Quick start
- Type a fraction such as 3/4.
- Optionally type a second fraction to compare, such as 12/16.
- Read the list of equivalent fractions and the comparison result.
What makes fractions equivalent
Two fractions are equivalent when they name the same amount. Multiplying or dividing the top and bottom by the same non-zero number never changes the value. 3/4 = 6/8 = 9/12 = 12/16, because each time both parts were multiplied by the same number.
Checking two fractions
Cross-multiply. For a/b and c/d, they are equal exactly when a × d = b × c. For 3/4 and 12/16: 3 × 16 = 48 and 4 × 12 = 48, so they are equivalent. For 3/4 and 10/14: 42 and 40 differ, so they are not.
Using lowest terms
Another check is to simplify both fractions. If they reduce to the same lowest-terms fraction, they are equivalent. 12/16 and 15/20 both reduce to 3/4.
Where this helps
Equivalent fractions are how you build a common denominator for adding, and how you compare sizes. To see whether 3/5 or 5/8 is bigger, rewrite both over 40: 24/40 and 25/40, so 5/8 is larger.
Common questions
Is 2/3 equivalent to 4/6?
Yes. 2 × 6 = 12 and 3 × 4 = 12.
Can I add the same number to top and bottom?
No. 1/2 and 2/3 are not equal. Only multiplying or dividing keeps the value.
How many equivalent fractions are there?
Infinitely many, one for every whole number you multiply by.