Comparing fractions by size
In 3rd grade, children learn to tell which of two fractions is greater when they share a denominator (bottom number), like 2/6 and 5/6, or a numerator (top number), like 3/4 and 3/8.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 3rd 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
Which fraction is greater, 1/4 or 3/4?
- They are equal
- 1/4
- 3/4
Why this matters
Knowing which of two fractions is bigger helps your child see fractions as real amounts, not as two numbers stacked up. In 4th grade they compare fractions with different numerators and denominators, and later they use that sense to check whether a fraction answer is reasonable. It is useful right away, too: deciding whether 1/3 or 1/4 of a pan of brownies is the bigger share, or whether a glass is more or less than half full.
Both skills rest on picturing the pieces, so if comparing feels hard, your child can review finding equal fractions, like 1/2 = 2/4.
Where kids can get stuck
- Deciding 3/8 is greater than 3/4 because 8 is larger than 4, forgetting that eighths are smaller pieces.
- Overusing the idea that bigger numbers can mean smaller pieces, and deciding 2/6 is more than 5/6.
- Mixing up the > and < signs, writing 2/3 < 1/3 even after saying out loud that 2/3 is more.
How you can help
- Ask your child which they would rather have, 3/4 of a pizza or 3/8 of the same pizza, while you order dinner. Then ask why, and listen for talk about the size of the slices.
- Fill two identical glasses with water, one about 1/4 full and one about 3/4 full. Ask your child which holds more, and how they could tell from the fractions alone.
- Play a quick “which is more?” game on a walk. Name two fractions with the same top or bottom number, such as 2/8 and 5/8, and ask your child to picture the pieces before answering.
For more, Bobby's Math Club has free practice at your child’s level.
Questions parents ask
What about fractions that share neither number, like 2/3 and 3/4?
Those come in 4th grade. In 3rd grade, the two fractions share a top or bottom number, so your child only has to think about one thing: how big the pieces are, or how many there are. If a pair like 2/3 and 3/4 comes up at home, drawing both on same-size strips is a fine way to see it.
Does it matter if the wholes are different sizes?
Yes. Comparing fractions only works when they are parts of the same whole. Half of a large pizza is more food than half of a small one, even though both are 1/2. In 3rd grade, your child learns to check that the wholes match before comparing. Mealtimes make a natural place to talk about it.
My child knows 1/2 and 2/4 are equal but mixes up which fraction is bigger. What helps?
That’s common. Comparing asks two questions at once: how big are the pieces, and how many are there? Saying the fractions in words helps. “Five eighths” and “three eighths” use the same size of piece, so five of them is more. “One third” and “one sixth” are one piece each, so the bigger piece wins. Drawing two same-size rectangles side by side lets your child see it too.
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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 3.NF.A.3: “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1, recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the 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 3.NF.3)