Equivalent Fractions Calculator
Generate equivalent fractions and check if two fractions represent the same value.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this equivalent fractions calculator
- Enter the numerator and denominator of your fraction in the two input boxes (for example, 1 and 2 for one-half).
- Choose how many equivalent fractions to generate — 3, 5, or 10 — using the dropdown.
- Press Calculate to see the simplified base fraction and a complete chain of equivalents with the multiplier used for each one.
- Switch to Check if Equivalent mode, enter two separate fractions, and press Check to confirm whether they share the same value with a full cross-multiplication breakdown.
- Use Copy to capture the result as plain text, or Reset to clear all fields and start fresh.
About this equivalent fractions calculator
Two fractions are equivalent when they represent exactly the same portion of a whole, even though their numerators and denominators look different. For example, 1/2 and 4/8 both describe one half of something — they sit at the same position on a number line.
The standard way to find equivalent fractions is to multiply both the numerator and the denominator by the same non-zero whole number. Because you are scaling the top and bottom equally, the ratio — and therefore the value — stays unchanged. Starting from 1/2, multiply top and bottom by 2 to get 2/4, by 3 to get 3/6, by 4 to get 4/8, and so on indefinitely. Every fraction in that chain equals 1/2.
To check whether two given fractions are equivalent, use cross-multiplication: multiply the numerator of the first by the denominator of the second, then multiply the numerator of the second by the denominator of the first. If both products are equal, the fractions are equivalent. For instance, comparing 1/2 and 2/4: 1 × 4 = 4 and 2 × 2 = 4, so 4 = 4 confirms they are the same value. If the products differ, the fractions are not equivalent.
This tool first simplifies your input to its lowest-terms base using the greatest common divisor, then scales that base to produce a clean, canonical chain of equivalents.
FAQ
- What are equivalent fractions?
- Equivalent fractions are fractions that represent the same rational value even though their numerators and denominators are different numbers. For example, 1/2, 2/4, 3/6, and 5/10 are all equivalent because they each describe exactly one half.
- How do you find equivalent fractions?
- Multiply both the numerator and the denominator of a fraction by the same non-zero whole number. Because you scale both parts equally, the value of the fraction does not change. Starting from 1/3, multiplying by 2 gives 2/6, multiplying by 3 gives 3/9, and so on.
- How can I check if two fractions are equivalent?
- Use cross-multiplication: multiply the numerator of the first fraction by the denominator of the second, then multiply the numerator of the second by the denominator of the first. If the two products are equal, the fractions are equivalent. If they differ, the fractions have different values.
- Are 2/4 and 1/2 the same?
- Yes. Cross-multiplying gives 2 × 2 = 4 and 1 × 4 = 4, so both products are equal, confirming that 2/4 and 1/2 are equivalent. Simplifying 2/4 by dividing numerator and denominator by their greatest common divisor (2) also yields 1/2 directly.
- Can equivalent fractions be simplified back to one base?
- Yes. Every set of equivalent fractions reduces to a single simplest form — the fraction whose numerator and denominator share no common factor other than 1. This is called the fraction in lowest terms, and it is the unique base for the entire family of equivalents. The tool shows you this base before listing the scaled versions.
- Is the calculator free and private?
- Yes. The equivalent fractions calculator is completely free to use with no account required. All calculations happen directly in your browser; no numbers you enter are sent to any server or stored anywhere.