Which Fraction Is Larger? Using Benchmarks and Equivalence
Comparing fractions requires flexible thinking. Same denominator? Compare numerators. Same numerator? Compare denominators. Different? Find common denominators or use benchmarks.
Comparing fractions is not a single procedure — it requires choosing the right strategy based on what the fractions look like. Same denominator? Compare numerators. Same numerator? Compare denominators. Different? Find common denominators or use benchmarks. Children who struggle with comparing fractions often try to use the same strategy for every problem.
These worksheets build comparing skills systematically — starting with the easiest cases (same denominator) and progressing to the hardest (unlike denominators). For students who need equivalent fraction fluency before comparing, see our equivalent fractions worksheets.
Three stages — master simple cases first
Worksheets show fractions with the same denominator (3/8 vs 5/8). The child compares numerators — larger numerator means larger fraction. Spend 3-5 days on this stage.
Worksheets show fractions with the same numerator (3/4 vs 3/8). The child compares denominators — smaller denominator means larger fraction. Spend 3-5 days on this stage.
Worksheets show fractions with different numerators and denominators (3/4 vs 2/3). The child finds common denominators using equivalent fractions, then compares numerators. Spend 7-10 days on this stage.
Teach this decision tree — choose the right strategy
If denominators are the same, the fraction with the larger numerator is larger. Example: 5/8 > 3/8 because 5 > 3.
If numerators are the same, the fraction with the smaller denominator is larger. Example: 3/4 > 3/8 because fourths are larger than eighths.
Find a common denominator using equivalent fractions. Then compare numerators. Example: 3/4 = 9/12, 2/3 = 8/12, so 3/4 > 2/3.
For some children, the gap isn't in practice — it's in the underlying number sense that makes fractions make sense. If your child still thinks 1/8 is larger than 1/4, cannot generate equivalent fractions, or struggles with finding common denominators, worksheets alone won't bridge that gap. Our Number Sense Foundations course (K-2) builds the conceptual groundwork that makes fraction fluency stick. You can also browse all available courses and planners on the resources page.
View Number Sense Foundations — $57Build foundational understanding before comparing
Essential for comparing unlike denominators
The next step after comparing
Apply comparing to real-world scenarios
Full 4th grade math overview
Where comparing fractions is applied
Real questions parents ask about comparing fractions
There are three main strategies: (1) Same denominator — compare numerators (3/8 vs 5/8). (2) Same numerator — compare denominators (3/4 vs 3/8, smaller denominator = larger fraction). (3) Different numerator and denominator — find common denominator using equivalent fractions, or use benchmark fractions (compare each to 1/2, 1, etc.). Teach all three strategies.
This is a reversal of the "same numerator" rule. Children learn that with same numerator, smaller denominator is larger (3/4 > 3/8). Some then incorrectly apply this to same denominator problems. The fix is explicit teaching: "Same denominator — look at the numerator. Larger numerator means larger fraction." Use fraction bars to show that 5/8 covers more area than 3/8.
Benchmark fractions are common reference points like 0, 1/2, and 1. To compare 3/8 and 5/12, ask: "Is each fraction greater than or less than 1/2?" 3/8 is less than 1/2 (since 4/8 = 1/2). 5/12 is also less than 1/2 (since 6/12 = 1/2). That does not help — so find common denominator: 3/8 = 9/24, 5/12 = 10/24, so 5/12 > 3/8. Benchmarks help eliminate obviously unequal comparisons.
Start comparing fractions after your child understands basic fraction concepts (numerator, denominator) and equivalent fractions. Typically this is in 4th grade. Start with same denominator (easiest), then same numerator, then unlike denominators using benchmarks, then unlike denominators using common denominators. Do not rush to unlike denominators until equivalence is solid.
The most common error is comparing only numerators or only denominators. A child might say 3/4 > 3/8 (correct, same numerator) but then also say 5/8 > 3/4 (incorrect, ignoring denominator size). The fix is explicit strategy teaching: "Same denominator? Compare numerators. Same numerator? Compare denominators. Different? Find common denominator." Have your child state the strategy before comparing.
Fraction bars show the size relationship visually. A child can see that 5/8 bar is longer than 3/8 bar (same denominator comparison). They can also see that 3/4 bar is longer than 3/8 bar (same numerator comparison). For unlike denominators, they can overlay bars or use common denominator bars. The visual model prevents the most common comparison errors.
15-20 problems per session is effective. Start with 5-7 same denominator, then 5-7 same numerator, then 5-7 unlike denominators. Spend 2-3 weeks on comparing fractions before moving to addition and subtraction. Most children need this much practice to internalize the different strategies.
Answer keys show the correct comparison symbol (<, >, or =). Encourage your child to check their work by using fraction bars or benchmark fractions. If they made an error, have them draw a visual model to see why the correct symbol is right.
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