Ans. 17. 5919 17 EXAMPLES. 115. 7. Reduce 791; to an improper fraction. 1513. 8. Reduce 100%to an improper fraction. III. To reduce an improper Fraction to a whole oi mixed number. RULE.--Divide the numerator by the denominator, and the quotient will be the whole or mixed number. EXAMPLES. 9. Reduce 5 to its equivalent or proper number. Ans. 21. 10. Reduce iz to its proper number. Ans. 4. 11. Reduce 13 62 to its equivalent number: 542 12. Reduce 2918 to its equivalent number. 17111. IV. To reduce a compound Fraction to a single one. RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator. EXAMPLES. 13. Reduce of of $ to a single fraction. 1x2x3 of of 1 = Ans. 2x3x4 14. Reduce s of of 10 to a simple fraction. Ans. 15. Reduce of of S1, to a single fraction. 16. Reduce of of 1 of 4, to a single fraction. V. To reduce given fractions to others of a common denominator. Rule.--Multiply each numerator into all the denominators except its own, for a new numerator, and all the denominators together for a common denominator. EXAMPLES. 17. Reduce #, and ę to a common denoininator. 3x5x7 4X4X7 6X4X5 -11, &= 7X4X5 18. Reduce and to fractions of a common demominator. Ans. 19. Reduce }, {, . and } to a common denominator. Ans. 140, 120, 120, 140 20. Reduce , 2 and 4 to fractions of a common denominator. Ans. toler olur 105 4 1405 120 140 18 35 63' 63 35 78 120 25 165 VI. To reduce a fraction of one denomination to the fraction of another, but greater, retaining the same value. Rule-Reduce the given fraction to a compound one, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly reduce this compound fraction to a single one. EXAMPLES. 21. Reduce of a penny to the fraction of a pound. Ans. ਉਲ 22. Reduce dwt. to the fraction of a lb. troy. Ans. 23. Reduce Ž of a lb. avoirdupois to the fraction of a cwt. Ans. รงร 24. Reduce of 58. to the fraction of 21 shillings. Ans. VII. To reduce a fraction of one denomination to the fraction of another, but less, retaining the same value. RULE-Multiply the given numerator by the parts of the denominations between it and that denomination you would reduce it to, for a new numerator, which place over the given denominator. EXAMPLES. 25. Reduce its of a pound to the fraction of a penny. Ans.ee 36. Reduce és of alb. troy to the fraction of a pennyweight. Ans. 27. Reduce 3 of a cwt. to the fraction of a lb. Ans. 28. Reduce 25 of 21s. to the fraction of 5 shillings. Ans. . VIII. To find the value of a fraction, in the known parts of coin, weight, measure, &c. Rule-Multiply the numerator by the integer, and divide by the denominator : if any thing remain, multiply it by the next inferior denomination, and divide as before. EXAMPLES. 29. Required the value of of a pound? Ans. 12s, 30. What is the value of of £5 9s. ? £4 13s. 57d. 31. What is the value of of a ton ? Ans. 3 cwt. Oqrs. 816. 9oz. 13,dr. 32. Required the value of i. of a mile ? Ans. 1 fur. 28po. 34 yds. -33. I demand the value of of an acre? 34. What is the value of is of a day? 7ho. 12min. Ans. 2 ro. 20 po. IX. To reiluce any given quantity to the fraction of any greater den nomination of the same kind. RULE-Reduce the given quantity to the lowest term mentioned, for a numerator ; then reduce the integral part to the same term, for a denominator, which will be the fraction required. EXAMPLES 35. Reduce 12s. to the fraction of a pound. Ans. 36. Reduce £4 138. 5ąd. to parts of £5 9s. 37. Reduce 3 cwt. O qrs. 8lb. 9oz. 13. dr. to the fraction of a Ans. 6 ton. 38. Reduce 1 fur. 28 po. 3. yds. to the fraction of a mile. Ans. 39. Reduce 2ro. 20po, to the fraction of an acre. 40. Reduce 7ho. 12min. to the fraction of a day. 1103 90 100 ADDITION OF VULGAR FRACTIONS. RULE.