OR, If you chuse, you may take that easy method in Problem I. (page 74.) Multiply the whole number by the denominator of the given fraction, and to the product add the numerator, this sum written above the denominator will form the fraction required. EXAMPLES. 1. Reduce 457 to its equivalent improper fraction. 45x8+7=987 Ans. 2. Reduce 1913 to its equivalent improper fraction. 3. Reduce 16-18 to an improper fraction. Ans. 35 18 Ans. 1618 TOO 4. Reduce 61% to its equivalent improper fraction. CASE III. Ans. 22085 360 To find the value of an improper fraction. RULE. Divide the numerator by the denominator, and the quotient will be the value sought. CASE IV. To reduce a whole number to an equivalent fraction, hay ing a given denominator. RULE. Multiply the whole number by the given denominator; place the product over the said denominator, and it will form the fraction required. 12. EXAMPLES. 1. Reduce 7 to a fraction whose denominator shall be 9. Thus, 7x9 63, and 63 the Ans. 2. Reduce 18 to a fraction whose denominator shall be Ans. 216 3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 9000-900-100 CASE, V. To reduce a compound fraction to a simple one of equal value. RULE. 1. Reduce all whole and mixed numbers to their equivalent fractions. 2. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required. 2. Reduce of of to a single fraction. Ans. 4. Reduce of of 8 to a simple fraction. Ans. 836 1500 Ans. 180=3 5. Reduce of 18 421 to a simple fraction. Ans. 12660-217 NOTE.-If the denominator of any member of a compound fraction be equal to the numerator of another mem ber thereof, they may both be expunged, and the other members continually multiplied (as by the rule) will produce the fraction required in lower terms. 6. Reduce of of to a simple fraction. Thus 2×5 7. Reduce of of of 1 to a simple fraction. CASE VI. Ans. To reduce fractions of different denominations to equiva lent fractions having a common denominator. RULE I. 1. Reduce all fractions to simple terms. 2. Multiply each numerator into all the denominators except its own, for a new numerator: and all the denomi nators into each other continually for a common denominator; this written under the several new numerators will give the fractions required. EXAMPLES. 1. Reduce to equivalent fractions, having a com mon denominator. } + } + {-24 common denominator. The foregoing is a general Rule for reducing fractions to a common denominator; but as it will save much labour to keep the fractions in the lowest terms possible, the following Rule is much preferable. RULE II. For reducing fractions to the least common denominator, (By Rule, page 155) find the least common multiple of all the denominators of the given fractions, and it will be the common denominator required, in which divide each particular denominator, and multiply the quotient by its own numerator for a new numerator, and the new numerators being placed over the common denominator, will express the fractions required in their lowest terms. tor. EXAMPLES. 1. Reduce and to their least common denomina“ 4)2 4 8 2)2 1 2 1 1 1 4x2=8 the least com. denominator. 8÷2x1-4 the 1st. numerator. 8÷8x5-5 the 3d. numerator. These numbers placed over the denominator, give the answer equal in value, and in much lower terms than the general Rule, which would produce # 2. Reduce and to their least common denomi Ans. 12 12 ** nator. 48 40 REDUCTION OF VULGAR 169 3. Reduce and to their least common denom inator. 1 3 283 Ans. 188 4. Reduce and to their least common denommator. Ans. 111 CASE VII. 9 16 16 To reduce the fraction of one denomination to the fraction of another, retaining the same value. RULE Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly, reduce this com pound fraction to a single one, by Case V. EXAMPLES. 1. Reduce & of a penny to the fraction of a pound. By comparing it, it becomes of of of a pound. 2. Reduce 6 × 12 × 20 of a pound to the fraction of a penny. Compared thus, T of 20 of 4 d. Then 5 x 20 x 12 +!3%=# 1300 3. Reduce of a farthing to the fraction of a shilling Ans.. 4. Reduce of a shilling to the fraction of a pound. Ans. 100 5. Reduce of a pwt. to the fraction of a pound troy. Ans. 1880-336 6. Reduce of a pound avoirdupois to the fraction of a cwt. Ans.cwt.. 7. What part of a pound avoirdupois is of a cwt Compounded thus, 7 of 4 of 28=1}}=} Ans. 8. What part of an hour is of a week. |