Quick answer
Equivalent fractions are found by multiplying numerator and denominator by the same number: n/d = (n × k)/(d × k). 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 7/14.
Enter a numerator and denominator. The calculator lists equivalent fractions for multipliers 2 to 7.
Related tools: Compare Fractions Calculator: Which of two fractions is larger? Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers.
How to use the Equivalent Fractions Calculator
- Enter numerator (a whole number, 0 or more).
- Enter denominator (a whole number, 1 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator | A whole number | ≥ 0 |
| Denominator | A whole number | ≥ 1 |
Formula and method
Formula
n/d = (n × k)/(d × k)
IEEE-754 double precision; shown to at most 6 decimal places.
Multiplies numerator and denominator by k = 2…10.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator = 1; Denominator = 2.
| Result | Value |
|---|---|
| Fraction | 1/2 |
| ×2 | 2/4 |
| ×3 | 3/6 |
| ×4 | 4/8 |
| ×5 | 5/10 |
| ×6 | 6/12 |
| ×7 | 7/14 |
The first line is the headline result (fraction). Below it the equivalent Fractions Calculator lists ×2, ×3, ×4, ×5, ×6 and ×7, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Why they are equal
Multiplying top and bottom by k multiplies by k/k = 1, so the value is unchanged. 3/6 and 1/2 both equal 0.5.
Uses
Equivalent fractions are needed to add fractions with different denominators (1/2 + 1/3 uses 3/6 + 2/6). To go the other way, divide by the GCD with the Fraction Simplifier.
How the result changes with numerator
Holding every other input at the first worked example, this table changes only numerator. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator | Fraction | ×2 | ×3 |
|---|---|---|---|
| 1 | 1/2 | 2/4 | 3/6 |
| 2 | 2/2 | 4/4 | 6/6 |
| 4 | 4/2 | 8/4 | 12/6 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator: entering "0" shows "Denominator must be at least 1." beside that field and no result.
Choosing between the Equivalent Fractions Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Compare Fractions Calculator](/math/compare-fractions/) | numerator 1, denominator 1 and numerator 2 | Comparison |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
| [Long Division Calculator](/math/long-division-calculator/) | dividend and divisor | Quotient |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Denominator ≥ 1
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator to confirm this.
Frequently asked questions
What is equivalent to 2/3?
Multiply top and bottom by the same number: 4/6, 6/9 and 8/12 all equal 2/3.
How do I check equivalence?
Cross-multiply: a/b = c/d if ad = bc.
Is 0/5 equal to 0/3?
Yes. Both equal zero because zero divided by any non-zero number is zero.
What does the Equivalent Fractions Calculator calculate?
Fractions equal to a given fraction. It returns Fraction, ×2, ×3, ×4 and ×5.
What formula does the Equivalent Fractions Calculator use?
n/d = (n × k)/(d × k). Multiplies numerator and denominator by k = 2…10.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Denominator ≥ 1.
What is an example of a equivalent Fractions result?
With numerator 1 and denominator 2, the fraction is 1/2.
Related calculators
- Compare Fractions Calculator — Which of two fractions is larger?
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Percent Off Calculator — Find the sale price and savings after a percentage discount.
- Squaring Calculator — Square and cube of a number.
- Modulo Calculator — Remainder of a division, with floored and truncated conventions.
- Cube Root Calculator — Cube root of a number.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.