LCD Least Common Denominator
● Free Ordering Tool

Comparing Fractions Calculator

Type in two to five fractions and watch them get converted to a common denominator and ranked from smallest to largest in real time, complete with comparison symbols and proportional fraction bars.

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Compare Fractions Live

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Enter at least two fractions to compare them.
01 · METHOD

How to Compare Fractions with Unlike Denominators

Fractions can only be measured against each other honestly once they are cut into the same-size pieces. That shared piece size is the least common denominator, and finding it turns any comparison into simple whole-number arithmetic.

  1. Find the least common denominator. List the denominators of every fraction you want to compare, then find their least common multiple. That LCM becomes the least common denominator (LCD) that all the fractions will share.
  2. Convert each fraction to the LCD. Divide the LCD by each fraction's original denominator to get a scale factor, then multiply both the numerator and the denominator by that factor to produce an equivalent fraction written over the shared denominator.
  3. Compare the numerators. Once every fraction sits over the same denominator, the fraction with the larger numerator is the larger value. No estimating, no decimals, just read the numerators.

Before and after: 2/3 vs 3/4

On the left, 2/3 is split into thirds and 3/4 is split into fourths. These are two different piece sizes that cannot be compared directly. On the right, both fractions have been rewritten over the LCD of 12, so every piece is exactly the same size and the numerators (8 versus 9) can be compared on sight.

2/3 3/4 8/12 9/12 convert to LCD 12 Same two fractions, now split into the same 12 equal pieces. 9 pieces beats 8 pieces.
02 · ORDERING

Ordering Fractions from Least to Greatest

The two-fraction method above extends cleanly to three, four, or five fractions at once. The only extra work is finding the least common multiple of a longer list of denominators. After that, ordering is just sorting numbers.

  1. Collect every denominator. Write down the bottom number of each fraction you want to order.
  2. Find one LCD for the whole set. Compute the least common multiple of all the denominators together, not just pairs of them.
  3. Convert every fraction to that LCD. Scale each numerator and denominator by the same factor so every fraction shares the LCD.
  4. Sort by numerator only. Because the denominators now match, the numerators alone determine the order. The smallest numerator is the smallest fraction, and the largest numerator is the largest.
1/2, 2/5, and 3/8 over a shared LCD of 40
20 16 15
Sorted numerators → 15 < 16 < 20  =  3/8 < 2/5 < 1/2

Notice that nothing about the original fractions changed. 3/8, 2/5, and 1/2 are still exactly the values they always were. Rewriting them over 40 just gave every fraction the same ruler, so the numerators could stand in for a direct size comparison. This is why the common-denominator method scales so well: it costs one extra LCM calculation up front, and every comparison after that is pure whole-number sorting, no matter how many fractions are in the list.

03 · VISUAL

Fraction Bar Comparison

Numbers on a page can be misleading, but a bar chart never lies about relative size. Below, three fractions with different denominators are drawn first at their true proportional length, then measured again on one shared 24-unit scale.

Before: each fraction on its own scale
1 / 2
value 50% of the whole
5 / 8
value 62.5% of the whole
2 / 3
value 66.7% of the whole
After: all three measured on the same 24-unit scale
1/2 = 12/24
5/8 = 15/24
2/3 = 16/24

Once every bar is chopped into the same 24 equal segments, the comparison is immediate: 12 < 58 < 23 . The fraction whose bar reaches the fewest shaded segments is the smallest, and the one reaching the most is the largest. That is exactly what the live calculator above shows for any fractions you enter.

04 · SHORTCUTS

Quick Comparison Methods

Finding a full least common denominator is the most reliable way to compare fractions, but these three shortcuts can save time in common situations.

Cross Multiplication for Two Fractions

To compare a/b and c/d without finding the LCD, multiply diagonally across the fractions: compare a×d against b×c. Whichever product is larger tells you which original fraction is larger, because both products are proportional to the fractions after being placed over the same denominator (b×d).

2/3 vs 3/4 → 2×4 = 8 vs 3×3 = 9 → 9 wins, so 3/4 is larger

When Denominators Are Already Equal, Compare Numerators

If two fractions already share a denominator, skip every conversion step entirely. The fraction with the larger numerator is automatically the larger value, since both fractions are built from identically sized pieces.

3/8 vs 5/8 → 5 > 3, so 5/8 is larger

When Numerators Match, the Larger Denominator Means the Smaller Fraction

When two fractions share the same numerator, the one with the larger denominator is cut into more pieces, so each individual piece is smaller. That makes it the smaller fraction overall, even though its denominator is the bigger number.

