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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. 8.102 (page 958)

Simplify: $\frac{\frac{3}{4} - \frac{1}{3}}{\frac{1}{8} + \frac{5}{6}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{10}{23}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{3}{4} - \frac{1}{3}}{\frac{1}{8} + \frac{5}{6}}$

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.

$= \frac{\frac{9 - 4}{12}}{\frac{3 + 20}{24}} = \frac{\frac{5}{12}}{\frac{23}{24}} = \frac{5}{12} 梅 \frac{23}{24}$

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

$= \frac{5}{12} 路 \frac{24}{23} = \frac{10}{23}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{10}{23}$ .

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Most popular questions from this chapter

Simplify

In the following exercises, use either method.

$\frac{\frac{3}{4} 鈭� \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}}$

In the following exercises, simplify.

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In the following exercises, use either method.

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Electronics The resistance of a circuit formed by connecting two resistors in parallel is $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .

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