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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.

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.

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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