Module Four:

Fractions

This module reviews algebraic fractions. We will begin by reducing fractions. This will be followed by reviewing the four basic operations: multiplication, division, addition and subtraction.

Example 1.

Reduce to lowest terms:

Step 1.

Step 2.

Step 3. 2a

Example 2.

Reduce to lowest terms:

Method A.

Step 1.

Step 2.

Step 3.

This problem can also be solved using an exponent rule as shown in Method B.

Method B.

Reduce to lowest terms:

Rule:

Step 1.

Step 2.

Step 3.

Example 3.

Reduce to lowest terms:

Step 1.

Step 2.

Step 3. 2 + a

Example 4.

Reduce to lowest terms:

Step 1.

Step 2.

Step 3.

Example 5.

Multiply:

Step 1.

Step 2.

Step 3.

Example 6.

Divide:

Step 1.

Step 2.

Step 3.

Step 4. 4pt²

Example 7.

Add:

Use the lowest common denominator to add and subtract fractions.

Step 1. The lowest common denominator is 24.

Step 2. and

Step 3.

Step 4.

Example 8.

Perform the indicated operations.

Step 1. The lowest common denominator is 20y.

Step 2.

Step 3.

Step 4.

Step 5.

Example 9.

Add:

Step 1. The lowest common denominator is b(b + 3)

Step 2. and

Step 3.

Step 4.

The last example in this module combines several operations. The problem is given in complex fraction form.

Example 10.

Simplify:

Step 1.

Step 2. Simplify within parentheses first.

Step 3.

Step 4.

Practice problems:

Solution to problem 1:

Solution to problem 2:

= – 5y⁸ + 4y⁷ – 9y

Solution to problem 3:

Solution to problem 4:

Solution to problem 5:

Solution to problem 6:

Solution to problem 8: