FRACTIONS. (Continued from page 226.) 186. TO SUBTRACT COMMON FRACTIONS. RULE. Reduce the fractions if necessary to equivalent fractions having a common denominator, find the difference of their numerators, and write it over the common denominator. (a) Find the sum of the eighteen differences. Fractions. 187. TO SUBTRACT ONE MIXED NUMBER FROM ANOTHER WHEN THE FRACTION IN THE SUBTRAHEND IS GREATER THAN THE FRACTION IN THE MINUend. EXAMPLE. From 583 take 323. Explanation. is greater than 4, therefore we take 1 unit from the 8 units, change it to 24ths, and add it to the 9 24ths. 2 units from 7 (8 − 1) units = 5 units. 3 tens from 5 tens tens. (a) Find the sum of the ten differences. II. Reduce to simplest form 1. 51 +31 – 51. 2. 63-34. 6. 31 +41 – 31 – 23 + 13. (b) Find the sum of the eight results, 1. Observe that by the first operation we obtain are 6 times as many parts as there are in 74, and of the same size as those in 24. 2. Observe that by the second operation we obtain ; that in there are the same number of parts as there are in, and that the parts are 6 times as great as those in 4. NOTE.—The 7 of 74 may be regarded as a dividend; the 24, as a divisor, and itself as a quotient. In 1, we have a dividend 6 times as great as that in, the divisor remaining unchanged. In we have a divisor 1 sixth as great as that in, the dividend remaining unchanged. Multiplying the dividend or dividing the divisor by any number multiplies the quotient by the same number. RULE. To multiply a fraction by an integer, multiply its numerator or divide its denominator by the integer. (a) Find the sum of the twelve products. 7.3 x 8. 9. (b) Find the sum of the twelve products, 1. Observe that by the first operation we obtain ; that in there are 1 third as many parts as there are in §, and that the parts are of the same size as those in §. 6 2. Observe that by the second operation we obtain ; that in ♬ there are the same number of parts as there are in §, and that the parts are 1 third as great as those in . NOTE 1.-The 6 of may be regarded as a dividend; the 7 as a divisor, and the itself as a quotient. In ‡ we have a dividend 1 third as great as that in, the divisor remaining unchanged. In we have a divisor 3 times as great as that in, the dividend remaining unchanged. Dividing the dividend or multiplying the divisor by any number divides the quotient by the same number. RULE. To divide a fraction by an integer, divide its numerator or multiply its denominator by the integer. (a) Find the sum of the nine quotients. (b) Find the sum of the nine quotients. 9. 166. Fractions. 190. TO MULTIPLY BY A FRACTION. $6 multiplied by 3, means, take 3 times $6. $6 multiplied by 2, means, take 2 times $6. $6 multiplied by 2, means, take 2 of $6. $6 x 2 = $15. $6 × 3 = $18. $6 × 2 times $6; or 2 times $6 $6 × 1 = $3. $6 × = $4. $6 multiplied by, means, take of $6. $6 multiplied by 3, means, take of $6. TO THE TEACHER.-Require the pupil to examine the preceding statements until he clearly understands that to multiply by a fraction is to take such part of the multiplicand as is indicated by the fraction. Thus: to multiply 48 by & is to take three fourths of 48; that is, three times 1 fourth of 48. It will thus be clear that multiplication by a fraction involves both multiplication and division. RULE. To multiply by a fraction, divide the multiplicand by the denominator of the fraction and multiply the quotient thus obtained by the numerator of the fraction. Observe that in practice we may, if more convenient, multiply the multiplicand by the numerator of the fraction, and divide the prod uct thus obtained by the denominator. To multiply 12 by ą we may take 3 times 1 fourth of 12 or 1 fourth of 3 times 12, as we choose. |