7. Multiply 471 by fr. Ans. 875. Ans. 2337. 8. Multiply 871 by 3't. 9. Multiply 867 by Tic Ans. 6136 155. To multiply a whole and mixed number together. Ex. 1. Multiply 17 by 61. Ans. 1143. OPERATION. 17 OPERATION. 7 63 We first multiply 17 by 6, the whole number of the multiplier, and then by the 102 fractional part, #, which is simply taking of 17 - 12t of it; and add the two products. 1143 Ex. 2. Multiply 7 by 4. Ans. 30%. We first multiply in the multiplicand by 4, the multiplier ; thus, 4 times are 4 equal to 2%, which is in effect taking of the of 4 - 2 multiplier, 4. We then multiply the whole 28 number, 7, by 4; and add the two products. Hence, in performing like examples, 303 Multiply the fractional part and the whole number separately, and add the products. EXAMPLES FOR PRACTICE. .3. Multiply 9g by 5. Ans. 464. 4. Multiply 123 by 7. Ans. 885 5. Multiply 9 by 813. Ans. 801 6. Multiply 10 by 7. Ans. 713. 7. Multiply 114 by 8. Ans. 946. 8. What cost 787lb. of beef at 5 cents per pound? Ans. $ 0.37 11 9. What cost 2372bbl. of flour at $ 6 per barrel ? Ans. $1411 10. What cost 8fyd. of cloth at $ 5 per yard ? Ans. $ 417 11. What cost 9 barrels of vinegar at $ 6% per barrel ? Ans. $575. 155. The rule for multiplying a whole and mixed number together? Does it make any difference which is taken for the multiplier ? 12. What cost 12 cords of wood at $ 6.374 per cord ? Ans. $ 76.50. 13. What cost 11cwt. of sugar at $ 93 per cwt. ? Ans. $ 1033. 14. What cost 43 bushels of rye at $ 1.75 per bushel ? Ans. $ 7.65. 15. W at cost 7 tons of hay at $ 117 per ton ? Ans. $ 835 16. What cost 9 doz. of adzes at $ 10% per doz. ? Ans. $ 95%. 17. What cost 5 tons of timber at $ 3} per ton ? Ans. $ 15%. 18. What cost 15cwt. of rice at $ 7.624 per cwt. ? Ans. $ 114.374. 19. What cost 40 tons of coal at $ 8.374 per ton ? Ans. $ 335. 156. To multiply a fraction by a fraction. Ex. 1. Multiply } by : Ans. Tz OPERATION BY CANCELLATION 7 OPERATION. 3 X4= 구 9 X4 12 3 To multiply by is to take of the multiplicand, f (Art. 154). Now, to obtain of y, we simply multiply the numerators together for a new numerator, and the denominators together for a new denominator (Art. 138). Therefore, Multiplying one fraction by another is the same as reducing compound fractions to simple ones. RULE. — Multiply the numerators together for a new numerator, and the denominators together for a new denominator. Note. - When there are factors common to the numerators and denomi. nators, the work may be shortened by canceling those factors. EXAMPLES FOR PRACTICE. 2. Multiply } by it: 3. Multiply ý by it. 156. What is the first rule for multiplying one fraction by another? How does it appear that this operation multiplies the fraction of the multiplicand ? What is the inference drawn from it? What is the note ? Ans. Ans. š. Ans. 1 Ans. 153 Ans. $. 4. Multiply 1 by it. bushel? Ans. } of a dollar. 10. If a man travels it of a mile in an hour, how far would he travel in fi of an hour ? Ans. I of a mile. 11. If a bushel of corn will buy o of a bushel of salt, how much salt might be bought for of a bushel of corn ? Ans. 47 of a bushel. 12. If of f of a dollar buy one bushel of corn, what will / of is of a bushel cost ? Ans. 7 of a dollar. 13. If of of It of an acre of land cost one dollar, how much may be bought with of $ 18? Ans. 147 acres. 157. To multiply a mixed number by a mixed number. Reduce them to improper fractions, and then proceed as in Art. 156. Ex. 1. Multiply 4f by 63. Ans. 30%. OPERATION. 4 = id; 6 = 2. 4 2 3 92 X 304 3 3 EXAMPLES FOR PRACTICE. 2. Multiply 7+ by 84. Ans. 6036 3. Multiply 47 by 97. Ans. 45 4. Multiply 114 by 84. Ans. 9935. 