denominators over their product; thus, if it were required to find the sum of and, we should add the 3 and 7 together for a numerator, and multiply them together for a denominator, and the fraction would be 19. Add to, to f, to, to f, to f. 20. Add to, to, to, to, to to. 21. Add to,to,to,to,to,to. 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. 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 18 take √ OPERATION. Ans. 1. 4)16 12 4×4 × 3 = 48 common denominator. 4)8 12 4× 2 × 3 = 2 4 common denominator. 6X8X1=48 common denominator. 48 1 x 231=231 6 III. To subtract a proper or mixed fraction from a whole number. 26. From 16 take 14. OPERATION. From 16 Take 14 142 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. 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 143. The same result will be obtained, if we adopt the following RULE. Subtract the numerator from the denominator of the frac tion, 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 adopted. 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 33 to other fractions of the same value, having a common denominator. We now subtract as in question 26th by adding 1 (35) to 18, which makes, and from this we subtract; thus, 1521, 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 5. 43. From a hhd. of wine there leaked out 123 gallons, how much remained? Ans. 50g. 44. From $10, $2 was given to Benjamin, $34 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 ? 46. Take from 1, + from 1, Į from †, ✈ from §. 47. Take ₫ from †, † from 4, † from 1, † from 1. 48. Take from §, ↓ from †,† from 4, I 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. 3. If a man receive of a dollar for one day's labor, what will he receive for 21 days' labor? Ans. $73. 4. What cost 56lbs. of chalk at of a cent per lb. ? 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 1 by 189. 9. Multiply 471 by 7. 10. Multiply 871 by 34. 11. Multiply 11 by 365. 12. Multiply 867 by τ. Ans. $691. 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. |