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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. 8.107 (page 961)

Simplify: $\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{7}{3}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

02

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is 10. Clear the fractions by multiplying the numerator and denominator by that LCD.

$= \frac{10 路 (\frac{1}{2} + \frac{1}{5})}{10 路 (\frac{1}{10} + \frac{1}{5})} = \frac{10 路 \frac{1}{2} + 10 路 \frac{1}{5}}{10 路 \frac{1}{10} + 10 路 \frac{1}{5}} = \frac{5 + 2}{1 + 2} = \frac{7}{3}$

03

Step 3. Conclusion.

The simplified form of the given expression is $\frac{7}{3}$ .

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