Free comparing fractions worksheets

Comparing fractions is where children find out whether they really understand what a fraction is. A child who thinks 1/8 is bigger than 1/4 because 8 is bigger than 4 is reading fractions as two whole numbers. These eight worksheets build the idea in the order teachers use: same denominators first (count the pieces), then same numerators (compare the size of the pieces), then pictures, then a common denominator, and finally the shortcuts that fluent students use: the one-half benchmark, ordering, and the number line. Every sheet has a worked example at the bottom and its answer key on page 2. Denominators stay at 12 or below throughout, so the arithmetic never gets in the way of the reasoning.

What's in this set

1. Same denominator. Sixteen pairs; write <, > or =. Same-size pieces, so more pieces means more.
2. Same numerator. Twelve pairs like 2/5 and 2/8; the bigger denominator means smaller pieces. A pictured example shows why.
3. Compare with pictures. Eight pairs of bars and circles to shade, then circle the one with more shaded.
4. Unlike denominators. Twelve pairs that need a common denominator (12 or less) before comparing, with a box for it.
5. Compare to one half. Twelve fractions to sort as less than, equal to or more than 1/2, the benchmark trick.
6. Order least to greatest. Eight sets of three fractions with related denominators.
7. Fractions on a number line. Four lines (eighths, sixths, tenths, twelfths); place four fractions on each and circle the largest.
8. Word problems. Six pizza, ribbon, book and race problems that ask who has more, with a written explanation.

Comparing sits between the fractions worksheets (naming and shading) and the operations pages (adding, subtracting, multiplying and dividing).

Frequently asked questions

What grade are these comparing fractions worksheets for?

Grades 3 to 5. Sheets 1 to 3 match grade 3 (compare fractions with the same numerator or denominator, 3.NF.A.3d); sheets 4 to 8 match grade 4 (compare with different numerators and denominators using common denominators or benchmarks, 4.NF.A.2). Fifth graders use them as review before fraction operations.

Why keep the denominators at 12 or below?

So that the thinking, not the multiplication, is the hard part. A child who can compare 5/6 and 7/12 correctly has the concept; larger denominators only add arithmetic.

Do the worksheets have answer keys?

Yes, all eight. Page 2 of each PDF shows the signs, the renamed fractions, the shaded pictures with the larger one ringed, and the letters placed on the number lines.

Which method should children learn first?

Same denominator, then same numerator, then common denominators. The one-half benchmark and cross-multiplying are shortcuts for later; if a child cannot explain a comparison with pieces, the shortcut is hiding a gap.

More fractions practice

Start with the fractions worksheets and the equivalent fractions worksheets, which supply the renaming skill used here. Continue with adding and subtracting fractions, mixed numbers and multiplying and dividing fractions. Younger children can compare whole numbers first on the greater than, less than worksheets; the Montessori fraction circles give a hands-on version of the picture comparisons.