Comparing Fractions — Which Is Bigger? (Grades 4–5)
To compare two fractions is to decide which is larger (or whether they're equal). The easiest case is when the denominators (bottom numbers) are the same: then you just compare the top numbers, because the pieces are the same size. 3/5 is bigger than 2/5 because three fifth-sized pieces are more than two of them.
Understanding comparing fractions
To compare two fractions is to decide which is larger (or whether they're equal). The easiest case is when the denominators (bottom numbers) are the same: then you just compare the top numbers, because the pieces are the same size. 3/5 is bigger than 2/5 because three fifth-sized pieces are more than two of them.
When the bottoms are different, the pieces are different sizes, so you can't compare top numbers directly. Two reliable moves: (1) rewrite both fractions with a common denominator (same-size pieces), then compare tops; or (2) compare each to a benchmark like 1/2 — e.g. 3/8 is less than 1/2 and 5/8 is more than 1/2, so 5/8 is bigger.
Key Idea
When the bottoms are different, the pieces are different sizes, so you can't compare top numbers directly. Two reliable moves: (1) rewrite both fractions with a common denominator (same-size pieces), then compare tops; or (2) compare each to a benchmark like 1/2 — e.g. 3/8 is less than 1/2 and 5/8 is more than 1/2, so 5/8 is bigger.
Seeing it in action
Worked example
Which is bigger, 3/5 or 2/5?
Same denominator (fifths), so compare tops: 3 > 2. → 3/5 is bigger. (Visual: two equal bars in fifths, 3 shaded vs 2 shaded.)
Worked example 2: unlike denominators
Which is bigger, 2/3 or 3/4?
Common denominator of 3 and 4 is 12. Rewrite: 2/3 = 8/12, 3/4 = 9/12.
Compare tops: 9 > 8. → 3/4 is bigger.
Try a few
Compare 4/7 and 6/7.
same denominator.
Compare 1/2 and 5/8 using a benchmark.
it's more than half.
Compare 1/3 and 2/5.
1/3 = 5/15, 2/5 = 6/15.
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Put the reasoning on paper.
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