $13 per bushel; what is gained on the sale of the corn? Ans. $321. 43. What is the continued product of the following numbers: 127 878 급 81TI? Ans. 37' 98' 21' and 128 SECTION XX. DIVISION OF VULGAR FRACTIONS. CASE I. To divide a fraction by an integer or whole number. 1. How many times will contain 8? OPERATION. To illustrate this question we will sup× = Ans. pose of an orange to be divided equally among 8 persons. Now, if we divide of an orange into 8 equal parts, one of these parts will be equal to of a whole orange, but as there are to be divided among 8 persons, each will receive 5 times Ans. person RULE. Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Or, divide the numerator of the fraction by the whole number, if it can be done without a remainder, and write the quotient over the denominator. To divide a whole number by a fraction. 1. How many times will 17 contain ? OPERATION. ¥ × 98223 Ans. = It is evident that 17 will contain as many times as there are fourths in 17, which are 4 X 17 =68 times. Again, if 17 contain 1 fourth 68 times, it will contain 3 fourths as many times as 68 will contain 3=223 Ans. RULE. Multiply the whole number by the denominator of the frac tion, and divide the product by the numerator. To divide a mixed number by an integer or whole number. 1. Divide 27% by 6. OPERATION. 6)273 = We divide 27 by 6, and find that it is contained 4 times, which we write under the 27, and we have 3 remaining, which we multiply by 5, the denominator of the fraction, and to the product we add the numerator 3, and the amount is 18. This we write over the product of 6, the divisor, multiplied by the denominator, 5, 6 × 5=30. We then reduce the fraction. RULE. = Divide the integers as in whole numbers, and if any thing remains multiply it by the denominator of the fraction, and to the product add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator. |