Fraction operations

Math

Definition

The four basic operations—addition, subtraction, multiplication, and division—performed on fractions. To add or subtract, you need a common denominator; to multiply, multiply straight across; to divide, multiply by the reciprocal.

How It Works

  1. Find a common denominator for addition or subtraction.
  2. Rewrite each fraction with the common denominator.
  3. Add or subtract the numerators while keeping the denominator.
  4. For multiplication, multiply numerators together and denominators together.
  5. For division, flip the second fraction and multiply.
  6. Simplify the result by dividing numerator and denominator by their GCF.

Examples

  • 1/3 + 1/4 = 4/12 + 3/12 = 7/12
  • 2/5 × 3/7 = 6/35
  • 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8
Key Fact

To divide fractions: a/b ÷ c/d = a/b × d/c

Related Terms

Comparing fractions Mixed numbers Order of operations

Study This Concept

Practice fraction operations with free review games in these units:

Pre-Algebra Unit 2: Fractions and Decimals