denominators over their product; thus, if it were required to find the sum of 1 and 4, we should add the 3 and 7 together for a numerator, and multiply them together for a denominator, and the fraction would be a 19. Add to , 7 to }, } to }, } to t, 1 to g. 20. Add fto ti, p to $, + to , } to T', f to to, } to 1. 21. Add } to 4, 7 to 1', $ to $, $ to t'h, } to š, I' to it. Section 22. SUBTRACTION OF VULGAR FRACTIONS. I. To subtract fractions, that have a common denominator. RULE. Subtract the less numerator from the greater, and under the remainder write the common denominator, and reduce the fraction if necessary. OPERATION. 1. From 7 take. 7-2=5, Ans. Ans. Á II. To subtract fractions whose denominators are unlike. RULE, Reduce the fractions to a common denominator, as in Addition of fractions ; then write the difference of the numerators over the common denominator. 9. From 1 take a Ans. 15. OPERATION 4)1 6 12 4 X 4 X 3 = 48 common denominator. 16 3 x 13=39 11 48 Ans. 10. From 97 take 511. Ans. 33 OPERATION. 97=79, 511 = 12. 4)8 12 4 X 2 X 3 = 24 common denominator. 2 3 8 3 x 79=237 122 X 71=1 42 95 = 33 Ans. 24 11. From of 128 take of 977. Ans. 3. OPERATION 12 = 761, 912 = 12 8 1 48. 1 X 231=231 47 48 Ans. 12. From 1 take 1. Ans. 26 13. From take it. Ans. t. 14. From take jo. Ans. 15. From 11 take it. 16. From t take 16 17. From 3 take it Ans. 87 18. From 241 take 15. Ans. 1988 19. From to take rotoo Ans. 1880 Ans. 12 Ans. 43 144. 20. From of I take of 4. Ans. 14 21. From s of take I's of 14. Ans. To 22. From 71 take 37. Ans. 315 23. From 8 take 5%. Ans. 2. 24. From 91 take 37. Ans. 53. 25. From 10% take 101'5. Ans. . III. To subtract a proper or mixed fraction from a whole number. 26. From 16 take 11. Ans. 141. To subtract the in this example, 1 From 16 must be borrowed from the 6 in the Take 11 minuend, and reduced to fourths, (4), 147 and the must be taken from them ; from leaves . 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 I, placed at the right hand of it, gives the answer 144. The same result will be obtained, if we adopt the following OPERATION. 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. 1 143 154 311 54 10153 If it be required to subtract one mixed number from another mixed number, the following method may be adopted. 32. From 9 take 3. Ans. 535. In this question, we Minuend 94 = 94% multiply the 2 and the 7, Subtrahend 3 = 341 the numerator and de nominator of the fraction 534 Ans. in the minuend by 5, the OPERATION 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, 91%. We then multiply the numerator and denominator of the subtrahend by 7, the denominator of the minuend, and we have another new fraetion, ft, which we place at the right hand of the other 3, thus, 315 It will now be perceived, that we have changed the fractions 99 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 }}, which makes us, and from this we subtract f'}; thus, - f}=$, 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 534 33. 34. 35. 36. From 124 971 8715 Take 94 54 154 1831 194 211 336 7811 6762 37. 16 195 1034 43. From a hhd. of wine there leaked out 123 gallons, how much remained ? Ans. 50%. 44. From $ 10, $2} was given to Benjamin, $31 to Lydia, $ 11 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 1 and 4 ? OPERATION. 7—3= 4 Ans. 7x3=21 46. Take } from }, 7 from 1, from £, 4 from $. 47. Take 1 from 1, $ from 4, 4 from }, { from 1. 48. Take f from }, + from , i from , it from $. 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. 1. Multiply by 15. This question may be anX 4 = 196 = 134 Ans. alyzed as those in com pound fractions. 2. Multiply 13 by 83. OPERATION, OPERATION. 1 x =9=767 Ans. 3. If a man receive fe of a dollar for one day's labor, what will he receive for 21 days' labor ? Ans. $77. 4. What cost 56lbs. of chalk at of a cent per lb. ? Ans. $ 0.42. 5. What cost 396lbs. of copperas at ii of a cent per Ib. ? Ans. $ 3.24. 6. What cost 79 bushels of salt at of a dollar per bushel ? Ans. $ 693 7. Multiply 376 by 14. Ans. 243 17: 8. Multiply 1 by 189. Ans. 16614. 9. Multiply 471 by it. Ans. 835 10. Multiply 871 by at. Ans. 2337 11. Multiply 117 by 365. Ans. 3534147 12. Multiply 867 by ito. Ans. 6135 II. To multiply a mixed number by a whole number, or a whole number by a mixed number. 13. Multiply 4 by 7. Ans. 321. |