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
- Find common denominators
- Add and subtract unlike fractions
- Simplify fraction answers
Worked example
Problem. Compute 2/3 + 1/4.
- Use 12 as a common denominator.
- 2/3 = 8/12 and 1/4 = 3/12.
- 8/12 + 3/12 = 11/12.
- Connect the calculation back to Fractions with Unlike Denominators so the method, not just the arithmetic, is clear.
Answer: 11/12
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Compute 1/2 + 1/3.
Show solution
- Use 6 as a common denominator.
- 1/2 = 3/6 and 1/3 = 2/6.
- 3/6 + 2/6 = 5/6.
Answer: 5/6
2. Compute 3/4 - 1/2.
Show solution
- Rewrite 1/2 as 2/4.
- 3/4 - 2/4 = 1/4.
Answer: 1/4
3. Compute 1/6 + 1/3.
Show solution
- Rewrite 1/3 as 2/6.
- 1/6 + 2/6 = 3/6 = 1/2.
Answer: 1/2
4. Compute 5/8 - 1/4.
Show solution
- Rewrite 1/4 as 2/8.
- 5/8 - 2/8 = 3/8.
Answer: 3/8
5. Compute 2/5 + 1/10.
Show solution
- Rewrite 2/5 as 4/10.
- 4/10 + 1/10 = 5/10 = 1/2.
Answer: 1/2
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