Advanced Equivalent Fractions Calculator

Calculator Inputs

Large screens show three columns, smaller screens show two, and phones show one.

Maths Tool

Numerator

Denominator

Decimal Places

Start Multiplier

End Multiplier

Target Denominator

Target Numerator

Compare Numerator

Compare Denominator

Reset

Example Data Table

Sample values below use the fraction 2/3 and multipliers from 1 to 6.

Multiplier	Numerator	Denominator	Equivalent Fraction	Decimal
1	2	3	2/3	0.6667
2	4	6	4/6	0.6667
3	6	9	6/9	0.6667
4	8	12	8/12	0.6667
5	10	15	10/15	0.6667
6	12	18	12/18	0.6667

Formula Used

Equivalent Fraction Formula

Equivalent Fraction = (n × k) / (d × k), where k is any nonzero integer.

Simplification Formula

Simplified Fraction = (n ÷ gcd) / (d ÷ gcd), where gcd is the greatest common divisor of n and d.

Equivalence Test

Two fractions are equivalent when n₁ × d₂ = d₁ × n₂.

Target Denominator Rule

A requested denominator works only when target denominator ÷ simplified denominator is an integer.

How to Use This Calculator

Enter the numerator and denominator of your starting fraction.
Choose decimal places for displayed decimal values.
Set a starting and ending multiplier range.
Optionally enter a target denominator or target numerator.
Optionally enter another fraction for equivalence comparison.
Press the calculate button to generate results.
Review the summary, table, and graph above the form.
Use CSV or PDF export to save your work.

Frequently Asked Questions

1. What are equivalent fractions?

Equivalent fractions look different but represent the same value. For example, 1/2, 2/4, and 4/8 all describe one-half because the numerator and denominator were scaled equally.

2. How does this calculator generate matching fractions?

It multiplies both the numerator and denominator by each selected multiplier. Because both parts change by the same factor, the overall value stays unchanged.

3. Why does the tool also show a simplified fraction?

The simplified fraction gives the lowest whole-number form of the same value. This helps you check accuracy, compare fractions faster, and spot the base ratio used for all equivalents.

4. What happens if I enter a target denominator?

The tool checks whether your requested denominator can be reached by scaling the simplified fraction with a whole-number multiplier. If not, no exact equivalent fraction exists for that denominator.

5. Can this calculator compare two fractions?

Yes. Enter the comparison numerator and denominator. The calculator uses cross multiplication to test whether both fractions represent the same value.

6. Why is denominator zero not allowed?

A denominator of zero makes a fraction undefined. Division by zero has no valid numeric result, so the calculator blocks that input to keep results mathematically correct.

7. What does the graph show?

The graph plots generated numerators and denominators across the selected multipliers. It helps you see the scaling pattern visually while the underlying fraction value remains constant.

8. When is this calculator useful?

It is useful for homework, lesson planning, worksheets, exam revision, and quick checking. Teachers, students, and parents can all use it to verify equivalent fraction patterns quickly.