Tutorial · 5 min read

0% read

How to compare fractions — step by step (with a worked example)

Q: How do I compare 2/3 and 3/5?

Cross-multiply: 2 · 5 = 10 and 3 · 3 = 9. Since 10 > 9, you get 2/3 > 3/5. Checked in decimals: 0.667 > 0.6.

Q: Which is bigger, 3/8 or 1/2?

Work out 3 · 2 = 6 and 1 · 8 = 8. Since 6 < 8, 3/8 is smaller than 1/2. So the larger numerator alone does not decide it.

Q: What is the cross-multiplication method?

You multiply each fraction's numerator by the other's denominator and compare the two products. It replaces finding a common denominator and gives the same answer faster.

Q: When are two fractions equal?

When the cross-products are equal. For 1/2 and 2/4 you get 1 · 4 = 4 = 2 · 2, so the two fractions are the same size.

Q: How do I compare fractions with the same denominator?

Then only the numerator decides: 3/7 < 5/7 because 3 < 5. In that case you do not need to cross-multiply at all.

Q: Can I use a common denominator instead?

Yes. Rewrite both fractions over the least common multiple of the denominators and compare the numerators. The result is the same as with cross multiplication.

Which of two fractions is bigger? When the denominators differ, cross multiplication does the job: for a/b and c/d you compare a · d with c · b. Worked example: 2/3 and 3/5 → 2/3 > 3/5. Suitable for fractions work from Grade 5–6 onward.

By Valerij Hofmann · Fullstack Developer

Updated May 29, 2026Beginner

Quick answer

To compare two fractions, cross-multiply: for 2/3 and 3/5, work out 2 · 5 = 10 versus 3 · 3 = 9. Since 10 > 9, you get 2/3 > 3/5. The larger cross-product belongs to the larger fraction.

At a glance

Summary of this tutorial
Example	2/3 ? 3/5
Method	Cross multiplication
Steps	4
Cross-products	2 · 5 = 10 vs. 3 · 3 = 9
Result	2/3 > 3/5
Grade level	Grade 6 (ages 11–12)

Worked example: compare 2/3 and 3/5

EXAMPLE

2/3 ? 3/5

The two denominators differ, so we cross-multiply and compare the products.

The 4 steps to compare two fractions

These four steps work for any pair a/b and c/d with positive denominators.

Step 1 · Start
2/3 ? 3/5
The denominators differ, so we decide it with cross multiplication.
Step 2 · cross
2 · 5 ? 3 · 3
Numerator times the opposite denominator: a · d versus c · b.
Step 3 · evaluate
10 ? 9
The two cross-products come out as 10 and 9.
Step 4 · Result
2/3 > 3/5
Because 10 > 9, the first fraction is the larger one.

Why cross multiplication works

A fraction a/b is just the division a ÷ b. When you compare a/b with c/d and multiply both sides by the positive product b · d, the denominators cancel and you are left with a · d versus c · b — exactly the cross-products. Since b · d is positive, the inequality sign does not flip, so the order of the fractions carries straight over to the order of the products.

Practice it yourself

Open the compare-fractions calculator

Enter your own fractions. See every step.

Start practice set

3 questions + boss problem

Frequently asked questions

How do you compare two fractions?

Cross-multiply: for a/b and c/d, compare a · d with c · b. The larger product belongs to the larger fraction. Example: 2/3 and 3/5 → 2 · 5 = 10 versus 3 · 3 = 9, so 2/3 > 3/5.

How do I compare 2/3 and 3/5?

Which is bigger, 3/8 or 1/2?

What is the cross-multiplication method?

When are two fractions equal?

How do I compare fractions with the same denominator?

Can I use a common denominator instead?

Quick answer

At a glance

Worked example: compare 2/3 and 3/5

The 4 steps to compare two fractions

Step 1 · Start

Step 2 · cross

Step 3 · evaluate

Step 4 · Result

Why cross multiplication works

Practice it yourself

Frequently asked questions