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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. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

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.
  4. Connect the calculation back to Fraction Operations so the method, not just the arithmetic, is clear.

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

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