Comparing and Ordering Fractions Worksheets for Grades 3 to 6

In Sheet type, pick comparing two fractions with <, > or =, or ordering four from least to greatest, then press Print.

12 problems. Rename one fraction, then compare. Sheet 7P3UL9, with its answer key.

Rename one fraction, then compare

Name Date Score / 12

Write <, > or = in each circle. Rename the fractions with a common denominator when you cannot tell at a glance.

  1. 1.910 12
  2. 2.23 112
  3. 3.612 48
  4. 4.12 14
  5. 5.13 16
  6. 6.910 25
  7. 7.14 58
  8. 8.68 912
  9. 9.15 310
  10. 10.23 512
  11. 11.58 12
  12. 12.15 110

Sheet 7P3UL9 · Made at homeroomtools.com

Answer key. Rename one fraction, then compare

  1. 1.910 > 12 (9/10 > 5/10)
  2. 2.23 > 112 (8/12 > 1/12)
  3. 3.612 = 48 (12/24 = 12/24)
  4. 4.12 > 14 (2/4 > 1/4)
  5. 5.13 > 16 (2/6 > 1/6)
  6. 6.910 > 25 (9/10 > 4/10)
  7. 7.14 < 58 (2/8 < 5/8)
  8. 8.68 = 912 (18/24 = 18/24)
  9. 9.15 < 310 (2/10 < 3/10)
  10. 10.23 > 512 (8/12 > 5/12)
  11. 11.58 > 12 (5/8 > 4/8)
  12. 12.15 > 110 (2/10 > 1/10)

Sheet 7P3UL9 · Made at homeroomtools.com

Next step Add fractions with unlike denominatorsSee the other grade 4 fraction sheets

How it works

Free comparing and ordering fractions worksheets for the method you teach, from 5/12 < 7/12 to four fractions ordered over a common denominator. The first sheet renames one fraction, and its key prints both over the common denominator. Make a new sheet changes the fractions.

Read the full guide

Which grade compares which fractions

Common Core 3.NF.3d compares two fractions that share a numerator or a denominator. Standard 4.NF.2 moves on to unlike pairs by common denominators, common numerators or a benchmark such as 1/2. Texas takes the same steps in 3.3(H) and 4.3(D). Ordering fractions is first numbered in grade 6, in Common Core 6.NS.7 and Texas 6.2(D), so the ordering sheets stretch grade 4.

Pick the shortest method for the pair

For 3/4 and 5/8, rename one fraction: 3/4 = 6/8 > 5/8. For 2/5 and 3/8, matching the numerators is quicker: 6/15 > 6/16, because fifteenths are the bigger pieces. For 3/8 and 2/3 nothing is renamed, since 3/8 < 1/2 < 2/3.

  • Start on Rename one fraction, then compare. In nearly every pair only one fraction changes.
  • Run Less, greater or equal? Pairs with equals before a test. A pupil who never writes = is judging by looks.
  • Order four fractions, like numerators runs backward. When the numerators match, the largest denominator is the smallest fraction.

Questions and answers

How do you put four fractions in order?

Rename all four over one denominator, then order the numerators. 1/2, 2/3, 3/5 and 7/10 become 15/30, 20/30, 18/30 and 21/30, so 1/2 < 3/5 < 2/3 < 7/10. The key prints each set both ways. To leave the key off, clear Answer key.

Why does the bigger denominator make the smaller fraction?

More pieces means smaller pieces. With the numerator fixed at 3, 3/10 < 3/8 < 3/5 < 3/4. The rule holds only when the numerators match: 7/8 > 1/2, although 8 is larger than 2.

Does cross-multiplying work for comparing fractions?

Yes. It is the common denominator method with the denominator left unwritten. For 5/8 and 7/11, 5 × 11 = 55 and 8 × 7 = 56, so 5/8 < 7/11. Teach the renaming first, so pupils know why it works.

All 12 sheet types

Same denominator or same numerator 3

  • Like denominators to twelfths 5/12 < 7/12. The pieces are the same size, so the numerators decide: 5 pieces are fewer than 7. A warm-up that adds fifths, tenths and twelfths to the grade 3 denominators.
  • Like numerators to twelfths 5/6 > 5/12. Both fractions take 5 pieces, and sixths are bigger pieces than twelfths, so the smaller denominator wins. Pupils who pick 5/12 are still reading 12 as a whole number.
  • Order four fractions, like numerators 3/10 < 3/8 < 3/5 < 3/4. With the numerator fixed at 3, the largest denominator is the smallest fraction, so the denominators run backward: 10, 8, 5, 4.
Show all 12 sheet types (9 more)

Common denominators and other methods 4

  • Least common denominator pairs 5/6 = 20/24 < 21/24 = 7/8. Sixths and eighths meet at 24, the least common multiple. 6 × 8 = 48 also works, but the numerators come out twice as large. Every pair shares a factor, as 6 and 8 share 2.
  • Less, greater or equal? Pairs with equals 4/6 = 10/15, because both simplify to 2/3, while 4/6 > 9/15. About a third of the pairs on this sheet are equal, so nobody can guess from which fraction looks bigger.
  • Rename both fractions, then compare 2/3 = 10/15 > 9/15 = 3/5. The denominators 3 and 5 share no factor, so the common denominator is their product and both fractions change.
  • Rename one fraction, then compare 3/4 = 6/8 > 5/8. In nearly every pair one denominator is a multiple of the other, so only one fraction changes; an equal pair such as 2/4 and 5/10 can need both renamed. This is the first step past grade 3: the numerators differ and so do the denominators.

Ordering four or five fractions 3

  • Order four fractions, related denominators 1/3 < 5/12 < 1/2 < 3/4. Every denominator divides 12, so the set becomes 4/12, 5/12, 6/12 and 9/12 and the numerators give the order. Other sets settle in eighths or in tenths.
  • Order four fractions, unlike denominators 1/2, 2/3, 3/5 and 7/10 become 15/30, 20/30, 18/30 and 21/30, so 1/2 < 3/5 < 2/3 < 7/10. Eight sets to a page, least to greatest, with a line under each set for the renamed fractions.
  • Order mixed numbers and improper fractions 1 1/2 < 13/8 < 7/4 < 1 7/8. In eighths the four numbers are 12/8, 13/8, 14/8 and 15/8. Pupils choose one form, improper or mixed, and put every number into it before ordering.

Mixed numbers, decimals and negatives 2

  • Compare mixed numbers 2 3/4 = 2 6/8 > 2 5/8. When the whole numbers match, the fraction parts decide. When they differ, as in 3 1/5 > 2 9/10, the whole numbers settle it and no renaming is needed.
  • Improper fraction or mixed number, which is greater? 11/4 = 2 3/4 = 2 6/8 > 2 5/8. Change the improper fraction to a mixed number first, then compare as usual. The two numbers in each pair are never more than 1 apart.

How this list was compiled: Own list of sheet types. Every worked example was checked with exact fraction arithmetic. The comparison methods (same denominator, same numerator, common denominators, comparing ad with bc) were checked against https://en.wikipedia.org/wiki/Fraction. Standards were read in the full texts in September 2026: Common Core State Standards for Mathematics, https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf (3.NF.3d, 4.NF.2, 4.NF.6, 4.NF.7, 6.NS.6c, 6.NS.7, and the grade 3 and grade 4 denominator footnotes); Texas Essential Knowledge and Skills, 19 TAC chapter 111, https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf (3.3(H), 4.2(F), 4.3(D), 4.3(F), 4.3(G)) and https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111b.pdf (6.2(C), 6.2(D)). Licence: own work

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