Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10: 0134467795
ISBN 13: 978-0-13446-779-5

Chapter 2 - Multiplying and Dividing Fractions - 2.5 Multiplying Fractions - 2.5 Exercises - Page 148: 4


lowest term

Work Step by Step

Let's take a look on an example. $\frac{5}{4} \cdot \frac{2}{5}$. We can see that both fractions share the common factor $5$, one in the denominator and one in the numerator. So can divide $5$ and get as a result $\frac{5}{4} \cdot \frac{2}{5} = \frac{1}{4} \cdot \frac{2}{1}$. Rewriting the nominator of the first fraction $\frac{1}{2 \cdot 2} \cdot \frac{2}{1}$ shows us that both fractions share the common factor $2$ and we can divide by $2$ and get $\frac{1}{2 \cdot 2} \cdot \frac{2}{1} = \frac{1}{1 \cdot 2} \cdot \frac{1}{1} = \frac{1 \cdot 1}{2 \cdot 1} = \frac{1}{2 } $. Because of the short cut by all possible common factors the result is in lowest term.
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