—Reduce the given fractions to a common denominator, then add all the numerators together, under which place the common denominator. EXAMPLES. 1. Add į and { together. Ans. 13 2. Add į and and into one sum. 3. Add and and 21 into one sum. 4. Add and off, and 9 % together. When fractions are of several denominations. RULE.—Reduce them to their proper values, and add as before. 5. Add { of a pound to be of a shilling. Ans. 158. 10d. 6. What is the sum of £.3 +4s.tid. 15s. 9 d. 7. What is the sum of £1+ td. 3s. 1d. 121 988 8. Add $ of a pound Troy to of an ounce. Ans. 902. 3 dwt. 8 grs. I. Add of a ton to of a lb. 16 cwt. 13 oz. 54 dr. 10. Add of a mile to Z of a furlong. Ans. 6 fur. 28 po. 11. Add of a week, of a day, and į of an hour together. Ans. 2 days, 14 hours. 12. A grocer sold the following parcels of sugar, vız : 16{ lb. 194 Ib. 131 lb. 203 lb. 25146 lb. 305 lb. and 11. lh. Idemand how many lb, he sold in all ? Ans. 362 11 16 MULTIPLICATION OF VULGAR FRACTIONS. 55 SUBTRACTION OF VULGAR FRACTIONS Rule 1.—Reduce the given fractions to a common denominator, then subtract the less numerator from the greater and place the remainder over the common denominator. 2. In mixed numbers when the lower fraction is greater than the upper, subtract the numerator of the lower from the denominator, and to that difference add the upper numerator, carrying one to the units place of the lower whole number. EXAMPLES. 1. Subtract from 111. Ans. 2. Subtract from 970 3. Subtract 144 from 961 4. From 1: take { of s. 5. From 644 take of . 634 When fractions are of several denominations. Rule.-Reduce them to their proper values and subtract as before. 6. From of a pound take of a shilling. Ans. 145. 3d. 7. From of a lb. Troy, take of an ounce. 802. 1€ dwt. 8. From of a ton, take of a lb. Ans. 15 cwt. 3 qrs. 27 lb. 2 oz. 103 dr. 9. From of a league take 7 of a mile. Ans. 1 m. 2 fur. 16 po. 10. From of a chaldron take of a bushel. Ans. 17 bus. 13 pec. 27 112 379 700 8119. 21 35 9 422 MULTIPLICATION OF VULGAR FRACTIONS. RULE.-Reduce compound fractions to single ones, and mixed numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for a new denominator. EXAMPLES. 1. Multiply by 16 Ans. 2. Multiply 5 by i 3. Multiply s by 97. 841. 4. Multiply 67 by 8. 545 5. Multiply 9ž by } of 1. 6. Multiply 1 of by of of %. * 7. Multiply of 8 by of 5. 21. 8. Multiply of 72 by 1 of 3 716 45 56 RULE OF TAREE INVERSE IN VULGAR FRÀCTIONS. RULE.- Prepare the numbers if necessary by the rules of reduction ; and divide the numerator by the numerator, and the denominator by the denominator, if they will exactly di. vide ; but if not, then invert the terms of the divisor, and proceed as in multiplication. EXAMPLES. 1. Divide 2,5 by 25x3 ===lf Ans. Or thus, 2 == 9X5 =*=l1 Ans. 2. Divide by Ans. 3. Divide if by 4. Divide 5885 by 841 7. 5. Divide ; of by of 6. Divide 7 by of 7. 111 7. Divide of } by of 7. 8. Divide iç of 4 by 4. 7 RULE OF THREE DIRECT IN VULGAR FRACTIONS. RULE-Make the necessary preparations as before directed; then multiply continually together, the second and third terms, and the first with its parts inverted as in division, for the answer. EXAMPLES. 1. If of a gallon cost $$ what will of a tun cost ? gal. $. tun. 8x5X5X4x63 If :::$ 5X8X9x1x1 =$140 Ans. 2. What is the purchase of $1230 bank stock, at 1085 per sent? Ans. $1336 8fcts. 3. If 3 yards cost £2 what will 14+ yards cost? Ans. £13 15$. 4d. 4. If { of ý cwt. sugar cost £ 1% what will 82 cwt. cost ? Ans. £262 10s. 5. If | yards of silk cost i of his what is the price of 15} ells, Flemish ? Ans. £9 15s. 10d. 6. What part of 6d. is į of 2d. Ans. 5. RULE OF THREE INVERSE IN VULGAR FRAC. TIONS. RULE-State and prepare as in the rule of three direct, invert the third term in place of the first, and proceed as in die vision. 22 LUXI X 3 |