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Fractions with Unlike Denominators

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 added or subtracted only when the pieces are the same size. A common denominator rewrites fractions with matching-sized pieces. After adding or subtracting the numerators, simplify when possible. 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: Splitting a recipe between two cooks, combining gas-tank fill levels, and merging time entries to the nearest quarter-hour all need unlike denominators rewritten with a common one.

Worked example

Problem. Compute 2/3 + 1/4.

  1. Use 12 as a common denominator.
  2. 2/3 = 8/12 and 1/4 = 3/12.
  3. 8/12 + 3/12 = 11/12.
  4. Connect the calculation back to Fractions with Unlike Denominators so the method, not just the arithmetic, is clear.

Answer: 11/12

Practice problems

1. Compute 1/2 + 1/3.

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

Answer: 5/6

2. Compute 3/4 - 1/2.

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

Answer: 1/4

3. Compute 1/6 + 1/3.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 1/6 + 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. 1/6 + 2/6 = 3/6 = 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

4. Compute 5/8 - 1/4.

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

Answer: 3/8

5. Compute 2/5 + 1/10.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 2/5 + 1/10.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Rewrite 2/5 as 4/10.
  4. 4/10 + 1/10 = 5/10 = 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

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