# Comparing Fractions Calculator

URL: https://speedycalculator.com/calculators/math/comparing-fractions/
Last updated: 2026-10-30

> The comparing fractions calculator tells you which of two fractions or mixed numbers is greater by rewriting them over a common denominator, and shows the difference.

## Inputs

- Fraction form
- Fraction 1: whole
- Fraction 1: numerator
- Fraction 1: denominator
- Fraction 2: whole
- Fraction 2: numerator
- Fraction 2: denominator

## Results

- Comparison
- Which is greater?
- Difference (first − second)
- Steps

## Formula

```
Compare a/b and c/d: rewrite over LCD L and compare a·(L/b) with c·(L/d)  (or compare a·d with c·b)
```

## Explanation

Which is bigger, 5/8 or 3/5? With unlike denominators it is hard to tell at a glance. Rewriting both fractions over the same denominator – or cross-multiplying – makes the comparison a simple comparison of whole numbers.

### How to use the Comparing Fractions Calculator

- **Fraction form**
- **Fraction 1: whole**
- **Fraction 1: numerator**
- **Fraction 1: denominator**
- **Fraction 2: whole**
- **Fraction 2: numerator**
- **Fraction 2: denominator**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Mixed numbers are first turned into improper fractions. Both fractions are rewritten over their least common denominator, and the numerators are compared.

## Worked example

Inputs — Fraction form: Simple fraction; Fraction 1: numerator: 5; Fraction 1: denominator: 8; Fraction 2: numerator: 3; Fraction 2: denominator: 5.

Results — **Comparison = 5/8 > 3/5**; Which is greater? = 5/8 is greater; Difference (first − second) = 1/40 ≈ 0.025; Steps = 1. Common denominator 40: 25/40 and 24/40
2. Compare the numerators: 25 > 24.

## Key terms

- **Equivalent fractions**: Fractions with the same value, such as 1/2 and 4/8.

## FAQ

**Which is bigger, 5/8 or 3/5?**
5/8 = 25/40 and 3/5 = 24/40, so 5/8 is bigger.

**What is the cross-multiplication shortcut?**
a/b > c/d exactly when a·d > c·b (with positive denominators).

**How do I compare fractions with the same numerator?**
The one with the smaller denominator is larger.

**Can I compare by converting to decimals?**
Yes – 0.625 > 0.6 – but common denominators keep it exact.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Fraction](https://mathworld.wolfram.com/Fraction.html)