Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 1 - Section 1.3 - The Real Numbers - Exercise Set - Page 42: 50


$-\displaystyle \frac{5}{2} < -\frac{5}{3},$ fill the box with $ < .$

Work Step by Step

On the real number line, the real numbers increase from left to right. The lesser of two real numbers is the one farther to the left on a number line. The greater of two real numbers is the one farther to the right on a number line. The symbols $> $ and $< $ are called inequality symbols. These symbols always point to the lesser of the two real numbers when the inequality is true. --- Writing both numbers with a common denominator, $-\displaystyle \frac{5}{2}=-\frac{5\times 3}{2\times 3}=-\frac{15}{6},\qquad-\frac{5}{3}=-\frac{5\times 2}{3\times 2}=-\frac{10}{6}$ $-15 $ is farther (to the left) from zero than $-10$ is, so $-\displaystyle \frac{15}{6} < -\frac{10}{6},$ $-\displaystyle \frac{5}{2} < -\frac{5}{3},$ fill the box with $ < .$
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