Add and Subtract Fractions
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Learning Objectives
- 1Add fractions with the same denominator
- 2Subtract fractions with the same denominator
- 3Simplify fraction answers to lowest terms
- 4Solve word problems involving addition and subtraction of fractions
Mini Lesson
When two fractions have the same denominator, adding or subtracting them is straightforward: operate on the numerators only and keep the denominator unchanged.
The Same-Denominator Rule
- Same denominator: add or subtract only the numerators — keep the denominator the same.
- 2/5 + 1/5 = 3/5 (add tops: 2 + 1 = 3; keep bottom: 5).
- 7/8 - 3/8 = 4/8 = 1/2 (subtract tops: 7 - 3 = 4; simplify: 4/8 = 1/2).
- Never add denominators: 2/5 + 1/5 does NOT equal 3/10.
Simplifying the Result
- Divide both numerator and denominator by their greatest common factor (GCF).
- 4/8: GCF of 4 and 8 is 4 — divide both by 4 to get 1/2.
- If the numerator equals or exceeds the denominator, convert to a mixed number (e.g., 5/4 = 1 and 1/4).
Common mistake: do NOT add the denominators. 1/4 + 1/4 = 2/4 (not 2/8). The denominator tells you the piece size — it does not change when you combine pieces.
Tip: when you see same-sized pieces (same denominator), just count how many pieces you are adding or removing — the piece size (denominator) never changes.
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