Comparing Fractions
Grade 3 · Math · Study Guide
Learn how to tell which fraction is larger or smaller using different strategies.
Comparing fractions means figuring out which fraction is bigger, smaller, or if they are equal. There are a few clever tricks to do this without always drawing pictures.
The same denominator trick: If two fractions share the same bottom number, the one with the bigger top number is larger. So 3/5 > 2/5 because both are cut into 5 pieces but 3/5 has more pieces.
The same numerator trick: If two fractions share the same top number, the one with the smaller bottom number is larger. Sounds weird, but think about it — 1/2 of a pizza is a bigger slice than 1/8 of the same pizza. More cuts = smaller pieces. So 1/2 > 1/4 > 1/8.
Benchmark fractions: You can compare fractions to familiar benchmarks like 0, 1/2, and 1. Is the fraction less than 1/2, equal to 1/2, or greater than 1/2? A fraction is equal to 1/2 when its numerator is exactly half its denominator (like 3/6 or 4/8). If the numerator is less than half the denominator, the fraction is less than 1/2.
| Fraction A | Fraction B | Which is Greater? |
|---|---|---|
| 3/8 | 5/8 | 5/8 (more pieces) |
| 1/6 | 4/6 | 4/6 (more pieces) |
| 7/10 | 3/10 | 7/10 (more pieces) |
Key terms
- Greater than (>)
- A symbol meaning the number on the left is larger.
- Less than (<)
- A symbol meaning the number on the left is smaller.
- Equal to (=)
- Both fractions have the same value.
- Benchmark fraction
- A common fraction used as a reference point, like 0, 1/2, and 1.
- Common denominator
- The same bottom number shared by two or more fractions.
Flashcards
- Same denominator rule
- When denominators match, the fraction with the larger numerator is greater.
- Same numerator rule
- When numerators match, the fraction with the smaller denominator is greater.
- Is 1/2 > 1/4?
- Yes — halves are bigger pieces than fourths.
- Benchmark: 1/2
- A fraction equals 1/2 when the numerator is exactly half the denominator.
- 5/8 compared to 1/2
- 5/8 > 1/2 because 5 is more than half of 8 (which is 4).
- > symbol
- Greater than — the open side faces the bigger number.
Practice questions
Which is greater: 3/4 or 1/4?
- 3/4
- 1/4
- They are equal
- Cannot tell
Show answer
Answer: 3/4
Same denominator (4), so 3 pieces > 1 piece. 3/4 > 1/4.
1/3 is greater than 1/5 because thirds are larger pieces than fifths.
Show answer
Answer: True
Both have numerator 1. Smaller denominator means bigger pieces: thirds are larger than fifths.
Using >, <, or =: 5/8 ___ 3/8
Show answer
Answer: >
Same denominator (8): 5 pieces > 3 pieces, so 5/8 > 3/8.
Which fraction is greater than 1/2?
- 2/6
- 3/8
- 5/8
- 1/4
Show answer
Answer: 5/8
5/8: numerator 5 > half of 8 (=4), so 5/8 > 1/2. The others are all less than 1/2.
List these fractions from least to greatest: 2/4, 1/4, 3/4
- 1/4, 2/4, 3/4
- 3/4, 2/4, 1/4
- 2/4, 1/4, 3/4
- 1/4, 3/4, 2/4
Show answer
Answer: 1/4, 2/4, 3/4
Same denominator: 1 < 2 < 3, so 1/4 < 2/4 < 3/4.
Fun facts
- The symbols < and > were invented by English mathematician Thomas Harriot in 1631. He wanted symbols that clearly showed which side was 'open' (bigger) and which was pointed (smaller).
- Fractions are used constantly in cooking — a recipe might call for 3/4 cup of flour and you need to know if that's more or less than 1/2 cup!
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