01:640:107 Lecture Notes - Lecture 14: Rational Number, Natural Number, Commutative Property
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9 Dec 2016
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We consider one more example problem involving rational number operations that we did not do last time. In this problem, an initial quantity of 13/4 yards is to be used to make socks which take 5/12 yard apiece. This problem, of subdivision of a given amount into (smaller) quantities of equal size is a motivation for the division of fractions - division seen as repeated subtraction, as in the initial motivation for the division of whole numbers. The first natural steps are to convert the expressions into the common subunit of twelfths, and to rewrite the mixed number as an improper fraction. Thus we have 13/4 = 7/4 = 21/12, and the question is how many whole groupings of 5/12 are contained in this amount. The answer could be found by repeated subtraction of 5/12 - the answer would be 4 (with the quantity being socks).