CASE IV. To subtract one fraction from another, when both fractions have a unit for a numerator. The student will perceive, that this operation reduces the fractions to a common denominator. RULE. Write the difference of the denominators over their product. 2. Take 3. Take 4. Take from †, 1, 1, †, t, †, § ; 2% from tʊ, tí, 12, 1's. from t, t, t, t, t, ¿,; from 1, 1, 1. from t,,, ; from 1, 3, 4, 4, . from 1, 1, 1, 1, t, t, d, f, TO, TT. from 1, 1, 4, t, t, t, d, §. 1, NOTE. If the numerators of the given fractions be alike, and more than a unit, multiply the difference of the denominators by one of the numerators for a new numerator, then multiply the denominators together for a new denominator. 12. Take from &; } from ; & from ; from §. 19. Take from 40; 18 from 19; 18 from 19; 19 from 19. 20. Take 2 from 12; 12 from 12; 12 from 12; 13 from 12. NOTE.-The above questions, and those of a similar kind, may readily be performed mentally. CASE V. To subtract compound numbers. 1. From of a £. take of a £. Value of OPERATION. £. =12s. 8d. |33 common denominator d. 11 mon denominator of the fractional part, by multiplying together their denominators, 11 x 3 = 33. Case II., Sect XVIII. We then proceed as in This question can be performed by first subtracting the fracof a £., and then reducing the remainder tion of a £. from by Case XI., Sect. XVI.; thus: 71 £.£. = £.0£. 8s. 3d. 148qr. Ans. 2. From = This question may also be performed by first reducing of a cwt. to the fraction of a ton by Case IX., Sect. XVI., and subtracting it from of a ton, and then reducing the remainder to its proper terms by Case XI., Sect. XVI. Thus: 74% of a ton = 1qr. 26lb. 14oz. 10,82 dr. Ans. RULE. Find the value of the fractions in integers; then subtract as in the foregoing rules. 3. From of an ell English take of a yard. Ans. 3qr. Ona. 2in. 6. From of an acre take of a rod. Ans. 1R. 17p. 22yd. 2ft. 108in. 7. From of a cord take of a cord. Ans. 91ft. 16021 in. 8. From of a hhd. of wine there leaked out of it; what remained? Ans. 6gal. 3qt. Opt. 175gi. 9. From Boston to Concord, N. H., the distance is 72 miles; having travelled of this distance, how much remains ? Ans. 30m. 6fur. 34rd. 4ft. 8in. 11⁄2 bar. 10. From of a year take of a week. Ans. 101da. 5h. 54m. 174sec. 11. From of an acre take of a foot. Ans. 1R. 18p. 5yd. 4ft. Oin. SECTION XIX. MULTIPLICATION OF VULGAR FRACTIONS. CASE I. To multiply a simple fraction by a simple fraction. 1. Multiply by g. OPERATION. This process may be understood by sup} × 3 = ¦ Ans. posing a man to have found of a dollar, and that he gave of it to his wife, and that he wished to ascertain what part of a dollar his wife received. If of a dollar be divided into 5 equal parts, one of these parts of a dollar. And, if of of a dollar be of a ofwill be 7 times as much, and 7 times are will be dollar, If then, times of be, of will be 3 times as much, and 3 are. The wife will therefore receive of a dollar. RULE. Multiply the numerators together for a new numerator, and the denominators for a new denominator. The fraction should then be reduced to its lowest terms. The operation of the following questions may be abridged by 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. X== $77 Ans. To analyze this question, we say, if he earn 7 eighths of a dollar in 1 day, in 9 days he will earn 9 times as are 63 eighths = 63=$7% Ans. Multiply the whole number by the numerator of the fraction, and divide the product by the denominator, and the quotient is the much, and 9 times 7 eighths RULE. answer required. 2. Multiply 12 by §. 3. Multiply 15 by fr 4. Multiply by 11. 5. Multiply by 12. 6. Multiply by 19. 7. Multiply by 14. 8. Multiply 13 by 4. 9. Multiply 16 by 1. 10. Multiply 11 by 4. 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 5 eighths are 45 eighths, and 45 eighths are equal to 5g. We write down the and carry the 5 to the product of 9 times 768. 9 684 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. 11. What will 237 pounds of lead cost, at 8 cents a pound? Ans. $1.91. 12. What will 151 pounds of sugar cost, at 12 cents a pound? Ans. $1.881. 13. What will 29 cwt. of hay cost, at $1.12 per cwt.? Ans. $32.94. 14. What will 97 yards of broadcloth cost, at $8 per yard? Ans. $79.00. 15. What will 17 tons of potash cost, at $97 per ton? Ans. $1703.561. |