Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - 7-1 Ratios and Proportions - Got It? - Page 434: 4


a. $\frac{a}{13}$ = $\frac{7}{b}$ b. $\frac{a-7}{7}$ = $\frac{13-b}{b}$ c. $\frac{7}{a}$ = $\frac{b}{13}$

Work Step by Step

We are given the proportion $\frac{a}{7}$ = $\frac{13}{b}$ Cross multiply ab=7 x 13 ab = 91 Divide both sides of ab=91 by 13b $\frac{ab}{13b}$ = $\frac{91}{13b}$ Reducing down that leaves you with $\frac{a}{13}$ = $\frac{7}{b}$ b. Start with the initial proportion of $\frac{a}{7}$ = $\frac{13}{b}$ Subtract the denominator from the numerator $\frac{a-7}{7}$ = $\frac{13-b}{b}$ c. Reverse the original proportion $\frac{a}{7}$ = $\frac{13}{b}$ is the same as $\frac{7}{a}$ = $\frac{b}{13}$
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