1/4 vs 1/6 → 6 > 4, so 1/6 is the smaller fraction and 1/4 is larger
05 · EXAMPLES

Worked Comparison Examples

Six fully worked comparisons, from simple two-fraction match-ups to three-way orderings, showing every conversion step and the final result.

Example 1 2 fractions

Compare 2/3 and 3/4

2 3 vs 3 4
  • LCD(3, 4) = 12
  • 2/3 → 8/12
  • 3/4 → 9/12
  • 9 is greater than 8
LCD 12
8 12 , 9 12 → 3/4
Larger fraction: 3/4
Example 2 3 fractions

Order 1/2, 2/5, 3/8 from least to greatest

1 2 vs 2 5 vs 3 8
  • LCD(2, 5, 8) = 40
  • 1/2 → 20/40, 2/5 → 16/40, 3/8 → 15/40
  • Sorted numerators: 15 < 16 < 20
LCD 40
20 40 , 16 40 , 15 40 → 3/8, 2/5, 1/2
Least to greatest: 3/8, 2/5, 1/2
Example 3 2 fractions

Compare 5/6 and 7/8

5 6 vs 7 8
  • LCD(6, 8) = 24
  • 5/6 → 20/24
  • 7/8 → 21/24
  • 21 is greater than 20
LCD 24
20 24 , 21 24 → 7/8
Larger fraction: 7/8
Example 4 2 fractions

Compare 3/5 and 2/3

3 5 vs 2 3
  • LCD(5, 3) = 15
  • 3/5 → 9/15
  • 2/3 → 10/15
  • 10 is greater than 9
LCD 15
9 15 , 10 15 → 2/3
Larger fraction: 2/3
Example 5 3 fractions

Order 1/3, 1/4, 1/6 from least to greatest

1 3 vs 1 4 vs 1 6
  • LCD(3, 4, 6) = 12
  • 1/3 → 4/12, 1/4 → 3/12, 1/6 → 2/12
  • Sorted numerators: 2 < 3 < 4
LCD 12
4 12 , 3 12 , 2 12 → 1/6, 1/4, 1/3
Least to greatest: 1/6, 1/4, 1/3
Example 6 2 fractions

Compare 2/7 and 3/10

2 7 vs 3 10
  • LCD(7, 10) = 70
  • 2/7 → 20/70
  • 3/10 → 21/70
  • 21 is greater than 20
LCD 70
20 70 , 21 70 → 3/10
Larger fraction: 3/10
06 · FAQ

Frequently Asked Questions About Comparing Fractions

How do you compare fractions with different denominators?
Convert every fraction to an equivalent fraction that shares the same denominator, the least common denominator (LCD), by multiplying each numerator and denominator by the factor needed to reach the LCD. Once the denominators match, the fraction with the larger numerator is the larger value.
Which is larger, 2/3 or 3/4?
3/4 is larger. The LCD of 3 and 4 is 12, so 2/3 becomes 8/12 and 3/4 becomes 9/12. Since 9 is greater than 8, 3/4 is the bigger fraction. This matches the decimal check: 2/3 ≈ 0.667 and 3/4 = 0.75, confirming 3/4 is larger.
How do you order three fractions from least to greatest?
Find the LCD of all three denominators, convert each fraction to that denominator, then sort the resulting numerators from smallest to largest. The fraction with the smallest converted numerator comes first, and the one with the largest comes last. For example, 1/2, 2/5, and 3/8 convert to 20/40, 16/40, and 15/40, giving the order 3/8, 2/5, 1/2.
Can you compare fractions without finding the LCD?
Yes. Cross multiplication works for two fractions at a time: for a/b versus c/d, compare a×d against b×c. Whichever product is larger tells you which fraction is larger. You can also convert each fraction to a decimal by dividing the numerator by the denominator and comparing those decimals directly. Both shortcuts avoid the LCD but the common-denominator method scales best when comparing three or more fractions at once.
Which is bigger, 5/6 or 7/8?
7/8 is bigger. Using the LCD of 24, 5/6 becomes 20/24 and 7/8 becomes 21/24. Because 21 is greater than 20, 7/8 wins the comparison. This same result can be confirmed by cross multiplication: 5 × 8 = 40 and 6 × 7 = 42, and since 42 is greater, 7/8 is confirmed larger.
Does cross multiplication still work if the fractions are negative?
Cross multiplication and the common-denominator method both still work with negative fractions, but you have to keep track of signs carefully. A negative fraction is always smaller than a positive one, and between two negative fractions the one with the smaller absolute value is actually the larger number. When in doubt, convert both fractions to a common denominator first and compare the signed numerators directly.