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# Simplifying Complex Fractions

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## Carmela Mariano

on 25 August 2013

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#### Transcript of Simplifying Complex Fractions

Simplifying Complex Fractions
Method 1
Simplify a Complex Fraction by Multiplying by a Common Denominator
The mixed number should be changed to an improper fraction before starting Method 1. Remember that the unseen denominator for 9 is 1. The least common denominator for the ENTIRE problem is 3. Multiply the top and the bottom by 3.
Problem 2:
REMEMBER: a mixed number should be converted to an improper fraction (heavier on top) before simplifying.
REMEMBER: When dividing fractions, invert (flip over) the second fraction and multiply. Reduce the final answer if needed (or reduce as you multiply).
Method 2
Simplify a Complex Fraction by Simplifying the Numerator and Denominator
ex.
Complex fractions are fractions within a fraction.
This fraction is formed of two fractional expressions, one on top of the other.
What Are Complex Fractions?
We Will Be Using 2 Methods
Method 1: Simplify a Complex Fraction by Multiplying by a Common Denominator
Method 2: Simplify a Complex Fraction by Simplifying the Numerator and Denominator
1. Find the least common denominator (LCD) of all fractions appearing within the complex fraction.
2. Multiply both the numerator and the denominator of the complex fraction by the LCD of the complex fraction from step 1.
3. Simplify whenever possible.
Problem 1:
Problem 1:
Problem 2:
Solution:
Solution: The least common denominator for the ENTIRE problem is 8. Multiply the top and the bottom by 8.
Solution:
1. Create one single fraction in the numerator (if necessary).
2. Create one single fraction in the denominator (if necessary).
3. Remember the main fraction line means "divide". Rewrite the fraction using a division symbol .
4. Follow the normal rules for dividing fractions: Invert the the second term (the denominator of the complex fraction) and multiply (by the numerator of the complex fraction).
5. Simplify if needed.
Solution:
Solution: