About the Comparing Fractions Calculator
This comparing fractions calculator tells you which fraction is bigger and puts any list of fractions in order. Type fractions such as 3/4, 2/3 and 5/8 — mixed numbers like 1 1/2 and decimals like 0.7 work too — and it rewrites each one over the least common denominator (LCD) so you can compare the numerators directly, then lists them from least to greatest or greatest to least.
It is built for elementary and middle-school students learning to compare fractions, parents checking homework, and anyone who needs to know whether 5/8 inch is bigger than 9/16 inch or which recipe ratio is larger. The table shows each fraction in lowest terms, as a decimal and as an equivalent fraction over the LCD, which is exactly the method taught in class.
Comparisons are exact: the calculator cross-multiplies whole numbers instead of relying on rounded decimals, so fractions that are very close, or equal like 2/4 and 3/6, are always ordered correctly.
How to use the comparing fractions calculator
- 1Type the fractions separated by commas or new lines.
- 2Use a space for mixed numbers, e.g. 2 1/3.
- 3Choose least-to-greatest or greatest-to-least order.
- 4Read the ordered list and the comparison of the first two.
- 5Check the table to see every fraction rewritten over the common denominator.
Formula and method
To compare fractions with different denominators, rewrite them over a common denominator. The least common denominator is the least common multiple of all the denominators; each fraction is multiplied top and bottom by LCD ÷ its denominator. Once the denominators match, the fraction with the larger numerator is larger.
For two fractions the same result comes from cross-multiplying: a/b > c/d exactly when a·d > c·b (with positive denominators). The calculator uses exact whole-number cross-multiplication to sort the list, so it never mis-orders fractions because of decimal rounding.
- a/b, c/d
- Fractions being compared (denominators positive)
- LCD
- Least common denominator — the lcm of the denominators
Worked examples
Order 3/4, 2/3 and 5/8
The LCD of 4, 3 and 8 is 24, so the fractions become 18/24, 16/24 and 15/24. Comparing numerators gives 15 < 16 < 18, so 5/8 < 2/3 < 3/4, and the spread between largest and smallest is 3/4 − 5/8 = 1/8.
Which drill bit is bigger: 5/8 or 9/16 inch?
Rewriting 5/8 over 16 gives 10/16, which is larger than 9/16 by 1/16 inch.
Mixed numbers, decimals and equivalent fractions
1 1/2 = 30/20, 7/5 = 28/20, 1.45 = 29/20 and 3/2 = 30/20. So 7/5 is smallest, and 1 1/2 equals 3/2.
Frequently asked questions
How do you compare fractions with different denominators?+
Find a common denominator (ideally the least common multiple of the denominators), convert each fraction to it, then compare numerators. Alternatively cross-multiply: a/b > c/d when a × d > c × b.
How do you compare fractions with the same numerator?+
When the numerators are equal, the fraction with the smaller denominator is larger, because the whole is split into fewer, bigger pieces. For example 3/5 > 3/8.
How do you order fractions from least to greatest?+
Rewrite every fraction over the least common denominator, then sort by numerator. Converting to decimals also works for a quick check, but the common-denominator method is exact.
What is the least common denominator?+
The LCD is the least common multiple of the denominators — the smallest number each denominator divides into evenly. For 4, 6 and 8 it is 24.
How can I tell if two fractions are equivalent?+
Two fractions are equivalent when their cross products are equal (a × d = b × c) or when both reduce to the same lowest terms, like 2/4 and 3/6, which both simplify to 1/2.