Equivalent Fractions Calculator

Work out equivalent fractions instantly with clear inputs, formula shown and shareable results.

About Equivalent Fractions Calculator

Two fractions are equivalent when one is obtained from the other by multiplying or dividing both parts by the same non-zero number, which leaves the value unchanged. Dividing by the greatest common divisor gives the unique simplest form.

Formulas

Equivalent fractions

a/b = (a·k)/(b·k) for any k ≠ 0

Simplest form

divide both parts by gcd(a, b)

Worked example

With the default values below, Equivalent Fractions Calculator returns Simplest form of 1/4. Change any input above and every figure here is recalculated in your browser.

Inputs used

Numerator: 3
Denominator: 12
Multiply both parts by: 4

Results

Simplest form: 1/4
Scaled equivalent: 12/48
Decimal value: 0.25000000
Greatest common divisor removed: 3

Step by step

1Values used
2Equivalent fractions
3Simplest form
4Simplest form= 1/4
5Scaled equivalent= 12/48
6Decimal value= 0.25000000
7Greatest common divisor removed= 3

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Simplify 3/12?

The gcd is 3, so 3/12 = 1/4.

How can I check two fractions are equivalent?

Cross-multiply: a/b = c/d exactly when ad = bc.