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Simplifying Complex Fractions
Fractions
Complex Fractions
Fractions, Ratios, Money, Decimals and Percent
Fraction Arithmetic
Fractions Worksheet
Teaching Outline for Fractions
Fractions Section 5
Fractions In Action
Complex Fractions
Fabulous Fractions
Reducing Fractions and Improper Fractions
Fraction Competency Packet
Fractions
LESSON: FRACTIONS
ADDING FRACTIONS
Complex Fractions
Fractions, Ratios, Money, Decimals and Percent
Converting Fractions to Decimals and the Order of Operations
Adding and Subtracting Fractions
Complex Fractions
Equivalent Fractions
Review of Fractions
Adding Fractions
Fractions
Equivalent Fractions
Questions About Fractions
Adding Fractions & Mixed Numbers
Adding fractions using the Least Common Denominator
Introduction to fractions
EQUIVALENT FRACTIONS
MULTIPLY TWO OR MORE FRACTIONS
Simplifying Fractions
Multiplying and Dividing Fractions
ADDITION OF FRACTIONS
Multiplying Fractions
Multiplying and Dividing Fractions
Introduction to Fractions
Simplifying Fractions by Multiplying by the LCD

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Complex Fractions

1 Complex Fractions

Goal: Simplify complex fractions. Up to now, we are only able to manipulate
simple fractions, meaning the numerator and the denominator are all polyno-
mials or numbers.

Definition A complex fraction is a fraction where the numerator, denominator,
or both contain a fraction.

Example

1.1 Method I

To Simplify a Complex Fraction by Multiplying by a Common 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.

Example Simplify the complex fraction

1.2 Method II

To Simplify a Complex Fraction by Simplifying the Numerator and Denominator

• 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 nu-
merator of the complex fraction).

• 5. Simplify if needed.

Example

Remark Complex Fractions are EASY to simplify if you remember that the
main fraction bar means DIVIDE.

To manipulate complex fractions, just convert them to simple fractions.
Then use the rules for simple fractions.

Example
Simplify and subtract:

Example Simplify and add:

2 Homework # 3

Problem set 4.4, 16-36(odd numbers), 40-60(even numbers).