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: 87

Answer

$\dfrac{-71}{150}$

Work Step by Step

Factor each denominator completely to obtain: $15=3(5) \\50=2(25) = 2(5)(5)$ Thus, the least common multiple of the two numbers is: $2(3)(5)(5)=150$ This means that the LCD is also $150$. The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $150$. $\dfrac{1}{15} - \dfrac{27}{50} \\= \dfrac{1\color{blue}{(10)}}{15\color{blue}{(10)}}-\dfrac{27\color{blue}{(3)}}{50\color{blue}{(3)}} \\=\dfrac{10}{150}-\dfrac{81}{150}$ Now that the fractions are similar, subtract the numerators and copy the denominator to obtain: $=\dfrac{10-81}{150} \\=\dfrac{-71}{150}$
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