Home › Lessons › Math › Grade 4 › Comparing Fractions (Grade 4)
Comparing Fractions (Grade 4)
The rule for same and different denominators, four worked examples, an online practice with instant checking and printable worksheets with an answer key.
A fraction's denominator tells you how many equal pieces the whole is cut into, and the numerator tells you how many of those pieces you have. Pieces from different denominators are different sizes, so before you compare two fractions you need to know whether the pieces are the same size or not.
If two fractions have the same denominator, the pieces are the same size, so you only compare the numerators: the fraction with the bigger numerator is bigger. For 4/13 and 8/13 the pieces are both thirteenths, and 8 pieces are more than 4 pieces, so 4/13 < 8/13.
If two fractions have the same numerator, you compare the denominators, but the rule flips: the fraction with the smaller denominator is bigger, because the whole is cut into fewer, bigger pieces. Ninths are bigger pieces than elevenths, so 5/9 > 5/11. The same rule gives 5/11 < 5/8, because eighths are bigger pieces than elevenths.
When the denominators and the numerators are both different, rewrite both fractions with a common denominator first. For 2/5 and 1/3, multiply the denominators to get 15: 2/5 = 6/15 and 1/3 = 5/15. Now the pieces are the same size, fifteenths, and 6 pieces are more than 5 pieces, so 2/5 > 1/3.
A quick way to check your answer is to cross-multiply: multiply the first numerator by the second denominator, and the second numerator by the first denominator, then compare those two products. For 2/5 and 1/3 that is 2 × 3 = 6 and 5 × 1 = 5, and 6 is more than 5, so 2/5 is the bigger fraction, matching the common-denominator method.
Worked examples
59 ☐ 19 = >
210 ☐ 211 = >
25 ☐ 27 = >
Practice: solve 10 problems
Examples with answers
| Problem | Answer |
|---|---|
| 310 ☐ 510 | < |
| 710 ☐ 410 | > |
| 19 ☐ 112 | > |
| 35 ☐ 45 | < |
| 49 ☐ 410 | > |
| 38 ☐ 48 | < |
| 58 ☐ 511 | > |
| 212 ☐ 612 | < |
| 28 ☐ 26 | < |
| 27 ☐ 37 | < |
| 38 ☐ 68 | < |
| 511 ☐ 59 | < |
Common mistakes
4/11 and 4/12 have the same numerator, but 12 cuts the whole into smaller pieces than 11 does, so 4/12 is the smaller fraction: 4/11 > 4/12, not the other way round.
3/8 and 2/3 cannot be compared by just looking at 3 and 2. Using a common denominator of 24, 3/8 = 9/24 and 2/3 = 16/24, so 2/3 is actually bigger: 2/3 > 3/8.
For 5/9 and 5/11 the correct answer is 5/9 > 5/11, because ninths are bigger pieces than elevenths. It is easy to write the sign the wrong way round and put 5/9 < 5/11 instead.
Practice in the game
Each right answer builds a tower that defends the fortress. Free, no sign-up, phone or computer.
For parents: practising at home
Practice 5 to 10 comparisons a day instead of a long worksheet at once. Ask your child to say the rule out loud before writing the sign: same denominator, compare numerators; same numerator, compare denominators and flip the rule. If a comparison feels hard, go back to equivalent fractions and simple multiplication facts, because finding a common denominator depends on both.
Assign comparing fractions to a student in ZnayQuest: they practice at home in the game, and you see every mistake, what they answered and the correct answer, so you know which rule they mix up.
FAQ
How do you compare fractions with different denominators?
Rewrite both fractions with a common denominator, then compare the numerators. The fraction with the bigger numerator is bigger.
How do you compare fractions with the same denominator?
Compare the numerators directly. The fraction with the bigger numerator is bigger, because the pieces are the same size.
Is it free?
Yes. The lesson, the practice and the worksheets are free, with no sign-up.