8. *Reduce 7s. 3d. to the fraction of a pound. Ans.. 9. Express 6fur. 16pls. to the fraction of a mile. Ans.. ADDITION OF VULGAR FRACTIONS. RULE.t Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same; and all of them to a common denominator; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required. EXAMPLES. 1. Add 34, 7, of, and 7 together. First 38=39, 4 of 21%, 7=4• 7 7 8 Then the fractions are 2,3,7%, and 7 ; ··· 29x8x10x 1=2320 7x8x10x 1= 560 7x8x 8x 1= 448 7x8x 8x10=4480 7808 --12-12 the answer. 8x8x10x1=640. = = 87d. and 11. = 240d. .. 87 *Thus 7s. 3d. the answer. + Fractions, before they are reduced to a common denomina❤ tor, are entirely dissimilar, and therefore cannot be incorporated with one another; but when they ae reduced to a common denominator, and made parts of the same thing, their sum or difference may then be as properlyexpressed by the sum or difference of the numerators, as the sum or difference of any 5. Add 1. s. and of a penny together. 3139 Ans. 131. Ans. 13, or 3s. 1d. 11. the sum of of 151. 331. 1 of 1⁄2 of % of a of of a shilling? 6. What is pound, and er. Ans. 71. 17s. 54d. 7. Add of a yard, of a foot, and of a mile together. Ans. 660yds. 2ft. 9in. 8. Add of a week, of a day, and of an hour togethAns. 2d. 14th. SUBTRACTION OF VULGAR FRACTIONS. RULE. Prepare the fractions as in Addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required. two quantities whatever by the sum or difference of their individuals; whence the reason of the rules, both for Addition and Subtraction, is manifest. 6. From oz. take dwt. Ans. 11dwt. 3gr. 7. From 7 weeks take 9 days. Ans. 5w. 4d. 7h. 12'. MULTIPLICATION OF VULGAR FRACTIONS. RULE.* Reduce compound fractions to single ones, and mixed numbers to improper fractions; then the product of the numerators is the numerator; and the product of the denominators, the denominator of the product required. EXAMPLES. 1. Required the continued product of 21,,of, and 2. 6. Multiply 4, of 4, and 183, continually together. Ans. 9120 Multiplication by a fraction implies the taking some part or parts of the multiplicand, and therefore may be truly expressed by a compound fraction. Thus multiplied by is the same as of §; and as the directions of the rule agree with the method already given to reduce these fractions to single ones, it is shown to be right. DIVISION OF VULGAR FRACTIONS. RULE.* Prepare the fractions as in Multiplication; then invert the divisor, and proceed exactly as in Multiplication. A Decimal is a fraction, whose denominator is an unit, or 1, with as many cyphers annexed, as the numerator has *The reason of the rule may be shown thus. Suppose it were required to divide by. Now÷2 is manifestly of 3 or 4×2; but = of 2, .. of 2, or 4 must be contained 5 3X5 times as often in as 2 is; that is = the answer; which 4X3 is according to the rule; and will be so in all cases. places; and is commonly expressed by writing the numerator only, with a point before it, called the separatrix. A finite decimal is that, which ends at a certain number But an infinite decimal is that, which is understood to be indefinitely continued. of places. A repeating decimal has one figure, or several figures, continually repeated, as far as it is found. As .33, &c. which is a single repetend. And 20-2424, &c. or 20-246246, &c. which are compound repetends. Repeating decimals are also called circulates, or circulating decimals. A point is set over a single repetend, and a point over the first and last figures of a compound repetend. The first place, next after the decimal mark, is 10th parts, the second is 100th parts, the third is 1000th parts, and so on, decreasing toward the right by 10ths, or increasing toward the left by 10ths, the same as whole or integral numbers do. As in the following NOTE. A fraction is multiplied by an integer, by dividing the denominator by it, or multiplying the numerator; and divided by an integer, by dividing the numerator, or multiplying the denominator. |