Checking with cross products
Two fractions a/b and c/d are equivalent when ad equals bc, assuming nonzero denominators. This cross-product test checks an expanded fraction without converting either value to a rounded decimal.
Math calculator
Equivalent Fractions Calculator
Scale a fraction’s numerator and denominator by the same nonzero integer. The displayed equivalent fraction includes enough working to inspect signs and scale.
Equivalent Fractions inputs
Numerical setup
Situations modeled by Equivalent Fractions
Equivalent forms help create common denominators, resize ratios, and compare work written with different fractional units.
Documenting Equivalent Fractions for the next step
Link Numerator to its Equivalent Fractions role. Link Denominator to its Equivalent Fractions role. The retained Equivalent Fractions formula identifies the Equivalent Fractions model.
Boundary checks for Equivalent Fractions
Reverse Equivalent Fractions through Denominator. Confirm that the reversed Equivalent Fractions step reproduces Numerator.
If Numerator was rounded, mark Denominator as an approximate Equivalent Fractions result. Keep the denominator or reference whole with Equivalent Fractions.
Review Numerator inside the Equivalent Fractions relation. Hold Denominator steady while testing Scale factor. A rough Equivalent fraction gives Equivalent Fractions an independent scale check. Keep the revised Equivalent Fractions inputs beside their own Equivalent fraction.
Cross-checking Equivalent Fractions
An independent estimate makes Equivalent Fractions easier to trust. Derive a rough Equivalent fraction from Numerator and Denominator, then compare its magnitude with the calculated Equivalent fraction. Large disagreement deserves attention before the Equivalent Fractions output is rounded or reused.
Substitute the calculated Equivalent fraction into the defining Equivalent Fractions relationship when that reversal is possible. The recovered value should agree with Numerator under Denominator. A mismatch points to rounding, entry order, or an assumption involving Scale factor.
Units and conventions belong with a Equivalent Fractions answer. Confirm that Numerator and Denominator use the intended interpretation, then label Equivalent fraction the same way. A numerically correct Equivalent fraction can still answer the wrong Equivalent Fractions question when that context changes.
A boundary case can expose a Equivalent Fractions setup error. Choose a simple Numerator, preserve Denominator, and predict Equivalent fraction. If the new Equivalent fraction conflicts with that prediction, inspect the Equivalent Fractions entries before relying on the less convenient case.
Reviewing Equivalent Fractions in context
Equivalent forms preserve a fraction's value while changing its numerator and denominator. For that connected step, see fraction arithmetic.
Questions about Equivalent Fractions
Must the scale factor be an integer?
This page uses integers so the new terms remain integers.
Is 6/10 equivalent to 3/5?
Yes.
Can there be infinitely many equivalents?
Yes; every nonzero integer factor creates another form.
Why is zero excluded?
It would make the new denominator zero.