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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 1: Q 194. (page 53)

Use the Order of Operations to Simplify Fractions.
$\frac{8 路 9 - 7 路 6}{5 路 6 - 9 路 2}$

Short Answer

Expert verified

The value of the given fraction is $\frac{5}{2}$ .

Step by step solution

01

Step 1. Given information

Consider the fraction.

$\frac{8 路 9 - 7 路 6}{5 路 6 - 9 路 2}$

02

Step 2. Simplify the numerator by applying the order of operations.

$\begin{array}{rcl} \frac{8 路 9 - 7 路 6}{5 路 6 - 9 路 2} & = & \frac{72 - 42}{5 路 6 - 9 路 2} \\ = & \frac{30}{5 路 6 - 9 路 2} \end{array}$

03

Step 3. Simplify the denominator by applying the order of operations.

$\begin{array}{rcl} \frac{8 路 9 - 7 路 6}{5 路 6 - 9 路 2} & = & \frac{30}{30 - 18} \\ = & \frac{30}{12} \end{array}$

04

Step 4. Divide the numerator by the denominator and simplify.

$\begin{array}{rcl} \frac{8 路 9 - 7 路 6}{5 路 6 - 9 路 2} & = & \frac{6 路 5}{6 路 2} \\ = & \frac{5}{2} \end{array}$

Hence,the value is $\frac{5}{2}$ .

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