Equivalent Fractions Calculator
Enter any fraction and get a list of fractions that are equal to it in value. Whether you want 1/2 written as 4/8, or a full set of equivalents for 3/4, this calculator makes them in seconds — and shows the simple rule behind them.
What Are Equivalent Fractions?
Equivalent fractions are fractions that look different but have the same value. For example, 1/2 and 4/8 are equivalent. They are written with different numbers, but they are worth the same amount.
Think of a pizza cut into 2 slices. If you eat 1 slice, you have eaten 1/2. Now think of the same pizza cut into 8 slices. If you eat 4 of them, you have eaten 4/8. Both times you ate the same amount of pizza. That is why 1/2 and 4/8 are equivalent.
Every fraction has an endless number of equivalent fractions. For example, 1/2 also equals 2/4, 3/6, 5/10, and many more. They all sit at the same spot on the number line. The only thing that changes is how many pieces the whole is cut into.
How to Make Equivalent Fractions
To make an equivalent fraction, multiply the numerator (top number) and the denominator (bottom number) by the same whole number. Because you multiply both parts by the same number, the value of the fraction stays the same.
For example, take 3/4:
- Multiply the top and bottom by 2: 3/4 = 6/8
- Multiply the top and bottom by 3: 3/4 = 9/12
- Multiply the top and bottom by 4: 3/4 = 12/16
You can keep going forever. You can also work the other way. If the top and bottom share a common factor, you can divide them by that number to get a simpler equivalent fraction. This is how 4/6 becomes 2/3.
Two rules to remember:
- Only multiply or divide. Never add or subtract.
- Always do the same thing to both the top and the bottom. If you add 1 to the top and bottom of 1/2, you get 2/3, which is a different value — not an equivalent fraction.
Steps to Find Equivalent Fractions
- Choose a whole number to multiply by
- Multiply the numerator by that number
- Multiply the denominator by the same number
- Write the results as the new fraction
- Repeat with other numbers to make more equivalent fractions
Example
Input: find equivalent fractions for 2/3
- Multiply top and bottom by 2: 2 × 2 = 4 and 3 × 2 = 6, so 2/3 = 4/6
- Multiply top and bottom by 3: 2 × 3 = 6 and 3 × 3 = 9, so 2/3 = 6/9
- Multiply top and bottom by 4: 2 × 4 = 8 and 3 × 4 = 12, so 2/3 = 8/12
- Multiply top and bottom by 5: 2 × 5 = 10 and 3 × 5 = 15, so 2/3 = 10/15
So the equivalent fractions for 2/3 are 4/6, 6/9, 8/12, 10/15, and more.
How to Check If Two Fractions Are Equivalent
Sometimes you just want to know if two fractions are equal. The easy way is called cross multiplication. Multiply the top of one fraction by the bottom of the other, both ways, and check if the answers match.
For example, check 3/4 and 12/16:
- 3 × 16 = 48
- 4 × 12 = 48
The answers are equal, so 3/4 and 12/16 are equivalent.
Now check 3/4 and 13/16:
- 3 × 16 = 48
- 4 × 13 = 52
The answers are not equal, so these two are not equivalent. You can also turn both fractions into decimals and compare them.
Where You Use Equivalent Fractions
Equivalent fractions are useful in many places:
- Adding and subtracting fractions. You need the same bottom number first, and equivalent fractions help you get there.
- Comparing fractions. Once two fractions share a denominator, you can see which is bigger.
- Scaling recipes. Doubling or halving a recipe uses equivalent fractions.
- Simplifying fractions. This is the same skill in reverse. It turns a large fraction like 18/24 into a simple 3/4.
Frequently Asked Questions
How many equivalent fractions does a fraction have?
An endless number. You can keep multiplying the top and bottom by bigger numbers forever.
Can whole numbers have equivalent fractions?
Yes. Any whole number can be written as a fraction over 1. So 2 is the same as 2/1, which is equal to 4/2, 6/3, and so on.