Fractions, decimals and percentsGrades 3–4
Comparing fractions worksheets
Each problem shows two fractions with an empty box between them, and the student writes <, > or = in the box. Choose like, unlike or mixed denominators and the largest denominator, then print with an answer key.
- Fresh problems every time
- Answer key on its own page
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On this page
Why comparing is harder than it looks
Whole numbers train children to think that bigger digits mean bigger numbers. Fractions break that habit: 1/8 has a larger denominator than 1/3 and is still the smaller fraction. A comparing sheet is a quick way to find out whether a student has moved from "which digits are bigger" to "how much of the whole is this".
This page is the comparison-only view of the fractions generator. Every problem is one line, two fractions with a box between them. It suits third graders who are comparing fractions with the same numerator or denominator, and fourth graders who compare any two fractions.
Choosing the settings
- Denominators is the main control. Like (the same) gives problems such as 3/7 and 5/7, where only the numerators matter. Unlike (different) is the page default and forces the student to find a strategy. A mix alternates, which is useful for review.
- Largest denominator accepts 4 through 20. At 6 or 8, most fractions are easy to picture. At 12, common denominators start to get larger, and at 20 the sheet becomes a real challenge.
- Number of problems can be anywhere from 8 to 30, and the default of 20 prints in three columns.
- Every fraction on this sheet is a proper fraction, so the mixed-number setting is not offered for comparing.
Because the two fractions are chosen independently, some pairs will be equal, such as 2/3 and 4/6, so the equals sign gets used. That is deliberate, and it is worth pointing out to students who think every answer is < or >.
Worked example: 5/8 and 3/5
Three strategies work. A student should know at least two.
- Common denominator. The smallest number both 8 and 5 divide into is 40. Rename 5/8 as 25/40 (multiply top and bottom by 5) and 3/5 as 24/40 (multiply by 8). 25/40 is larger than 24/40, so 5/8 > 3/5.
- Cross-multiplying. Multiply each numerator by the other fraction's denominator: 5 × 5 = 25 and 3 × 8 = 24. The larger product sits on the side of the larger fraction, so again 5/8 > 3/5.
- Benchmarks. Compare each fraction with 1/2. 5/8 is a little more than half (4/8 would be exactly half), while 3/5 is also more than half, so this strategy cannot decide this pair. That is a useful lesson: benchmarks are fast, but only when the fractions land on opposite sides.
The sheet's printed tip suggests renaming with a common denominator or cross-multiplying, so students always have a method to fall back on.
Reading the answer key
The key fills the box with the correct symbol. When a student misses several, look at what kind of pair they missed.
- Always choosing the larger denominator. The child treated 1/8 as bigger than 1/3. Draw two bars of the same length, one cut into 8 pieces and one into 3, and compare a piece from each.
- Mistakes only on unlike pairs. The comparing idea is fine, but the renaming step is shaky. Practice equivalent fractions before returning.
- Wrong when the numerators match. With 3/4 and 3/7, the child must remember that cutting the whole into more parts makes each part smaller.
- Never writing =. Include equivalent pairs in a quick talk before the next sheet.
What comes next
Once comparing is steady, ordering fractions applies the same skill to four fractions at a time. Students who need practice renaming can try simplifying fractions.