5. Multiply 121 by 115. Ans. 147*. 6. What cost 7fcords of wood at $ 5% per cord ? Ans. $ 4141 7. What cost 7fyd. of cloth at $34 per yard ? Ans. $ 251%. 8. What cost 64 gallons of molasses at 231 cents per gallon ? Ans. $ 1.524. 9. If a man travel 34 miles in one hour, how far will he travel in 9 hours ? Ans. 347. 157. How do you multiply a mixed number by a mixed number : 10. What cost 36117 acres of land at $ 25% per acre ? Ans. $9167 438. 11. How many square rods of land in a garden, which is 97% rods long, and 497 rods wide ? Ans. 481036 rods. Ans. . FIRST OPERATION. Ans. obro DIVISION. 158. Division of Fractions is the process of dividing wben the divisor or dividend, or both, are fractions. 159. To divide a fraction by a whole number. Ex. 1. Divide by 4. We divide the numerator of the fraction by 4, 8 2 and write the quotient, 2, over the denominator. ; 4 It is evident this process divides the fraction S 9 by 4, since the size of the parts into which the whole number is divided, as denoted by the denominator, remains the same, while the number of parts taken is only 4 as many as before. Therefore, Dividing the numerator of a fraction by any number divides the fraction by thal number. Ex. 2. Divide & by 9. We multiply the denominator of the fraction by 5 5 the divisor, I, and write the product under the 7 numerator, 5. 63 It is evident this process divides the fraction, since multiplying the denominator by 9 makes the number of parts into which the whole number is divided 9 times as many as before, and consequently each part can but have of its former value. Now, if each part has but $ of its former value, while only the same number of parts is expressed by the fraction, it is plain the fraction has been divided by 9. Therefore, Multiplying the denominator of a fraction by any number divides the fraction by that number. RULE. Divide the numerator of the fraction by the whole number, when it can be done without a remainder, and write the quotient over the denominator. Or, Multiply the denominator of the fraction by the whole number, and write the product under the numerator: SECOND OPERATION. 158. What is division of common fractions? - 159. How is the fraction divided by the first operation? What inference may be drawn from this operation? How is å fraction divided by the second operation? What inference is drawn from this operation? The rule ? Ans. • Ans. obs EXAMPLES FOR PRACTICE. Ans. As 3. Divide by 3. Ans. . ਸੰਤ 4. Divide is by 6. Ans. 137 5. Divide TT by 12. Ans. 46 6. Divide 11 by 8. 7. Divide by 9. 8. Divide by 15. Ans. 56 9. Divide * *by 75. Ans. To 10. Divide ž by 12. 11. John Jones owns $ of a share in a railroad, valued at $ 117 ; this he bequeaths to his five children. What part of a Ans. 4. share will each receive ? Ans. ris: 12. Divided by 15. Ans. zs. 13. Divide by 28. 14. James. Page's estate is valued at $ 10,000, and he has given & of it to the Seamen's Society; of the remainder he gave to his good minister; and the remainder he divided equally What sum will each of his among his 4 sons and 3 daughters. Ans. $ 6801 children receive? 160. To divide a whole number by a fraction. Ex. 1. How many times will 13 contain ? Ans. 30 13 will contain as many times as there are sevenths in 13, equal 91 sevenths. Now, if 13 contain 1 seventh 91 times, it will contain as many times as 91 will contain 3, or 30%. RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. EXAMPLES FOR PRACTICE. 2. Divide 18 by }. 3. Divide 27 by 13. 4. Divide 23 by 1. Ans. 204. Ans. 29 : Ans. 92. 160. The rule for dividing a whole number by a fraction? The reason for the rule ? |