Equivalent Fractions Calculator

What Are Equivalent Fractions?

Equivalent fractions are fractions that look different but represent exactly the same value. You can turn any fraction into an equivalent one by multiplying — or dividing — both the numerator and the denominator by the same non-zero number. Because you are really just multiplying the fraction by a form of 1 (like \(\dfrac{2}{2}\) or \(\dfrac{3}{3}\)), the value itself never changes, even though the numbers look bigger or smaller.

For example, start with \(\dfrac{3}{4}\). Multiply the top and bottom by 2:

$$\dfrac{3}{4} = \dfrac{3 \times 2}{4 \times 2} = \dfrac{6}{8}$$

\(\dfrac{3}{4}\) and \(\dfrac{6}{8}\) are equivalent fractions — they both represent three-quarters of a whole, they simply use different-sized "pieces" to describe it. You can keep going, multiplying by 3, 4, 5, and so on, to generate an entire family of fractions that are all equal to \(\dfrac{3}{4}\): \(\dfrac{9}{12}\), \(\dfrac{12}{16}\), \(\dfrac{15}{20}\), and infinitely more. The "Generate a List" mode above builds this family for you automatically.

Finding a Specific Equivalent Fraction

Sometimes you don't just want a family of equivalent fractions — you need one with a particular denominator or numerator. The most common reason for this is preparing to add or subtract fractions, which requires every fraction in the problem to share a common denominator first. If you already know that a common denominator is, say, 20, you need to know exactly what \(\dfrac{3}{4}\) becomes when written over a denominator of 20.

This calculator solves that with cross-multiplication. If you know the target denominator \(d\) for a fraction \(\dfrac{a}{b}\), the missing numerator is:

$$? = a \times \dfrac{d}{b}$$

If instead you know the target numerator \(c\), the missing denominator is:

$$? = b \times \dfrac{c}{a}$$

Both approaches only produce a true equivalent fraction — one connected by a whole-number multiplier — when the target value divides evenly. The "Find a Specific Equivalent" mode above shows this multiplier explicitly and flags the result whenever it isn't a whole number, since a fraction like \(\dfrac{3}{4}\) cannot be rewritten with a denominator of, say, 10, without changing its value.

Related Calculators

Need to work with fractions in a different way? Try these related tools:

• Fraction Calculator — for adding, subtracting, multiplying, or dividing fractions
• Simplify Fraction — to reduce a fraction to its lowest terms
• Compare Fractions Calculator — to compare or order fractions by size

Frequently Asked Questions

What is an equivalent fraction?

An equivalent fraction is a fraction that has a different numerator and denominator from another fraction but represents the exact same value. You get one by multiplying (or dividing) both the numerator and denominator of the original fraction by the same non-zero number — for example, \(\dfrac{1}{2}\), \(\dfrac{2}{4}\), and \(\dfrac{5}{10}\) are all equivalent fractions.

How do I find an equivalent fraction with a specific denominator?

Divide the target denominator by the original denominator to get the multiplier, then multiply the original numerator by that same multiplier. For \(\dfrac{3}{4}\) with a target denominator of 12, the multiplier is \(12 \div 4 = 3\), so the new numerator is \(3 \times 3 = 9\), giving \(\dfrac{9}{12}\). The "Find a Specific Equivalent" mode above does this automatically and shows every step.

Why would I need equivalent fractions?

The most common reason is finding a common denominator before adding or subtracting fractions. You cannot add \(\dfrac{1}{4}\) and \(\dfrac{1}{6}\) directly because the "pieces" are different sizes, so each fraction is first rewritten as an equivalent fraction over a shared denominator (in this case 12) before the numerators can be combined.

Can every fraction be converted to any target denominator?

No. A fraction can only be rewritten as a true, whole-number equivalent over a target denominator if that target is a whole-number multiple of the original denominator. For example, \(\dfrac{3}{4}\) converts cleanly to a denominator of 8, 12, 16, or 20, but not to a denominator of 10, since \(10 \div 4\) is not a whole number. In that case the calculator will show the exact decimal result and explain that it isn't a whole-number equivalent.

Is 2/4 the same as 1/2?

Yes. \(\dfrac{2}{4}\) and \(\dfrac{1}{2}\) are equivalent fractions — dividing both the numerator and denominator of \(\dfrac{2}{4}\) by their common factor of 2 gives \(\dfrac{1}{2}\), and since dividing top and bottom by the same non-zero number never changes a fraction's value, the two fractions are equal.