Add and Subtract Fractions
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What you will learn
- 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 simple: add or subtract the numerators only and keep the denominator the same.
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 is greater than the denominator, write it as a mixed number (e.g., 5/4 = 1 1/4); if they are equal, the fraction is 1 whole (e.g., 3/3 = 1).
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.
Words to know
Like fractions
Fractions that share the same denominator
e.g. 3/8 and 5/8 are like fractions.
Common denominator
A denominator shared by two or more fractions
e.g. 12 is a common denominator for 1/3 and 1/4.
Sum
The answer to an addition problem
e.g. The sum of 3/8 and 2/8 is 5/8.
Difference
The answer to a subtraction problem
e.g. The difference of 7/10 and 3/10 is 4/10.
Simplify
To reduce a fraction to its lowest terms
e.g. Simplify 6/8 to 3/4 by dividing by 2.
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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