Fraction comparison calculator

Enter two integer numerators and positive denominators to compare their values.

First numerator (a)
Second numerator (c)
First denominator (b)
Second denominator (d)

Exact comparison

3/4 > 2/3

a ร— d9
c ร— b8

Contents

How the fraction comparison works

A bar with three of four parts filled above a bar with two of three parts filled

Enter two fractions with positive denominators. The calculator multiplies across them and compares the exact integer products, so it can tell which fraction is greater without converting either one to a rounded decimal.

Compare across a common denominator

For a/b and c/d, the first cross-product is a ร— d and the second is c ร— b. Because b and d are positive, whichever product is larger belongs to the larger fraction.

ab?cdโ€…โ€ŠโŸบโ€…โ€Šad?cb,b,d>0\frac{a}{b} \mathrel{?} \frac{c}{d} \iff ad \mathrel{?} cb,\quad b,d>0

The sign can be greater than, less than, or equal to. Equal products mean equivalent fractions, even when their numerators and denominators look different.

Compare close, equal and negative values

For 3/4 and 2/3, the products are 3 ร— 3 = 9 and 2 ร— 4 = 8. Since 9 is larger, 3/4 > 2/3. The first bar in the illustration therefore covers more of a whole.

For 1/2 and 2/4, both products are 4. The calculator returns 1/2 = 2/4: dividing a whole into more pieces does not change the amount when twice as many pieces are taken.

For โˆ’2/3 and โˆ’3/4, the products are โˆ’8 and โˆ’9. Since โˆ’8 is greater, โˆ’2/3 > โˆ’3/4. Among negative values, the one closer to zero is greater.

Input rules and exactness

Each field accepts an integer of up to 60 digits. Numerators can be negative or zero; denominators must be positive. A zero denominator does not define a fraction. The tool uses exact integer arithmetic, so a large cross-product is not rounded.

If both denominators are the same, comparing the numerators is quicker. For general fractions, cross-multiplication gives the same answer without first reducing them. For addition or subtraction, use the fraction calculator.

Questions about comparing fractions

These cases clarify what the comparison sign means and which inputs the calculator accepts.

Do I have to simplify first?

No. Equivalent fractions have equal cross-products even before simplification. For 1/2 and 2/4, both products are 4.

Can a numerator be zero?

Yes. Zero divided by any positive denominator is zero; 0/7 and 0/3 compare as equal.

Why must denominators be positive?

A positive product of the denominators preserves the comparison direction when both fractions are put over one common denominator.

Does the calculator round recurring decimals?

No. It compares integer products directly, so a recurring decimal never needs to be written or rounded.

Can I enter a mixed number?

Enter it as an improper fraction first. For example, 2 1/3 becomes 7/3, which can then be compared exactly.

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