Use fraction bars
Best when you are learning what “same value” looks like.
Equivalent fractions check
How to Know if Fractions Are Equivalent
Two fractions are equivalent when they represent the same value. Check with fraction bars, by simplifying both fractions, or by cross-multiplying.
Worked check
3/4
same endpoint
6/8
3 × 8 = 24
4 × 6 = 24
Quick answer
How to check if fractions are equivalent
Choose the method that makes the relationship easiest to see. Start with a picture when learning, simplify when common factors are obvious, and use cross-multiplication for a fast number check.
Simplify both fractions
Best when both fractions have common factors you can spot.
Cross-multiply
Best for a quick number check with larger or less familiar fractions.
Method one
Check equivalent fractions with fraction bars
Put equal-length bars under each other. If each bar is divided into equal pieces and the shaded parts stop at the same point, the fractions are equivalent. A number line checks the same idea: both fractions land at the same place.
3/4 = 6/8
3/4
6/8
There are more pieces in the second bar, but the total colored length has not moved.
Method two
Check by simplifying both fractions
Reduce each fraction to simplest form. You may use different factors for the two fractions; the check works when both end at the same simplest fraction.
6/8 → 3/4
Divide both 6 and 8 by 2: 6/8 ÷ 2/2 = 3/4.
8/20 → 2/5
Divide both 8 and 20 by 4. If another fraction also simplifies to 2/5, the two are equivalent.
Method three
Check by cross-multiplying
For a/b and c/d, multiply across the diagonals. Matching products mean the fractions are equivalent. This is fast, but the bars explain why the values match.
Equivalent
3/4 and 6/8
3 × 8 = 24
4 × 6 = 24
The products match, so the fractions are equivalent.
Not equivalent
2/5 and 3/8
2 × 8 = 16
5 × 3 = 15
The products differ, so the fractions do not have the same value.
Try a check
Are these fractions equivalent?
2/5 and 8/20Check answer
Yes, they are equivalent.
Simplify 8/20 by dividing both numbers by 4: 8/20 = 2/5.
8/20 ÷ 4/4 = 2/5
3/6 and 4/8Check answer
Yes, they are equivalent.
Both fractions simplify to one-half.
3/6 = 1/2 and 4/8 = 1/2
2/3 and 3/4Check answer
No, they are not equivalent.
Cross-multiply: the diagonal products are different.
2 × 4 = 8, but 3 × 3 = 9
Avoid these errors
Common mistakes when checking equivalent fractions
Using different-sized wholes
Fraction bars can only be compared when the whole bars have the same length.
Simplifying only one number
Divide the numerator and denominator by the same factor. Changing only one changes the value.
Multiplying the wrong numbers
Cross-multiplication uses diagonals: top left × bottom right, then bottom left × top right.
Explain it to a child
Look for the same stopping point
“Put both fraction bars under each other. If the colored parts stop at the same place, the fractions are equal—even if one bar has more pieces.”Ask: “Can you point to where the shaded color ends on each bar?”
Common questions
How to Check Equivalent Fractions FAQ
Check whether they have the same value. You can compare equal-length fraction bars, simplify both fractions, or cross-multiply the two diagonal pairs.