# Equivalent Fractions Calculator

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

> The equivalent fractions calculator lists fractions equal to a given fraction, or checks whether two fractions are equivalent using cross products.

## Inputs

- I want to…
- Numerator
- Denominator
- Number of equivalent fractions
- Second numerator
- Second denominator

## Results

- Result
- Equivalent fractions / cross products
- Simplest form

## Formula

```
a/b = (k·a)/(k·b) for any k ≠ 0;  a/b = c/d ⇔ a·d = b·c
```

## Explanation

Equivalent fractions name the same amount in different ways: 2/3 = 4/6 = 6/9. They are needed to add fractions, compare them and simplify answers.

### How to use the Equivalent Fractions Calculator

- **I want to…**
- **Numerator**
- **Denominator**
- **Number of equivalent fractions**
- **Second numerator**
- **Second denominator**

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

### How it works

Multiplying the numerator and denominator by the same number gives an equivalent fraction. Two fractions are equivalent exactly when their cross products are equal.

## Worked example

Inputs — I want to…: Find equivalent fractions; Numerator: 2; Denominator: 3; Number of equivalent fractions: 10.

Results — **Result = 2/3 in lowest terms**; Equivalent fractions / cross products = 2/3, 4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, 18/27, 20/30; Simplest form = 2/3.

## Key terms

- **Equivalent fractions**: Different fractions with the same value.

## FAQ

**Are 2/3 and 10/15 equivalent?**
Yes: 2 × 15 = 30 = 3 × 10.

**How do I find an equivalent fraction with denominator 12 for 3/4?**
Multiply top and bottom by 3: 9/12.

**Is there a "simplest" equivalent fraction?**
Yes – the one in lowest terms.

**Do equivalent fractions have the same decimal?**
Yes.


## Sources

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