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MasterMath

Compare Fractions Calculator

Order up to three fractions from smallest to largest, with the common denominator that makes the comparison obvious.

Smallest to largest

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Smallest to largest—
Common denominator—
With a common denominator—
The largest—
The smallest—

How this was worked out

    The rule

    put them over a common denominator, then compare numerators

    Why it works

    Fractions with different denominators are pieces of different sizes, so their numerators cannot be compared directly. Rewriting them all over one denominator makes the pieces the same size, and then the larger numerator simply wins.

    How to do it by hand

    1. Find the lowest common multiple of the denominators
    2. Rewrite each fraction with it
    3. Compare the numerators directly
    4. Order the originals accordingly

    What is worth knowing

    For just two fractions, cross-multiplying is quicker: a/b beats c/d exactly when a × d beats c × b, with a sign check if anything is negative. The common-denominator method scales to any number of fractions and shows the working, which is why it is what gets taught. There is also a shortcut worth knowing: when two fractions have the same numerator, the one with the smaller denominator is larger, because the pieces are bigger. 3/4 beats 3/5 without any calculation at all.

    Frequently asked questions

    How do you compare fractions?

    Put them over a common denominator and compare the numerators. For two, cross-multiplying is faster.

    Is cross-multiplying reliable?

    For two positive fractions, yes. With negatives you have to watch the direction of the inequality.

    What if the numerators are the same?

    The one with the smaller denominator is larger, because it is divided into fewer, bigger pieces.

    Do I need the lowest common denominator?

    Any common denominator works. The lowest just keeps the numbers manageable.