Parent guide · 6 min read
Comparing fractions for kids: which is bigger, 3/4 or 5/8?
Asking which of two fractions is larger sounds simple, but it is where many children first discover that bigger digits do not mean a bigger number. 1/8 looks bigger than 1/5 if you only look at the 8, and a child who has memorised one method, such as "make the bottoms the same", may use it on every question, even when a ten-second check would do. This guide gives four ways to compare fractions, when each is quickest, and worked examples a parent can verify.
Try this tonight
4 things you can do at home
Draw two strips the same length
Cut two paper strips of equal length. Fold one into 4 equal parts and one into 8. Shade 3 parts of the first and 5 of the second and lay them side by side. Seeing 3/4 reach further than 5/8 makes the later rules feel true rather than arbitrary. The strips must be the same length, or the picture misleads.
Ask "same top or same bottom?" first
Before any method, look at the two fractions. If the denominators match, compare the numerators. If the numerators match, the one with the smaller denominator is larger. A child who checks this first avoids long working on easy questions.
Try the half test
Ask whether each fraction is less than, equal to or more than 1/2. A fraction is less than a half when its numerator is under half the denominator. 3/8 is under 4/8, so less than a half, while 5/9 is over 4.5/9, so more. If one is above half and the other below, you are done.
Make a common denominator when the others fail
Pick a number both denominators divide into, such as 12 for 3, 4 and 6. Rewrite each fraction with that denominator by multiplying top and bottom by the same number, then compare numerators. Check the answer once with the strips.
Why bigger digits can mean a smaller fraction
The denominator says how many equal pieces the whole is cut into. The more pieces, the smaller each one is, so eighths are smaller than fifths. 1/8 is one small piece and 1/5 is one bigger piece, which is why 1/5 is the larger fraction even though 8 is the larger digit.
The same idea gives the same-numerator rule. 3/5 and 3/8 both mean "three pieces", but fifths are bigger than eighths, so 3/5 is bigger. Children who can say this in their own words, "same number of pieces, so look at the size of the piece", rarely mix it up.
A worked example: common denominators
Which is larger, 3/4 or 5/8? The denominators 4 and 8 are linked, because 4 × 2 = 8. Multiply the top and bottom of 3/4 by 2 to get 6/8. Now compare 6/8 with 5/8: the numerator 6 is larger, so 3/4 is bigger.
Putting three fractions in order uses the same step. For 2/3, 3/4 and 5/6, use 12, which 3, 4 and 6 all divide into. That gives 8/12, 9/12 and 10/12, so the order from smallest to largest is 2/3, 3/4, 5/6. A common denominator works every time, even if it is not always the quickest.
Shortcuts: the half test and the missing piece
Compare 3/8 with 5/9. Half of 8 is 4 and 3 is less than 4, so 3/8 is under a half. Half of 9 is 4.5 and 5 is more than 4.5, so 5/9 is over a half. That settles it: 5/9 is larger, with no common denominator needed.
Compare 7/8 with 5/6. Each is one piece short of a whole: 7/8 is missing 1/8 and 5/6 is missing 1/6. The missing piece 1/8 is smaller than 1/6, so 7/8 is closer to a whole and is larger. Written as decimals, 0.875 is more than about 0.833, so the answer checks out.
What about cross-multiplying?
To compare 4/7 with 3/5, multiply each top by the other fraction’s bottom: 4 × 5 = 20 and 3 × 7 = 21. The side with the larger product is the larger fraction, so 3/5 is bigger. As decimals this is about 0.571 against 0.6, which agrees.
The method works, but it hides the meaning, and a child can easily put the products on the wrong sides. It is a good last shortcut once the picture and the common-denominator method are secure, and a poor first one.
Signs it’s time for outside help
When home help has done what it can
- Says 1/8 is bigger than 1/5 because 8 is bigger than 5.
- Compares numerators only, or denominators only, whatever the question.
- Uses a common denominator for every question, even 3/4 against 1/4.
- Rewrites one fraction but forgets to change the other to match.
- Multiplies only the bottom number when making an equivalent fraction.
- Can follow a method but cannot say which of two fractions is closer to a half.
Questions parents ask
FAQ
What grade do children learn to compare fractions?
In the US Common Core, comparing fractions with the same numerator or denominator starts in Grade 3, and comparing fractions with different denominators is a Grade 4 standard (4.NF.A.2). The Australian Curriculum covers comparing and ordering fractions in the upper primary years.
How do you compare fractions with different denominators?
Rewrite both with a common denominator and compare the numerators. For 2/3 and 3/5, use 15: 10/15 and 9/15, so 2/3 is larger. Benchmarks such as one half are quicker when the fractions sit on opposite sides of it.
Is a larger denominator a larger fraction?
Not when the numerators are the same. With the same numerator, a larger denominator means smaller pieces, so 3/8 is less than 3/5. The denominator on its own does not tell you the size of a fraction.
Is cross-multiplying the same as finding a common denominator?
It is a shortcut for it. The two products are the numerators you would get after rewriting both fractions with the product of the denominators as the bottom number, so the comparison is the same.
How can I practise at home?
Fold paper strips, or use a pizza or a chocolate bar cut into equal parts. Ask which of two shares is larger before working it out, then check on paper.
Further reading
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