How do you compare two fractions?

The most reliable method is cross-multiplication. To compare a/b and c/d, multiply the numerator of the first fraction by the denominator of the second (a x d), and the numerator of the second by the denominator of the first (c x b). If a x d is greater than c x b, then a/b is the larger fraction. If a x d equals c x b, the fractions are equal. You can also convert each fraction to a decimal by dividing numerator by denominator and then compare the decimals directly.

Can you compare fractions with different denominators?

Yes. When fractions have different denominators, the simplest approach is cross-multiplication, which avoids the need to find a common denominator. Alternatively, convert both fractions to equivalent fractions with the same denominator (the lowest common denominator, or LCD), then compare the numerators directly. For example, to compare 2/3 and 3/4, find the LCD of 3 and 4 which is 12: 2/3 becomes 8/12 and 3/4 becomes 9/12. Since 9 is greater than 8, 3/4 is the larger fraction.

How do you compare mixed numbers?

First compare the whole-number parts. If one whole number is greater, that mixed number is larger regardless of the fractional parts. If the whole numbers are equal, compare the fractional parts using cross-multiplication or a common denominator. For example, 3 2/5 versus 3 3/7: the whole numbers are both 3, so compare 2/5 and 3/7. Cross-multiplying: 2 x 7 = 14 versus 3 x 5 = 15. Since 15 is greater, 3/7 is larger, so 3 3/7 is the bigger mixed number.

Comparing Fractions Calculator

Enter two fractions to find out which is greater, lesser, or equal. The calculator uses cross-multiplication to compare them accurately and shows full step-by-step working, decimal equivalents, and a common-denominator breakdown.

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Standard maths method Cross-multiplication and LCD comparison. Works for positive and negative fractions.

First Fraction

Numerator and denominator

Fraction A

Second Fraction

Numerator and denominator

Fraction B

Comparison Result

Fraction A (decimal)

Result
-
-

Fraction B (decimal)

Conclusion: Enter two fractions above.

Step-by-Step Working

Cross-Multiplication

A numerator x B denominator-

B numerator x A denominator-

Comparison-

Common Denominator Method

Least common denominator (LCD)-

Fraction A as equivalent-

Fraction B as equivalent-

Numerator comparison-

How to Compare Fractions

Comparing fractions means determining whether one fraction is greater than, less than, or equal to another. There are three common methods: cross-multiplication, finding a common denominator, and converting to decimals.

Method 1: Cross-Multiplication

Cross-multiplication is the quickest method and works for any two fractions, regardless of their denominators. To compare a/b and c/d:

Multiply the numerator of the first fraction by the denominator of the second: a x d
Multiply the numerator of the second fraction by the denominator of the first: c x b
Compare the two products. If a x d > c x b, then a/b > c/d. If a x d < c x b, then a/b < c/d. If the products are equal, the fractions are equal.

Example: Compare 3/4 and 2/3. Cross-multiply: 3 x 3 = 9, and 2 x 4 = 8. Since 9 > 8, we know that 3/4 > 2/3.

Method 2: Common Denominator

Convert both fractions to have the same denominator, then compare the numerators. The common denominator to use is the least common multiple (LCM) of the two denominators, also called the least common denominator (LCD). Once both fractions share a denominator, the one with the larger numerator is the greater fraction.

Example: Compare 3/4 and 2/3. The LCD of 4 and 3 is 12. Convert: 3/4 = 9/12 and 2/3 = 8/12. Since 9 > 8, we confirm 3/4 > 2/3.

Method 3: Decimal Conversion

Divide each numerator by its denominator to get a decimal, then compare the decimals. This is useful for quick mental checks but can introduce rounding errors with repeating decimals. For exact comparison, cross-multiplication or the LCD method is more reliable.

Example: 3/4 = 0.75 and 2/3 = 0.6667. Since 0.75 > 0.6667, we confirm 3/4 > 2/3.

Comparing Negative Fractions

The same methods apply to negative fractions, but remember that negative numbers work in reverse: -1/4 is greater than -3/4, even though 1/4 is less than 3/4. When comparing negative fractions, the one closer to zero is the larger value.

Worked Example

Default inputs: Fraction A = 3/4 and Fraction B = 2/3.

Cross-multiply: 3 x 3 = 9, and 2 x 4 = 8. Since 9 > 8, Fraction A (3/4) is greater.
As decimals: 3/4 = 0.75, 2/3 = 0.6667. Confirms 3/4 is greater.
With LCD 12: 3/4 = 9/12, 2/3 = 8/12. Numerators 9 > 8, so 3/4 is greater.

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Method: Cross-multiplication (a/b vs c/d: compare a x d with c x b). Least common denominator found using Euclidean GCD algorithm. Decimal values computed by dividing numerator by denominator.

This calculator compares fractions as exact rational numbers. Results are mathematically precise for integer numerators and denominators. Decimal display is rounded to 6 significant figures.

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