III. To subtract a proper or mixed fraction from a whole number. 26. From 16 take 14. OPERATION. From 16 Take 11 14 Ans. 14. To subtract the in this example, 1 must be borrowed from the 6 in the minuend, and reduced to fourths, (), and the must be taken from them; from leaves 2. To pay for the 1, which was borrowed, 1 must be added to the 1 in the subtrahend, 1+1=2; and 2 taken from 16 leaves 14, and' the, placed at the right hand of it, gives the answer 142. The same result will be obtained, if we adopt the following RULE. Subtract the numerator from the denominator of the fraction, and under the remainder write the denominator, and carry one to the subtrahend to be subtracted from the minuend. If it be required to subtract one mixed number from another mixed number, the following method may be denominator of the fraction in the subtrahend, and we have a new fraction, which we write at the right hand of the other 9, thus, 91g. We then multiply the numerator and denominator of the subtrahend by 7, the denominator of the minuend, and we have another new fraction, , which we place at the right hand of the other 3, thus, 3. It will now be perceived, that we have changed the fractions 92 and 3 to other fractions of the same value, having a common denominator. We now subtract as in question 26th by adding 1 (35) to 1o, which makes, and from this we subtract; thus, 1-11, we then carry the 1 we borrowed to the 3, 1+3=4, which we take from 9, and find 5 remaining. The answer therefore is 53. 43. From a hhd. of wine there leaked out 123 gallons, how much remained? . Ans. 50g. 44. From $10, $21 was given to Benjamin, $3 to Lydia, $1 to Emily, and the remainder to Betsey; what did she receive? Ans. $31. NOTE. If it be required to find the difference between two fractions, whose numerators are a unit, the most ready way will be to write the difference of the denominators over their product. 45. What is the difference between and 4 ? Section 23. MULTIPLICATION OF VULGAR FRACTIONS. I. To multiply a fraction by a whole number, or a whole number by a fraction. Multiply the numerator of the fraction by the whole number, and under the product write the denominator of the fraction. 11 × 22=21376 Ans. 3. If a man receive of a dollar for one day's labor, what will he receive for 21 days' labor? Ans. $77. of a cent per lb. ? 4. What cost 56lbs. of chalk at 5. What cost 396lbs. of copperas at Ans. $0.42. of a cent per lb. ? Ans. $3.24. 6. What cost 79 bushels of salt at of a dollar per bush el? 7. Multiply 376 by 14. 8. Multiply by 189. 9. Multiply 471 by 7. 10. Multiply 871 by 34. 11. Multiply +1 by 365. 12. Multiply 867 by 16. Ans. $69. Ans. 243. Ans. 1661. Ans. 83. Ans. 2337. Ans. 353. Ans. 6 II. To multiply a mixed number by a whole number, or a whole number by a mixed number. 13. Multiply 43 by 7. Ans. 324. OPERATION. 49 7. 32 Ans. In performing this question, we say 7 times 3 fifths are 21 fifths, and 21 fifths are equal to 44. We write down the and carry the 4 to the product of 7 times 432. Hence the following 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 fraction to be affixed to the product. Ans. 37r. 19. What cost 7lbs. of beef at 5 cents per pound? 20. What cost 237bbs. flour at $6 per barrel ? Ans. $141. 21. What cost 8 yds. cloth at $5 per yard? Ans. $417. 22. What cost 9 barrels of vinegar at $63 per barrel ? 23. What cost 12 cords of wood at $6.37 Ans. $578. per cord? Ans. $76.50. 24. What cost 11cwt. of sugar at $99 per cwt. ? Ans. $103. 25. What cost 48 bushels of rye at $1.75 per bushel ? Ans. $7.65§. 26. What cost 7 tons of hay at $117 per ton? 27. What cost 9 doz. of adzes at $10 28. What cost 5 tons of lumber at $3 29. What cost 15cwt. of rice at $7.62 Ans. $83. per cwt.? Ans. $114.37. 30. What cost 40 tons of coal at $ 8.37 per ton? 7 Multiply the numerators together for a new numerator, and the denominators together for a new denominator; then reduce the fraction to its lowest terms. 32. Multiply by fr OPERATION. 8 56 7 Ans. T CANCELLED. 7 -X Ans. 11 11 of a dollar. 39. What cost of a bushel of corn at Ans. bushel ? 40. If a man travels of a mile in an hour, how far T would he travel in 41. If a bushel of corn will buy of a bushel of salt, how much salt might be bought for corn? Ans. of a bushel of of a bushel. NOTE. If there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 42. Multiply 43 by 63. OPERATION. 47=23, 64 = 20, 23 × 20=480304 Ans. |