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
- Simplify fractions with common factors
- Add and subtract fractions with common denominators
- Multiply and divide fractions
Worked example
Problem. Compute 2/3 + 1/6.
- Use 6 as a common denominator.
- 2/3 becomes 4/6.
- 4/6 + 1/6 = 5/6.
- Connect the calculation back to Fraction Operations so the method, not just the arithmetic, is clear.
Answer: 5/6
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Which fraction is equivalent to 6/9?
Choices: 2/3 · 3/2 · 1/3 · 6/3
Show solution
- 6 and 9 share a common factor of 3.
- 6/9 simplifies to 2/3.
Answer: 2/3
2. Simplify 12/16.
Show solution
- 12 and 16 share a common factor of 4.
- 12/16 = 3/4.
Answer: 3/4
3. Compute 1/5 + 2/5.
Show solution
- The denominators already match.
- Add the numerators: 1 + 2 = 3.
Answer: 3/5
4. Compute 3/8 + 1/8.
Show solution
- Add numerators to get 4/8.
- Simplify 4/8 to 1/2.
Answer: 1/2
5. Compute 5/6 - 1/3.
Show solution
- Rewrite 1/3 as 2/6.
- 5/6 - 2/6 = 3/6.
- Simplify 3/6 to 1/2.
Answer: 1/2
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