Enter two or more fractions to find out which is bigger, or to put a whole list in order from least to greatest (or greatest to least). The calculator finds the least common denominator, rewrites each fraction and shows the decimal check.
Last updated:
Separate with commas or new lines. Mixed numbers (1 1/2), negatives (−3/5), whole numbers and decimals (0.7) work too.
Order
Enter your values to see the result.
Advertisement
Advertisement
How to use the Compare Fractions Calculator
Type your fractions separated by commas or new lines, e.g. 3/4, 5/8, 2/3.
Use a space for mixed numbers (1 1/2) and a minus sign for negatives.
Pick the order: least to greatest or greatest to least.
Press Compare fractions to see the comparison, the common denominator steps and the ranked table.
Three ways to compare fractions
Common denominator: rewrite every fraction over the least common denominator and compare numerators. Best for ordering a list.
Cross-multiplication: for a/b and c/d, a × d > c × b means a/b > c/d. Fastest for two fractions.
Decimals: divide numerator by denominator. Easy with a calculator, but repeating decimals such as 0.333… must be compared carefully.
Worked example
Order 1/2, 3/8, 5/6, 2/3 and 7/12 from least to greatest. The least common denominator of 2, 8, 6, 3 and 12 is 24:
Fraction
Multiply by
Over 24
Decimal
3/8
3/3
9/24
0.375
1/2
12/12
12/24
0.5
7/12
2/2
14/24
0.5833…
2/3
8/8
16/24
0.6667…
5/6
4/4
20/24
0.8333…
Result: 3/8 < 1/2 < 7/12 < 2/3 < 5/6.
Shortcuts
Same denominator: bigger numerator wins (5/9 > 4/9).
Same numerator: smaller denominator wins (2/5 > 2/7).
Benchmark 1/2: if one fraction is above half and the other below (numerator more or less than half the denominator), you are done: 4/7 > 5/11.
Distance from 1: 7/8 is 1/8 from a whole and 5/6 is 1/6 away; 1/8 is smaller, so 7/8 > 5/6.
Frequently asked questions
How do you compare fractions with different denominators?
Rewrite them with a common denominator, usually the least common denominator (LCD), then compare the numerators. For 3/4 and 5/8, the LCD is 8: 3/4 = 6/8, and 6/8 > 5/8, so 3/4 > 5/8.
What is the quickest way to compare two fractions?
Cross-multiply. For a/b and c/d with positive denominators, compare a × d with c × b. For 2/3 and 5/8: 2 × 8 = 16 and 5 × 3 = 15, and since 16 > 15, 2/3 > 5/8.
How do I order fractions from least to greatest?
Convert all of them to the same denominator and sort by numerator, or convert each to a decimal and sort. For 1/2, 3/8, 5/6, 2/3 and 7/12 the LCD is 24, giving 12/24, 9/24, 20/24, 16/24 and 14/24, so the order is 3/8 < 1/2 < 7/12 < 2/3 < 5/6.
What if the fractions have the same numerator?
Then the one with the smaller denominator is larger, because the whole is split into fewer, bigger pieces. For example 3/5 > 3/7. With the same denominator, the larger numerator is larger.
How do negative fractions compare?
A negative fraction is less than any positive fraction. Between two negatives, the one closer to zero is greater: −1/2 > −2/3 because −0.5 is to the right of about −0.667 on the number line.
Can I compare mixed numbers and decimals?
Yes. Mixed numbers like 1 3/8 are turned into improper fractions (11/8) and decimals like 1.45 into exact fractions (29/20) before comparing, so results are exact rather than rounded.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.