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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 193. (page 53)

Use the Order of Operations to Simplify Fractions.
$\frac{5 路 6 - 3 路 4}{4 路 5 - 2 路 3}$

Short Answer

Expert verified

The value of the given fraction is $\frac{9}{7}$ .

Step by step solution

01

Step 1. Given information

Consider the fraction.

$\frac{5 路 6 - 3 路 4}{4 路 5 - 2 路 3}$

02

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

$\begin{array}{rcl} \frac{5 路 6 - 3 路 4}{4 路 5 - 2 路 3} & = & \frac{30 - 12}{4 路 5 - 2 路 3} \\ = & \frac{18}{4 路 5 - 2 路 3} \end{array}$

03

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

$\begin{array}{rcl} \frac{5 路 6 - 3 路 4}{4 路 5 - 2 路 3} & = & \frac{18}{20 - 6} \\ = & \frac{18}{14} \end{array}$

04

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

$\begin{array}{rcl} \frac{5 路 6 - 3 路 4}{4 路 5 - 2 路 3} & = & \frac{2 路 9}{2 路 7} \\ = & \frac{9}{7} \end{array}$

Hence, the value is $\frac{9}{7}$ .

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