Equivalent Fractions Calculator
Enter a fraction and a scale factor to generate an equivalent fraction, see the simplified (lowest-terms) form, the decimal value, and a visual fraction bar.
How does this calculator work?
Equivalent fractions have the same value but different numerators/denominators. Simplify a/b by dividing both by GCD(a,b). Scale to an equivalent by multiplying both by any integer k: (a×k)/(b×k). Enter numerator, denominator and scale factor to generate the equivalent fraction, lowest-terms form, and a table of common multiples.
Formula
How this is calculated
Two fractions are equivalent if they represent the same portion of a whole — i.e., they have the same decimal value. Any fraction n/d can be converted to an equivalent form by multiplying (or dividing) both the numerator and denominator by the same non-zero integer k: (n×k)/(d×k) = n/d. The value does not change because you are multiplying by k/k = 1.
Simplifying (reducing) a fraction means dividing both parts by their greatest common divisor (GCD), the largest integer that divides both evenly. The result is the same fraction in lowest terms, where the numerator and denominator share no common factor other than 1. For example, 6/9 simplifies to 2/3 (GCD = 3), and 2/3 × 4 = 8/12 is an equivalent form.
This calculator first reduces the input to lowest terms using the Euclidean algorithm for GCD, then scales by the chosen factor. It also generates a table of common equivalents (×2 through ×10) for quick reference. The fraction bar visually represents the fraction as a proportion of a whole.
Frequently asked questions
Reduce both fractions to lowest terms and compare: they are equivalent if and only if the simplified forms are identical. Alternatively, cross-multiply: a/b = c/d if and only if a×d = b×c.
Multiplying by k/k is the same as multiplying by 1 (any non-zero number divided by itself equals 1), and multiplying by 1 does not change a value. So (n×k)/(d×k) = n/d × (k/k) = n/d × 1 = n/d.
The greatest common divisor (GCD) of two integers is the largest positive integer that divides both without a remainder. Dividing numerator and denominator by the GCD removes all shared factors at once, leaving a fraction where the only common factor is 1 — the definition of lowest terms.
Also known as
TG we-Calculate Editorial Team. (2026). Equivalent Fractions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/equivalent-fractions-calculator
TG we-Calculate Editorial Team. "Equivalent Fractions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/equivalent-fractions-calculator.
TG we-Calculate Editorial Team, "Equivalent Fractions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/equivalent-fractions-calculator
@misc{wecalculate_equivalent_fractions_calculator, title = {Equivalent Fractions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/equivalent-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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