We reduce to a common denominator. 3 28 This gives us 2123 28 3 28 and 1718. 1 is larger than so (since 2 + 2% = 33) we write the example as follows: NOTE. If the fraction of the minuend exceeds that of the subtrahend, there is of course no necessity of increasing it. 1. 27. RULES. 1. Reduce the fractions to a common denominator. 2. Subtract the numerator of the subtrahend from that of the minuend and place the result over the common denominator. 3. If there are mixed numbers subtract the whole numbers and fractions separately, placing the fractional remainder after that of the whole number. If the fraction of the minuend is less than that of the subtrahend increase it by writing one of the units of the whole number in fractional form with it as an improper fraction. Do the same if there is no fraction in the minuend. (10) A flag staff 50% feet high was broken off in a storm, so that it measured 437 feet. How much was broken off? Ans. 617 feet. (11) A box and its contents weighed 75 pounds. The box alone weighed 35 pounds. What was the contents? weight of its Ans. 71 lbs. MULTIPLICATION OF FRACTIONS. 28. It is not necessary to reduce fractions to a common denominator when we multiply them. 29. We know from paragraph 4 that when we increase the numerator we increase the fraction, and that when we decrease the denominator we increase the fraction. Now we can multiply fractions in two ways. Usually we multiply the numerator. The same effect is produced by dividing the denominator by the same number. Let us take an example of this: (by multiplying numerator and reducing to mixed number). (by dividing denominator by 4 and reducing to mixed number). 30. If we say "of" in multiplication of fractions, we mean times (X) just as we say three-quarters of a dollar. We could say three-fourths of a dollar just as we could say three-fourths of anything else. This is the same as multiplying by three-fourths, as 1 × 3=3, and if the 1 were one dollar, the three-fourths would represent three quarters of a dollar. 31. If we multiply one fraction by another, we multiply the numerator or divide the denominator of the multiplicand by the numerator of the multiplier and perform the reverse operation with the denominator of the multiplier. This will be seen by the following examples: Multiply by . The 4 of the multiplier makes the product larger. We must, therefore, either multiply the numerator or divide the denominator of the multiplicand by it. The 7 of the multiplier makes the product smaller. We must, therefore, either multiply the denomin ator or divide the numerator by it. Let us in this case take the usual course, and multiply the two numerators, and multiply also the two denominators. 5 4 5 X 4 20 5 = 8 7 8 X 7 56 14 We may solve the problem by cancellation, as follows: 32. In multiplying several fractions together it is the easiest method to use cancellation. The 11 in the denominator cancels with the 22 of the numerator leaving 2 in the numerator. The 9 of the numerator and 18 of the denominator cancel, leaving 2 in the denominator. The 2 over the 22, and the 2 under the 18 cancel. Multiplying the remaining figures of the numerator we get 3. Those of the denominator give 70. Hence our result is 70' 33. If we wish to get the product of mixed numbers, we ordinarily change them to improper fractions and multiply. For example. Multiply 22 by 51. Writing these as improper fractions we have 16 and 21. We obtain this by precisely the same process as in the preceding examples. 34. If we have an integer and mixed number we multiply them as they stand. 17/3/ 6 In detail 173 1038 = 1031 102 +12: =102+18=1038 = 1031 35. RULES. 1. duct of denominator. Divide product of the numerator by proIt is best first to cancel out all factors com mon to both numerator and denominator. 2. In multiplying mixed numbers first reduce them to improper fractions. 3. In multiplying a mixed number and an integer, first multiply fraction of mixed number by the integer (multiplier), reducing it, if it is an improper fraction, to a mixed number. Then multiply the integer of the mixed number by the integer. Add these two products. |
