By Marine Corps Institute (U.S.); Marine Barracks (Washington, D.C.)
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Additional info for Math for Marines
Sample text
Multiplying a fraction by a fraction (fig 2-3). In this operation you are interested in finding part of a part. The mechanics of the process are the same as the two already discussed except that the denominators are multiplied too. Symbolically stated, for any numbers a, b, c, and d (except when b and d 0), a x c = ac b d bd Find of 3 of an acre. - 4 5 3 x 3= 4 5 1 acre 3 acre 5 Fig 2-3. 1 acre 5 A fraction times a fraction. 2-12 IF 4~~~ 20 acre 9 _ 4 Fig 2-3. _ ~~~~20 2=0 of 1 acre 3 5 A fraction times a fraction--cont'd.
_ ~~~~20 2=0 of 1 acre 3 5 A fraction times a fraction--cont'd. d. Cancellation. Earlier in this lesson, the term cancellation was used to indicate reducing to lowest terms. Many times the proper use of canceling when multiplying fractions will enable you to work with smaller numbers and find answers more quickly. Look at the example worked first without canceling and then with canceling: - x 18 18 6 = ? 20 x 6 20 48 360 (This must now be reduced) 48 - 24 = 2 360 + 24 = 15 2 1 & x 6 = 2 0 -2-G 15 3 5 Note: (Divide 8 & 20 by 4 and then divide 6 & 18 by 6) You may cancel the numerator of one fraction with the denominator of another when reducing the individual fraction.
Here, as in the other discussions, the purpose is not to teach you an operation, but to give you some insight into why the decimal point is moved, or not moved, in dividing decimals. You learned earlier in this lesson that multiplication of a decimal by a power of ten has the effect of moving the decimal to the right. This in effect is what is done in division of decimals. If the divisor can be transformed into a whole number, the division can be accomplished in the same manner as division of integers.