Equivalent Fractions Calculator
This equivalent fractions calculator scales a fraction into many equal fractions, simplifies it, and finds the numerator for a target denominator. Example: 3/4 equals 6/8, 9/12, 12/16 and 15/20.
Example: What do you want: List of equivalent fractions · Numerator 3 · Denominator 4 · Number of multiples 6 → Result: 3/4 is equivalent to 6/8, 9/12, 12/16, 15/20 …. Source: Wikipedia – Bruchrechnung. Updated: .
How it is calculated
Equivalent fractions look different but have the same value, for example 1/2, 2/4 and 50/100. You get them by multiplying numerator and denominator by the same number (scaling up) or dividing both by a common factor (simplifying).
How it works
Scaling by k turns z/n into (z·k)/(n·k). To simplify, divide by the greatest common divisor (GCD) of numerator and denominator; the fraction is then fully reduced. If you want a specific denominator, for instance to add fractions, it must be a multiple of the simplified denominator. The calculator checks this and otherwise names the smallest suitable denominator.
Example
3/4 scaled by 2, 3, 4 and 5 gives 6/8, 9/12, 12/16 and 15/20. For the denominator 20 you need the factor 20 / 4 = 5 and therefore the numerator 3 · 5 = 15. The denominator 10 does not work because 10 / 4 = 2.5 is not a whole number. In reverse, 6/8 simplifies by the GCD 2 to 3/4.
- The decimal value is the same for all equivalent fractions: 3/4 = 0.75.
- A fraction is fully simplified when the GCD of numerator and denominator is 1.
Frequently asked questions
How do you find equivalent fractions?
Multiply numerator and denominator by the same number, such as 2, 3 or 4. 3/4 then becomes 6/8, 9/12 and 12/16.
How do I find the numerator for a given denominator?
Divide the target denominator by the old one and multiply the numerator by that factor. For 3/4 and denominator 20 that is 3 · 5 = 15, so 15/20.
Why does not every denominator work?
Because the factor must be a whole number. For 3/4 only denominators divisible by 4 work; 10 is out.
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