Comparing Fractions Calculator

This calculator tells you straight away which of two fractions is bigger, which is smaller, or whether they are equal, without you having to work through the maths by hand. You enter the numerator and denominator for Fraction A, then do the same for Fraction B - it accepts positive and negative whole numbers, so you can compare pairs like 3/4 against 2/3, or negative fractions such as -1/4 against -3/4. As you type, it returns each fraction as a decimal, shows the comparison symbol as the headline result, and gives a plain-English conclusion, for example "3/4 is greater than 2/3". Below that sits full step-by-step working, covering the cross-multiplication method (multiplying each numerator by the other fraction's denominator and comparing the two products) alongside a common-denominator breakdown showing the least common denominator, both fractions converted to equivalent fractions over it, and a direct comparison of the resulting numerators. Having both methods laid out side by side lets you check your own homework, confirm the two approaches agree, and see exactly why one fraction outranks the other rather than just being handed an answer. It suits students checking assignments, tradespeople comparing measurements, or anyone weighing up recipe quantities or proportions. Results are worked out as exact rational numbers, with decimal values rounded to six significant figures for display.

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

First Fraction

Fraction A

Second Fraction

Fraction B

Comparison Result

Fraction A (decimal)
0.75
3/4
Result
>
A is greater than B
Fraction B (decimal)
0.666667
2/3
Conclusion: Enter two fractions above.

Step-by-Step Working

Cross-Multiplication

A numerator x B denominator3 x 3 = 9
B numerator x A denominator2 x 4 = 8
Comparison9 > 8 so A > B

Common Denominator Method

Least common denominator (LCD)12
Fraction A as equivalent3/4 = 9/12
Fraction B as equivalent2/3 = 8/12
Numerator comparison9 > 8 so A > B

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:

  1. Multiply the numerator of the first fraction by the denominator of the second: a x d
  2. Multiply the numerator of the second fraction by the denominator of the first: c x b
  3. 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.

Related Calculators

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.

Frequently asked questions

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.