By Reduction 1 is equal to 50 cents. 25 15 등 621 434 To add mixed or compound fractions. 1. Add s of a day of an hour, and is of a minute together? Ans. 16h. 48m. 18s. 2. Add į of a year, of a month, of a week, i of a day, I'y of an hour, and of a minute together? Ans, 4m. 1w. 1d. 8h. 5m. 48s. 3. Add of an eagle, i of a dollar, To of a dime, and of a cent? Ans. $8.821. 4. Add s of a week, of a day, and 1 an hour together? Ans. 2d. 143h. 5. Add of a dollar, í of a dollar, and ß of a dime together? Ans. $1.451. 6. Add } of a yard, šof a foot, and } of an inch together? Ans. 1 ft. 4 in. 1 barley corn. CASE XI. To add compound fractions together, connected by the pre position or (see Def. 9.) GENERAL RULE. Multiply the numerators together for a new numerator, and the denominators together for a new denominator. Reduce the fractions, and then add them together agreeably to Case VIII. or IX. 1. Example.--Add of l of 4, and 3 of j of 1 together? Ans. 17. Operation, f xx= Mr reduced is 3. Now, it is plain, that of off of the first compound is equal to 1, and 3 x 3 x 1 of the second compound is equal to To reduced is equal to 34, which added to į the sum is 17 as required. 2. How much is į of } of a dollar? Ans. 50. 3. How much is of 1 of a dollar? Ans. 7 or 18c. 4. How much is the į of }, the { of }, and the į off of a dollar? Ans. 11to or $1.00c. 8}m. 5. Add of off of a dollar, to šof j of of a dollar? Ans. $5 or 24c. Operation, 1 x * xf = 1 = 1o of a dollar or 10c. And 1/3 x 73 x 3 so of a dollar or 14c. Adding fractions together, 24c. 1. How much is the į and į of į of a dollar? Ans. 50c. 2. How much is the į and į of of a dollar? Ans. 65c. 3. How much is of of l of a yard? Ans. 1 ft. 3 in. 4. How much is į of 1 of į of $5.00? Ans. 124c. 5. How much is the } and of ofl of a year? “ 7m. 6. How much is the and of to of j ofe of an Eagle? Ans. $1.02. CASE XII. , To reduce mixed fractions to parts, or to an improper fraction. (See 11th Definition.) Rule.-Multiply the whole number by the denominator of the fraction, and add the numerator to the product for the numerator of the fraction sought, under which will be the given denominator. Example.-Reduce 171 dollars to half dollars. ILLUSTRATION. It is well known that two half dollars are equal to one dollar; consequently, as 1 dollar is = to 2 halves, 17 units or 17 dollars will contain 17 times as much, to which if we add one-half we get 35 halves for the required answer. 1. Bring $194 to quarters? CO 135 8 66 175 2 64 101 TO MULTIPLY FRACTIONS. CASE I. When the fractions are proper, RULE.—Multiply the numerators together for a new numerator, and the denominators together for a new denominator. ILLUSTRATION. It is manifest, that when a number is multiplied by 1, the product is equal to the multiplicand; therefore, when a number is multiplied by a fraction, which is less than 1, the product must be less than the multiplicand. Example 1.–Multiply by ? Ans. s. From the analysis of Geometry, we find, that if a line be divided into 2 equal parts, the square of the whole line is 4 times the square of half the line: thus, let the line A 1 -B be one mile, yard, &c. The square of 1 is 1, because 1 x 1 is 1, and squared is , hence, į x} = of 1. 1 1 2 2 CASE II, When the multiplier and multiplicand are both mixed numbers. RULE.—Bring them to improper fractions, agreeably to Case XII. (Addition,) this done, multiply the numerators together as before, for a new numerator, and the denominators together for a new denominator; divide the new numerator (so called) by the new denominator, and the result will be the product of the mixed numbers. ILLUSTRATION. In the rectangular or parallelo 10} yards. B В. gram A B C D, the length of the side A B is 10 yards, and the length of the line A C is 75 yards, the line A B is divided into 21 parts, C D and the line A Cinto 15 equal parts, which are drawn at right angles to each other, consequently, there are 315 rectangles in the whole figure A B C D, and every four of these make 1 square yard, this is manifest from the following example: therefore, 103 x 73=* X = 315 = 78% as required. CASE III. . To multiply a whole number by a fraction. Rule.-Multiply the whole number by the numerator of the fraction, and divide the product by the denominator, the quotient will be the result. From what has been already stated, it is evident, that the multiplication of a whole number by a fraction implies the taking some part of it; for instance, if we multiply 4 by }, agreeably to the rule 4 x t = f = 2, and 9 x} = 3, &c. Multiply 35 by š. Multiply 84 by 4. 39 by š. 96 by 4. 72 by 80 by š. APPLICATION OF FRACTIONS TO SHORT ACCOUNTS.' 1. Multiply 11} by 114 cts. Example, Yx* = 54° Ans. $1.32 2. What will 7ị lbs. come to at 8£c. pr. Ib? Ans. 61c. 3. What will 44 lbs. come to at $; per lb? Ans. 564c. 4. What will 19% yards come to at $; of a dollar? Ans. $7.40%. 5. What will 2 yards come to at $7 of a dollar? Ans. $2.403. 6. What will 67 lbs. of tea cost at 653 cts, per pound? Ans. $4.5231 SUBTRACTION OF FRACTIONS. CASE I. If the fractions have a common denominator. Rule.-Subtract the lesser numerator from the greater, and under the remainder write the common denominator, and reduce the fraction if necessary. 1. Example-From $take 1? Ans. 4 of a doll.or 50c. 3-1 t, or .75 — 25 = .50. 2. From $3 take 3? Ans. $f or .25c. 3. From $1, take ? 5. From $16 6. From } 4. From $1 take 1? Take $16 Take CASE II. Ans. 4. If the denominators of the fractions are unlike. Rule. - Find a common denominator according to Case VI. Addition, ("Second Method.”) 1. Example-From 1f take ? Here the denominators of the fractions are in the ratio of 11 to 7, then ji x 7 : 74 and x 11 = 44 70— 44 = 44. By Case I, or by Case VI. Addition, find a common denominator; thus, by cross multiplication. ji x 10 X 7= 70 11 x 4 = 48 11 x 7 = 77 common denominator, the result is 44. 1. From $1% take ? Ans. $7' or .02 c. 2. From $. take z? $1 or .50c. 3. From $15 take ? (Here the ratio is as 4 to 1.) 4. From $15 take 3? Ans. for .75c. 5. From $take ? 6. From $1 take 10? “ og or .15c. og or .45c. CASE III. When the fractions have a unit for a numerator. RULE.—Write the difference of their denominators over their product. |