CMClearMathAcademy

Fraction Operations

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Fractions can be simplified by dividing the numerator and denominator by the same common factor. To add or subtract fractions, use a common denominator. To multiply fractions, multiply straight across. To divide by a fraction, multiply by its reciprocal.

What you'll learn

Why it matters: Recipes, measuring cups, music time signatures, and construction lengths all rely on fraction operations. A common denominator is what lets unlike pieces be combined.

Worked example

Problem. Compute 2/3 + 1/6.

  1. Use 6 as a common denominator.
  2. 2/3 becomes 4/6.
  3. 4/6 + 1/6 = 5/6.

Answer: 5/6

Practice problems

1. Which fraction is equivalent to 6/9?

Choices: 2/3 · 3/2 · 1/3 · 6/3

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which fraction is equivalent to 6/9?
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 6 and 9 share a common factor of 3.
  4. 6/9 simplifies to 2/3.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 2/3

2. Simplify 12/16.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Simplify 12/16.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 12 and 16 share a common factor of 4.
  4. 12/16 = 3/4.
  5. Check the result by substituting or estimating: the response should match 3/4 and make sense in the original problem.

Answer: 3/4

3. Compute 1/5 + 2/5.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 1/5 + 2/5.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. The denominators already match.
  4. Add the numerators: 1 + 2 = 3.
  5. Check the result by substituting or estimating: the response should match 3/5 and make sense in the original problem.

Answer: 3/5

4. Compute 3/8 + 1/8.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 3/8 + 1/8.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Add numerators to get 4/8.
  4. Simplify 4/8 to 1/2.
  5. Check the result by substituting or estimating: the response should match 1/2 and make sense in the original problem.

Answer: 1/2

5. Compute 5/6 - 1/3.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 5/6 - 1/3.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Rewrite 1/3 as 2/6.
  4. 5/6 - 2/6 = 3/6.
  5. Simplify 3/6 to 1/2.
  6. Check the result by substituting or estimating: the response should match 1/2 and make sense in the original problem.

Answer: 1/2

Practice this interactively with instant feedback and an AI tutor.

Practice Fraction Operations Take the free placement check

More Pre-Algebra lessons