ConverterHub

Equivalent Fractions Calculator

List the equivalents of a fraction.

Result

6/8, 9/12, 12/16, 15/20, 18/24

How it is calculated

Enter a numerator n, a denominator d and how many equivalents you want. The tool multiplies both parts by the same whole number k, because n/d = (n × k)/(d × k) (the fraction is multiplied by k/k = 1). It lists the results for k = 2, 3, 4 and so on, one for each count requested, separated by commas. The original fraction (k = 1) is not repeated. All three boxes must be whole numbers, and the count must be from 1 to 10. A decimal numerator or denominator, a denominator of 0, a count of 0, 11 or 2.5, and empty boxes show no result. The input fraction is never reduced first (6/8 gives 12/16, 18/24, …), and a negative sign is carried through to every item.

Worked example

Take 3/4 and ask for 5 equivalents. The multipliers are 2, 3, 4, 5 and 6. Doubling gives 3 × 2 = 6 and 4 × 2 = 8, so 6/8. Tripling gives 9/12. Times 4 gives 12/16, times 5 gives 15/20, and times 6 gives 18/24. The tool prints 6/8, 9/12, 12/16, 15/20, 18/24. Each one equals 0.75, which you can confirm by dividing the top by the bottom.

Try this example →

Common mistakes

  • Expecting the original fraction in the list. The first item is already multiplied by 2, so 3/4 itself does not appear.
  • Expecting a simplified form. This tool only scales upward; entering 6/8 gives 12/16 next, not 3/4. To reduce a fraction you need a lowest-terms tool.
  • Changing only the numerator or the denominator by hand. 3/4 and 6/4 are different numbers; both parts must be multiplied by the same factor.
  • Asking for more than 10 equivalents, or for 2.5 of them. The count must be a whole number between 1 and 10, otherwise nothing is returned.
  • Entering a decimal numerator such as 1.5. Decimals are rejected, so convert to a whole-number fraction first (1.5/4 becomes 3/8).

About this calculator

Two fractions are equivalent when they represent the same value even though their numerator and denominator differ — 1/2, 2/4 and 50/100 are all the same quantity written differently. You generate equivalent fractions by multiplying (or dividing) both the numerator and denominator by the same nonzero number, since that operation is mathematically the same as multiplying by 1 and therefore never changes the fraction's actual value.

This is a foundational concept taught in elementary and middle-school math because nearly every fraction operation depends on it: finding a common denominator to add or subtract fractions requires converting them to equivalent forms first, simplifying a fraction to lowest terms is the reverse process (dividing out the greatest common factor), and comparing fractions like 3/4 and 5/8 is only possible once they share a common denominator. Recipe scaling, unit conversion, and probability problems all lean on the same idea of rewriting a ratio without changing what it represents.

Multiply the numerator and denominator by the same whole numbers and you get a list of fractions equal to the one you entered, which makes the pattern plain and helps you spot the form you need.

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