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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. 291 (page 967)

Simplify
In the following exercises, use either method.
$\frac{\frac{3}{4} 鈭� \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}}$

Short Answer

Expert verified

$\frac{\frac{3}{4} 鈭� \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}} = \frac{13}{24}$

Step by step solution

01

Step 1. Given information

We have been given a complex rational expression $\frac{\frac{3}{4} 鈭� \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}}$ .

We have to simplify it.

02

Step 2. Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.

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

03

Step 3. Simplify the numerator and denominator.

$\frac{\frac{3 鈰� 7}{4 鈰� 7} 鈭� \frac{2 鈰� 4}{7 鈰� 4}}{\frac{1 鈰� 7}{2 鈰� 7} + \frac{5}{14}} = \frac{\frac{21}{28} 鈭� \frac{8}{28}}{\frac{7}{14} + \frac{5}{14}}$

04

Step 4. Simplify the numerator and denominator, again

$\frac{\frac{21}{28} 鈭� \frac{8}{28}}{\frac{7}{14} + \frac{5}{14}} = \frac{\frac{21 - 8}{28}}{\frac{7 + 5}{14}} = \frac{\frac{13}{28}}{\frac{12}{14}}$

05

Step 5. Rewrite the complex rational expression as a division problem. Multiply the first times by the reciprocal of the second.

$\frac{\frac{13}{28}}{\frac{12}{14}} = \frac{13}{28} 脳 \frac{14}{12} = \frac{13}{24}$

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