Math
Comparing Fractions Calculator
Type two to six fractions, mixed numbers, whole numbers, or decimals and see them ordered from least to greatest and greatest to least.
The calculator shows the common-denominator method, decimal equivalents, cross products for pairs, and the gap between the largest and smallest.
One per line, or separated by commas. Mixed numbers (1 1/2), whole numbers, and decimals work too. 2 to 6 fractions.
Try an example
Result
Least to greatest
—
- Greatest to least
- —
- Largest (simplified)
- —
- Smallest (simplified)
- —
- Largest minus smallest
- —
- Least common denominator
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
Three ways to compare fractions
Common The bottom number of a fraction; it says how many equal parts make one whole.: rewrite every fraction over the The smallest bottom number two fractions can share so you can add or compare them. and compare The top number of a fraction; it counts how many parts you have.. Decimals: divide each numerator by its denominator and compare the decimals. Cross products (two fractions only): a/b is greater than c/d exactly when a × d is greater than b × c. The calculator shows all three so the ordering is easy to trust.
Ordering more than two fractions
With several fractions, the LCD method is the cleanest: 3/4, 5/8, 2/3, and 7/12 over the LCD 24 become 18/24, 15/24, 16/24, and 14/24, so the order is 7/12 < 5/8 < 2/3 < 3/4. A whole number written next to a fraction, like 2 1/3. are converted to A fraction whose top number is at least as big as its bottom number, like 7/3. first, and negative fractions sort below zero.
| Fractions | LCD | Over the LCD | Order |
|---|---|---|---|
| 1/2, 2/5 | 10 | 5/10, 4/10 | 2/5 < 1/2 |
| 3/4, 5/8, 2/3 | 24 | 18/24, 15/24, 16/24 | 5/8 < 2/3 < 3/4 |
| -1/2, 1/3, 0 | 6 | -3/6, 2/6, 0/6 | -1/2 < 0 < 1/3 |
| 1 1/4, 5/4 | 4 | 5/4, 5/4 | equal |
How to use it
- Type each fraction on its own line (or separate them with commas).
- Mixed numbers need a space (1 1/2); negatives take a leading minus sign; decimals are converted exactly.
- Read the least-to-greatest ordering in the main result and the greatest-to-least ordering below it.
- Open Show the work for the LCD, the rewritten numerators, decimals, and cross products.
How to read the answer
The ordering uses < between fractions of different value and = between equivalent ones. The largest and smallest are shown in simplest form, and the range tells how far apart they are. Rewritten numerators over the LCD are the direct evidence for the order.
Common mistakes and edge cases
- A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
- Comparing numerators only works when the denominators already match.
- Rounding decimals too early can make close fractions look equal. Use the exact decimals or the LCD method.
- Negative fractions reverse intuition: -3/4 is less than -1/4.
- A denominator of 0 is undefined; the calculator refuses it.
Worked examples
Four fractions
3/4, 5/8, 2/3, 7/12
Least to greatest
7/12 < 5/8 < 2/3 < 3/4
Two fractions
Which is bigger, 5/8 or 3/5?
Least to greatest
3/5 < 5/8
Negative and zero
-1/2, 1/3, 0
Least to greatest
-1/2 < 0 < 1/3
Equivalent fractions
1 1/4 and 5/4 are equal
Least to greatest
1 1/4 = 5/4
Mixed with decimals
0.7, 2/3, 3/4
Least to greatest
2/3 < 0.7 < 3/4
Six fractions
1/2, 1/3, 1/4, 1/5, 1/6, 1/7
Least to greatest
1/7 < 1/6 < 1/5 < 1/4 < 1/3 < 1/2
Only one fraction
Needs at least two
Least to greatest
Error
Bad denominator
1/2 and 3/0
Least to greatest
Error
Frequently asked questions
How do you compare fractions with different denominators?+
Rewrite them over a common denominator (the LCD is smallest) and compare numerators, or convert to decimals, or for two fractions use cross products.
Which is bigger, 5/8 or 3/5?+
5/8. Cross products: 5 × 5 = 25 and 3 × 8 = 24; 25 > 24, so 5/8 > 3/5. As decimals, 0.625 > 0.6.
How do you order fractions from least to greatest?+
Give all of them the same denominator and sort by numerator, or convert each to a decimal and sort. The calculator does both and shows both orderings.
How do you compare mixed numbers?+
Compare the whole parts first; if they tie, compare the fraction parts. The calculator converts mixed numbers to improper fractions so the LCD method works directly.
How do negative fractions compare?+
Any negative fraction is less than 0 and less than any positive fraction. Among negatives, the one with the larger absolute value is smaller: -3/4 < -1/4.
What if two fractions are equivalent?+
They are shown joined by an equals sign in the ordering, and the warning notes that some inputs are the same value.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026