15 5 Reduce 175 to a simple fraction. io to a simple fraction. RULE. Reduce the given fractions (if necessary) to simple fractions, and to a common denominator (omitting integers :) Place the sum of the numerators over the common denominator; then to the value of said fractions add the integers (if any.) If fractions be of different integers, find their values separately, and add as in compound addition. EXAMPLES. 1 Add į and together. +=*+1==13. facit. 2 Add to it and together. facit 2136 3 Add 19, 7 and of together. 265 4 Add off and of 18 together. 5 Add 1 of 95, and 3 of 14 together. 6 Add į, and 17} together. 7 Add 12, 3, and 43 together. 8 Add 6, 7 of 3, 4 of , and 74 together: 9 Add }, , of, and 9, together. 1037 10 Add of a penny to ] of a pound. 2s 3d. 1qr. 11 Add į of a pound to of a shilling. 18s 3d. 12 Add i of a lb. Troy to li of an oz. facit 6oz11dwt. 16gr. L 2 13 Add 240 1.17 4311 12 18% 2011 14321 567 ther. 13 Add of a ton to of an C.wt. facit 120. Igr. 8lb. 12oz. 124dr. 14 Add of a mile to žo of a furlong, facit 6 fur. 28 pls. 15 Add i of a yard to of a foot. facit 2ft. 2in. 16 Add of a day to į of an hour. facit shr. 30min. 17 Add of a week, of a day, and of an hour together. facit 2da. 14 hr. 18 Add of a yard, of a foot, and of a mile toge facit 1540yd. 2ft. Sin. 19. What is the sumof of a L. of a shilling, and fe of a penny? answer 3s 1d. lliqr. 20 What is the sum of of 15L. 3 L. of of of a L. and of of a shilling ? answer 71 17s 5d.0495. 21 Add şof 12 L. +4L. +} of ind of a L. +of of a shilling into one sum. facit 91 88 8d. 03.qr. 22. If a merchant owns of a ship, valued at 15001. and buys another person's share of her, which is Lo; what part belongs to him, and what is it worth ? answer it, worth 10311 5s. SUBTRACTION OF VULGAR FRACTIONS. RULE. Prepare the fractions as in addition, and subtract the lower numerator from the upper, placing the difference over the common denominator. If the lower numerator be the greater, subtract it from the common denominator, adding in the upper numerator, and carry 1 to the units place of the integer. If fractions be of different integers, find their values separately, and subtract as in compound subtraction. EXAMPLES, 1 From 11 take . H-4f-198= 12 facit. 2 From 7 take 3 From 961 take 147. 4 From 96 take } facit 97 811 95% 163 220 38 1 5d.! 5 From of 76, take of 21. facit 972 6 From 10%, take 4 of of 4. 7 From 71į, take 17. 8 From 141 take of 19. 9 From 1 of a L. take of a shilling. 9s. 3d. 10 From į of a shilling, take of a penny. 11 From of an oz. troy, take of a dwt. facit lidwt. 3gr. 12 From of an C.wt. take of a lb. facit iqr. 271b. 6oz. 10 dr. 13 From of a league, take ta of a mile. facit 1M. 2fur. 16pls. 14 From 1 ell English, take yo of a quarter. facit lyd. 1{na. 15 From 7 weeks, take 97 days, facit 5w. 4da. 7hr. 12min. 16 From 4 days, 7 hours, take 1 day, 9 hours. facit 2da. 22 hr. 17 Borrowed 5 L. paid 4 of 4 L. what remains ? answer 41 3s 8d. 14qr. 18 What is the difference between of a L. and of of a shilling? answer 10s. 7d. 1jqr. 19 Take of a shilling from of 53 L. and what is left ? answer ll. 8s. 11d. 20 If a merchant own of a ship, valued at 9001. and gell of his share, what part has he left, and what is it worth ? answer , worth 1871 10s. MULTIPLICATION OF VULGAR FRACTIONS. RULE. If a compound fraction, or mixt number, be given, reduce them to single, or improper fractions ; multiply the numerators together for a new numerator, and the denominators for a new denominator. EXAMPLES. 1 Multiply 1 by i x1= 4 facit. 2 Multiply k by š. facit 7 3 Multiply facit 750 613 9 16 3 Multiply off by 10 of 12. 1213 21 9 Multiply by 4 of 11. 10 Multiply of 91 by 71. 52053 11 Multiply i23 by 1 of 7. 292 12 Multiply 72 by 91. 69 13 What is the product of of }, and of 34 ? answer 14 What is the product of 5 x,x, of } x41? answer28 15 What is the continued product of }, 34, 5, and of answer 45 16 If 3 be multiplied by }, and this product again by of , what is the last product? 23 answer ito 33 RULE. Prepare the fractions, if necessary, as in multiplication : multiply the denominator of the divisor into the numerator of the dividend for a numerator; and the numerator of the divisor into the denominator of the dividend for a denominator. EXAMPLES. facit 137 1 Divide 17 by : }) =13facit., Or thus, 17-=175. 2 Divide is by . 3 Divide is by To * 4 Divide 11 by 48% 5 Divide 7 by 4. 6 Divide 4 by . 7 Divide of 19 by of . 8 Divide of by of 4. 9 Divide of by 1 of . 11 10 Divide 45 by 5 of 4. 225 11 Divide 11 Divide of 4 by 45. facit i 12 Divide şof 6 by 1 of 4 of it. 810 13 What is the quotient of 7{ divided by 95? answer 11 14 What is the quotient of of į divided by of 7} ? answer 7171 15 What is the quotient of 5205} divided by of 91 ? answer 713 THE SINGLE RULE OF THREE IN VULGAR FRACTIONS. RULE. Prepare the given terms, if necessary, by reduction, and state them as in whole numbers ; 'multiply the second and third terms together, and divide that product by the first; İnvert the dividing term, and multiply the three together for the fractional answer. Note. When the dividing term is inverted, the note to case 5 in reduction is applicable here. Or, EXAMPLES. :: 3 1 105 ! If } of a yard cost of a L. what cost yards ? ==3s 4d. answer. 1 Or, Cancelled ; L=3s 4d. 3 X XA 6 2x2 2 If } lb. of sugar cost 15$. what cost }lb. ? answer 4d. 3gr. 51 3 If 4 of an ell English cost 1 L. what is that per ell! answer 18s 10do1 4 When 2oz. of silver cost 16-js.'what is the value of answer 6s 1d 3qr. 5 If 6 yards cost 18s, what buys 91 yards ? answer 1l 5s 7d. Igr. 13 6 Sold 500 bushels of wheat, at 56d. per bu. what sum passes to the credit of that article ? answer 1171 18s 4d. |