Equivalent Fractions

Generate equivalent fractions for any fraction, mixed number, or integer. Create fractions with the same value.

Generate equivalent fractions by multiplying numerator and denominator by the same number. All fractions shown have equal value.

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help_outlineHow to Useexpand_more

This calculator generates a list of fractions that have the same value as your input. You can enter simple fractions like 2/3, mixed numbers like 1 1/2, or even whole numbers like 5.

Accepted Input Formats:

Fraction

2/3 or 15/16

Mixed Number

1 1/2 or 4 5/6

Integer

5 or 28

The Method:

Multiply both the numerator and denominator by the same whole number. Since you're multiplying by a form of 1 (like 2/2 or 3/3), the fraction's value stays the same.

infoWhat is Equivalent Fractions?expand_more

Equivalent fractions are different fractions that represent the exact same portion of a whole. They look different because they have different numerators and denominators, but when you simplify them or convert to decimals, they all give the same value.

Understanding Equivalent Fractions:

Think about 1/2. It means half of something.

But 6/12 is also half, and 50/100 is also half.

They all represent the same amount:

1/2 = 6/12 = 50/100 = 0.5

Making Larger Equivalents

Multiply top and bottom by same number

3/4 × 2/2 = 6/8

Simplifying to Smallest

Divide top and bottom by GCF

6/8 ÷ 2/2 = 3/4

functionsFormulaexpand_more

The Equivalent Fraction Rule:

a/b = (a × n) / (b × n)

where n is any non-zero whole number

Example: Finding Equivalents for 3/4

3/4 × 2/2 = 6/8

3/4 × 3/3 = 9/12

3/4 × 4/4 = 12/16

3/4 × 5/5 = 15/20

3/4 × 6/6 = 18/24

All of these equal 0.75 when converted to decimals.

Why This Works:

Multiplying by n/n is the same as multiplying by 1. Since anything times 1 equals itself, the value doesn't change—only how it's written.

lightbulbExamplesexpand_more

One Half

1/2 =

2/4, 3/6, 4/8, 5/10, 6/12...

Two Thirds

2/3 =

4/6, 6/9, 8/12, 10/15...

Three Quarters

3/4 =

6/8, 9/12, 12/16, 15/20...

Five Eighths

5/8 =

10/16, 15/24, 20/32, 25/40...

Already Simplified

4/6 = 2/3 =

4/6, 6/9, 8/12, 10/15...

Seven Twelfths

7/12 =

14/24, 21/36, 28/48, 35/60...

quizFAQexpand_more

How can I tell if two fractions are equivalent?expand_more

Use cross multiplication: for a/b and c/d, if a × d equals b × c, they're equivalent. Or simplify both fractions to lowest terms—if they match, they're equivalent. For example, 4/6 and 6/9 both simplify to 2/3.

Why are equivalent fractions important?expand_more

You need them to add or subtract fractions (finding common denominators), compare fractions, solve proportions, and scale recipes. They're used constantly in cooking, construction, and everyday math.

What's the simplest form of a fraction?expand_more

The simplest (or lowest) form is when the numerator and denominator share no common factors except 1. For instance, 1/2 is the simplest form of 2/4, 3/6, 4/8, and all their equivalents.

Can I create infinite equivalent fractions?expand_more

Yes! You can multiply by 2/2, 3/3, 4/4, and so on forever. Every fraction has infinitely many equivalents, but only one simplest form.

How do I find a common denominator?expand_more

Find the LCM (least common multiple) of the denominators, then convert each fraction to an equivalent with that denominator. For 1/2 and 1/3, the LCM of 2 and 3 is 6, so use 3/6 and 2/6.

What if I reduce all equivalent fractions?expand_more

They all simplify to the same fraction—the simplest form. That's actually a great way to verify that fractions are equivalent: if they reduce to the same thing, they're equal.