How to Compare Fractions: 3 Easy Methods

Last updated: February 13, 2026

The quickest way to compare fractions is cross multiplication: multiply each numerator by the other fraction's denominator and see which product is larger. Two other solid options are finding a common denominator or converting to decimals. This guide walks through all three methods with examples, then lets you practice.

Quick answer: Cross multiply. For a/b vs c/d, compute a × d and c × b. The bigger product points to the bigger fraction. Done in two multiplications.

Quick Summary
1
Cross Multiply

Compare a/b vs c/d: if a×d > c×b, then a/b is bigger. Two fractions, two multiplications, done.

2
Common Denominator

Rewrite both fractions with the same bottom number, then just compare the tops. Works great for 3+ fractions.

3
Convert to Decimals

Divide numerator ÷ denominator for each fraction, then compare the decimal values.

How Do You Compare Fractions Using Cross Multiplication?

Fastest Method

Cross multiplication lets you compare any two fractions without touching their denominators. You're really just finding a common denominator behind the scenes, but skipping all the busywork. It's the method Khan Academy covers first, and most elementary and middle school classrooms teach it because it takes about five seconds once you know the steps.

1
Write the fractions side by side. Place the first fraction (a/b) on the left and the second (c/d) on the right.
2
Cross multiply. Multiply the first fraction's numerator by the second fraction's denominator to get the left product (a × d). Then go the other way: multiply the second numerator by the first denominator for the right product (c × b).
3
Compare the products. Bigger left product means the first fraction is bigger. Bigger right product means the second fraction wins. Equal products? The fractions are equivalent.
Example: Compare 3/7 and 2/5

Left product: 3 × 5 = 15

Right product: 2 × 7 = 14

15 > 14, so 3/7 > 2/5.

Example: Compare 4/6 and 2/3

Left product: 4 × 3 = 12

Right product: 2 × 6 = 12

The products are equal, so 4/6 = 2/3. These are equivalent fractions.

Why Does Cross Multiplication Work?

Here's what's actually happening. If you wanted to compare a/b and c/d properly, you'd rewrite them as (a × d) / (b × d) and (c × b) / (b × d). Now they share the denominator b × d, so you only care about the numerators: a × d versus c × b. Cross multiplication just skips the denominator part and goes straight to those numerators.

How Do You Compare Fractions by Finding a Common Denominator?

Best for Understanding

This one's more work, but it makes the most sense if you want to understand why one fraction is bigger. The idea: rewrite both fractions so they have the same denominator, then the one with the larger numerator is the larger fraction. It's the same logic behind equivalent fractions, and it really shines when you need to compare three or more fractions at once.

1
Find the Least Common Denominator (LCD). The LCD is the smallest number that both denominators divide into evenly. You can use the LCD Calculator to find it quickly.
2
Rewrite each fraction with the LCD. Multiply the numerator and denominator of each fraction by whatever factor makes the denominator equal the LCD.
3
Compare the numerators. Bigger numerator = bigger fraction. That's the whole point of matching denominators.
Example: Compare 3/8 and 2/5

Step 1: The LCD of 8 and 5 is 40.

Step 2: 3/8 = (3 × 5)/(8 × 5) = 15/40. And 2/5 = (2 × 8)/(5 × 8) = 16/40.

Step 3: 15 < 16, so 3/8 < 2/5.

What If the Fractions Already Have the Same Denominator?

If two fractions already have the same denominator (sometimes called "like fractions"), you're done before you start. Just compare numerators. 5/9 > 2/9 because 5 > 2. No conversion needed.

What If the Fractions Have the Same Numerator?

This one trips people up. When the numerators match, the fraction with the smaller denominator is actually bigger. Think about it: cutting a pizza into 4 slices gives you bigger slices than cutting it into 7. So 3/4 > 3/7.

How Do You Compare Fractions by Converting to Decimals?

Most Practical

If you've got a calculator handy, this is the most straightforward approach. Just divide the top by the bottom for each fraction and compare the decimals. It connects directly to number-line thinking, which the NCTM standards emphasize starting in grade 3. And it's hard to beat when you're sorting three or more fractions at once. Need to convert? Try the Fraction to Decimal Converter.

1
Divide each numerator by its denominator. Use long division or a calculator to convert each fraction to a decimal.
2
Compare the decimals. Bigger decimal, bigger fraction. Simple as that.
Example: Compare 5/8 and 3/5

5/8 = 5 ÷ 8 = 0.625

3/5 = 3 ÷ 5 = 0.6

0.625 > 0.6, so 5/8 > 3/5.

What Happens When Fractions Convert to Repeating Decimals?

Some fractions don't convert cleanly. 1/3 becomes 0.333… and 2/7 turns into 0.2857… repeating forever. Don't panic. Just compare three or four decimal places and that's usually enough to tell which is bigger.

Which Comparison Method Should You Use?

Not sure which method to pick? Here's a quick cheat sheet.

