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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. 8.101 (page 958)

Simplify: $\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{14}{11}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

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 and rewrite the complex fraction as division.

$= \frac{\frac{3 + 4}{6}}{\frac{10 + 1}{12}} = \frac{\frac{7}{6}}{\frac{11}{12}} = \frac{7}{6} 梅 \frac{11}{12}$

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

$= \frac{7}{6} 路 \frac{12}{11} = \frac{14}{11}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{14}{11}$ .

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