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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 260 (page 966)

In the following exercises, simplify.
$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{25}{26}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

02

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B} 梅 \frac{C}{D} = \frac{A}{B} 路 \frac{D}{C}$

03

Step 3. Rewrite the expression and then simplify.

Simplify the numerator and denominator.

$= \frac{\frac{2 + 3}{4}}{\frac{6 + 7}{10}} = \frac{\frac{5}{4}}{\frac{13}{10}}$

Rewrite as the product of first times the reciprocal of the second.

$= \frac{5}{4} 路 \frac{10}{13} = \frac{5 路 10}{4 路 13} = \frac{25}{26}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{25}{26}$ .

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