### About Complex Fractions:

A complex fraction contains a fraction in its numerator, denominator, or both. There are two ways to simplify a complex fraction. We can simplify the numerator and denominator separately, then perform the main division. We can also simply multiply the numerator and denominator by the LCD of all fractions.

Test Objectives

- Simplify a complex fraction by taking on the numerator and denominator separately
- Demonstrate the ability to find the LCD for a group of fractions
- Demonstrate the ability to simplify a complex fraction using the LCD method

#1:

Instructions: Simplify each.

a) $$\Large{\frac{\frac{2}{9}- \frac{1}{27}}{\frac{4}{5}- \frac{3}{10}}}$$

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#2:

Instructions: Simplify each.

a) $$\Large{\frac{\frac{5}{6}+ \frac{1}{2}}{\frac{5}{8}+ \frac{3}{4}}}$$

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#3:

Instructions: Simplify each.

a) $$\Large{\frac{\frac{5}{6}- 3}{\frac{2}{5}+ 9 - \frac{1}{3}}}$$

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#4:

Instructions: Simplify each using the LCD method.

a) $$\Large{\frac{\frac{1}{2}+ \frac{3}{8}}{\frac{3}{4}+ \frac{1}{3}}}$$

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#5:

Instructions: Simplify each using the LCD method.

a) $$\Large{\frac{\frac{3}{5}- \frac{1}{3}+ \frac{5}{6}}{\frac{4}{5}+ \frac{1}{5}+ \frac{2}{3}}}$$

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Written Solutions:

#1:

Solutions:

a) $$\frac{10}{27}$$

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#2:

Solutions:

a) $$\frac{32}{33}$$

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#3:

Solutions:

a) $$-\frac{65}{272}$$

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#4:

Solutions:

a) $$\frac{21}{26}$$

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#5:

Solutions:

a) $$\frac{33}{50}$$