Comparing Fractions: 4 Methods That Actually Work

Comparing two fractions seems like it should be easy. It often isn’t. Is 3/5 bigger than 5/8? Your gut probably can’t tell you immediately; both feel like “a bit more than half.”

There are four methods that reliably answer the question. Each works better in different situations.

Method 1: Use a Visual Model

Draw both fractions as bar models: rectangles of the same length, divided into equal sections, then look at which shaded region is larger.

For 2/3 vs 3/5:

• Bar 1: divided into 3 equal parts, 2 shaded
• Bar 2: divided into 5 equal parts, 3 shaded

Looking at the two bars side by side, 2/3 takes up slightly more space. So 2/3 > 3/5.

When to use it: When you want to build intuition rather than just get an answer. Visual comparison is especially useful for teaching, because it shows why one fraction is larger, not just that it is.

Limitation: It’s hard to be precise with fractions that are close in value. 7/12 and 5/9 look almost identical drawn by hand. Use our Visual Fraction Models tool to generate accurate side-by-side diagrams.

Method 2: Find a Common Denominator

Convert both fractions so they share the same denominator, then compare numerators.

Compare 2/3 and 3/5:

1. Find the LCD: LCM(3, 5) = 15
2. Convert: 2/3 = 10/15 and 3/5 = 9/15
3. Compare numerators: 10 > 9
4. Result: 2/3 > 3/5

When to use it: When you need an exact answer and you’ll be doing further calculations with the fractions. Finding the common denominator is also the setup for adding or subtracting fractions, so you’re doing useful prep work.

Limitation: Finding the LCD can be slow for large or unfamiliar denominators.

Method 3: Cross-Multiply

A shortcut that skips the common denominator step.

To compare a/b and c/d:

• Multiply a × d (top-left times bottom-right)
• Multiply b × c (bottom-left times top-right)
• The fraction on the side of the larger product is the larger fraction

Compare 3/5 and 5/8:

• 3 × 8 = 24 (on the left side, for 3/5)
• 5 × 5 = 25 (on the right side, for 5/8)
• 25 > 24, so 5/8 > 3/5

When to use it: Fast mental comparisons when you don’t need to show your working step-by-step. It’s the quickest method once you’ve practised it.

Note: Cross-multiplication only tells you which fraction is larger. It doesn’t tell you by how much.

Method 4: Convert to Decimals

Divide each numerator by its denominator and compare the resulting decimals.

Compare 3/7 and 4/9:

• 3/7 = 0.4285...
• 4/9 = 0.4444...
• 0.4444 > 0.4285, so 4/9 > 3/7

When to use it: When you have a calculator available, or when the fractions are awkward enough that common denominators would take a long time to find. Decimal conversion also works well for ordering more than two fractions at once.

Limitation: You lose exactness: 0.333... and 1/3 are the same, but a calculator will round the decimal, which can cause errors in edge cases where fractions are very close.

Benchmark Comparison: A Bonus Shortcut

Sometimes you can compare two fractions without any calculation by checking them against 1/2.

• Is the fraction greater or less than 1/2?
• A fraction is greater than 1/2 when the numerator is more than half the denominator: 5/8: is 5 more than half of 8? Yes (half of 8 is 4). So 5/8 > 1/2.
• A fraction is less than 1/2 when the numerator is less than half the denominator: 3/8: is 3 less than 4? Yes. So 3/8 < 1/2.

If one fraction is greater than 1/2 and the other is less than 1/2, you’re done. No further comparison needed.

This also works with 0 and 1 as benchmarks, which makes it easy to sort a mixed set quickly.

Putting It Together

For any comparison, you can verify visually with our Visual Fraction Models tool, or use the Fraction Comparator for a side-by-side breakdown with multiple methods shown.