Method Best For Speed Limitation
Cross Multiplication Comparing two fractions quickly Very fast Only compares two fractions at a time
Common Denominator Comparing or ordering three+ fractions Moderate Finding the LCD takes an extra step
Decimal Conversion Quick estimation and number-line thinking Fast with calculator Repeating decimals can complicate things

How Do You Order Fractions from Least to Greatest?

Sometimes you don't just need to compare two fractions; you need to sort a whole bunch of them. Both the common denominator method and the decimal method work well here.

How Do You Use Decimals to Order Fractions?

Example: Order 1/3, 2/5, and 1/4 from Least to Greatest

Convert: 1/3 ≈ 0.333, 2/5 = 0.4, 1/4 = 0.25

Order the decimals: 0.25 < 0.333 < 0.4

Result: 1/4 < 1/3 < 2/5

How Do You Use a Common Denominator to Order Fractions?

Example: Order 2/3, 3/4, and 5/6 from Least to Greatest

Find the LCD: The LCD of 3, 4, and 6 is 12.

Convert: 2/3 = 8/12, 3/4 = 9/12, 5/6 = 10/12

Order by numerator: 8 < 9 < 10

Result: 2/3 < 3/4 < 5/6

Want to skip the arithmetic? The Comparing Fractions Calculator handles all of this automatically and shows each step.

Compare Fractions Instantly

Enter any two fractions and get the answer with step-by-step work shown.

Open Comparing Fractions Calculator →

Practice Problems: Test Your Skills

Ready to try it yourself? Pick your answer for each problem. You'll get instant feedback plus a quick explanation.

Choose the Correct Symbol: <, >, or =

1. Compare 3/4 and 2/5
2. Compare 2/7 and 5/9
3. Compare 3/4 and 6/8
4. Compare 5/6 and 5/8
5. Compare 7/12 and 3/5
6. Compare 4/9 and 3/11

Frequently Asked Questions

Cross multiplication. Multiply each fraction's numerator by the other's denominator, then compare the two products. Bigger product = bigger fraction. Two quick multiplications and you're done.
If both fractions already have the same denominator (called "like fractions"), just compare the numerators. Bigger numerator wins. For example, 5/8 > 3/8 because 5 > 3. That's all there is to it.
The fraction with the smaller denominator is bigger. Sounds backwards, but think of it this way: fewer slices means each slice is larger. So 3/4 > 3/7 because fourths are bigger pieces than sevenths.
Absolutely. Divide numerator by denominator for each fraction and compare the results. For example, 3/8 = 0.375 and 2/5 = 0.4, so 2/5 is bigger. This method is great when you've got three or more fractions to sort.
Two fractions are equivalent when they're just different ways of writing the same number. 2/4 and 3/6 both equal 1/2. A quick check: cross multiply the two fractions. If both products are equal, the fractions are equivalent.
Turn the whole number into a fraction by putting it over 1. To compare 5/3 and 2, rewrite 2 as 2/1. Now cross multiply: 5 × 1 = 5 and 2 × 3 = 6. Since 5 < 6, 5/3 < 2.
Give all fractions a common denominator, or convert them all to decimals, then line them up from smallest to biggest. For example, 1/3, 2/5, and 1/4 become 0.333, 0.4, and 0.25 as decimals. Sorted: 1/4 < 1/3 < 2/5.
A common denominator is a bottom number that all your fractions can share. Once they share it, you just compare numerators. The least common denominator (LCD) is the smallest one that works, which keeps the numbers manageable. The LCD Calculator can find it for you.
Yes. Cross multiply: 3 × 3 = 9 and 2 × 4 = 8. 9 beats 8, so 3/4 > 2/3. Decimals confirm it: 3/4 = 0.75 and 2/3 ≈ 0.667.
The fraction closer to zero is the greater one. Decimals help here: −1/4 = −0.25 and −1/3 ≈ −0.333. −0.25 is closer to zero, so −1/4 > −1/3. Picture a number line: the one further right is always bigger.
It's a shortcut for the common denominator method. To compare a/b and c/d, you'd normally rewrite both with the denominator b × d, giving numerators of a × d and c × b. Cross multiplication jumps straight to those two numerators and skips the denominator entirely.
Check the whole numbers first. If one is bigger, you're done. If they match, compare the fractional parts. For 23/4 vs 22/3, the whole numbers are both 2, so compare 3/4 and 2/3. Cross multiply: 3 × 3 = 9 and 2 × 4 = 8. 9 > 8, so 23/4 > 22/3.
Convert each fraction to a decimal and plot it between 0 and 1. Whichever sits further to the right is bigger. For example, 3/8 = 0.375 lands to the left of 2/5 = 0.4, so 3/8 < 2/5. It's a great way to see fraction size at a glance.

Related Tools and Guides

Want to keep going? These tools and tutorials pick up where this guide leaves off:

Comparing Fractions Calculator lets you plug in any two fractions and see the answer with visual bar charts and full step-by-step work.

Need the LCD for a set of numbers? The LCD Calculator finds it for you.

The Fraction to Decimal Converter handles conversions both ways: fractions to decimals and decimals back to fractions.

Or head to the Online Fractions Calculator for adding, subtracting, multiplying, and dividing fractions all in one place.