# 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).