Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 285: 88



Work Step by Step

Factor each denominator completely to obtain: $15=3(5) \\6=2(3)$ Thus, the least common multiple of the two numbers is: $2(3)(5)=30$ This means that the LCD is also $30$. The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $30$. $\dfrac{4}{15} - \dfrac{1}{6} \\= \dfrac{4\color{blue}{(2)}}{15\color{blue}{(2)}}-\dfrac{1\color{blue}{(5)}}{6\color{blue}{(5)}} \\=\dfrac{8}{30}-\dfrac{5}{30}$ Now that the fractions are similar, subtract the numerators and copy the denominator to obtain: $=\dfrac{8-5}{30} \\=\dfrac{3}{30} \\=\dfrac{1}{10}$
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