Comparing fractions like 2/3 and 5/6
In 4th grade, children learn to compare fractions with different denominators, like 2/3 and 5/6, using a common denominator or numerator, or comparing to 1/2; and to record and explain the result with >, =, or <.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Kai drinks 1/2 of his bottle of juice. Zoe drinks 1/2 of her bottle of juice. Zoe drinks more juice than Kai. How can that be?
- 1/2 of a bottle is always the same amount
- Zoe's bottle is bigger than Kai's
- Zoe's bottle is smaller than Kai's
Why this matters
A feel for which fraction is larger is what lets your child notice when an answer is unreasonable. It matters in everyday choices too, like whether 2/3 of a cup or 3/4 of a cup is more. Next year it supports adding fractions with different denominators, and it is closely tied to comparing decimals and, later, percents.
Where kids can get stuck
- Thinking bigger numbers mean a bigger fraction, so 3/10 seems greater than 2/3.
- Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4.
- Changing only the bottom number to get a common denominator, rewriting 2/3 as 2/6 to compare with 5/6.
How you can help
- Cut two equal sandwiches, one into thirds and one into sixths. Ask your child whether 2 of the thirds or 5 of the sixths is more food, then line the pieces up to check.
- Write two fractions on a napkin, such as 3/4 and 5/8, with a space between them. Have your child fill in >, =, or <, then prove it with a quick drawing of two bars the same length.
- Compare scores from a game, like making 3 out of 5 shots against 5 out of 8. Have your child decide which is more than half and which is the better result.
If it’s helpful, you can sign up for free, adaptive practice in Bobby's Math Club.
Questions parents ask
Why is my child learning to compare fractions this way?
Teachers show several strategies, such as common denominators, common numerators, and comparing to 1/2, because each one makes your child think about how big a fraction really is. A child who only cross-multiplies may get answers without understanding them. Choosing a strategy that fits the numbers, like noticing that 3/8 is less than half and 4/7 is more, builds a lasting sense of fraction size.
Why does a bigger denominator mean a smaller piece?
The denominator tells how many equal pieces make one whole. The more pieces you cut something into, the smaller each piece is. One slice of a pizza cut into 8 is smaller than one slice of the same pizza cut into 4. So 1/8 is less than 1/4. Folding paper strips into different numbers of pieces is a good way for your child to see this.
What does it mean that the fractions must refer to the same whole?
A fraction only describes a part of something. Half of a large pizza is more food than half of a small pizza, even though both are 1/2. When your child compares 2/3 and 5/6, the comparison is only fair if both fractions are of the same size whole. Teachers point this out so children understand that fractions always describe part of a particular whole.
Make learning math fun
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- Free, unlimited practice for every child in your family
- A few minutes a day, at just the right level
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 4.NF.A.2: “Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NF.2)