LumaMathLumaMathParent-friendly math tools
Explore Fractions

Equivalent fractions method

How to Find Equivalent Fractions

To find equivalent fractions, multiply or divide the numerator and denominator by the same number. Follow one complete example first, then use the same rule to make and check fractions yourself.

Worked example

3/4

Start here
× 2/2

6/8

Same amount

Each fourth is split into two equal eighths. Three shaded fourths become six shaded eighths, but both bars stop at exactly the same point.

Quick answer

The rule in one sentence

To find equivalent fractions, multiply or divide the numerator and denominator by the same non-zero whole number.

Doing the same operation to both numbers changes the size of each equal piece and the number of pieces you count together. Their relationship stays the same, so the fraction still names the same amount.

The method

How to find equivalent fractions in 3 steps

Use 3/4 = 6/8 as your model. You are not making the amount larger. You are giving the same shaded length a new name with more equal pieces.

  1. 1

    Choose the number you need

    Decide what new denominator you want. To change 3/4 into eighths, ask “4 times what equals 8?” The multiplier is 2.

  2. 2

    Multiply the numerator

    Use that multiplier on the top number: 3 × 2 = 6. You are counting the same shaded amount in smaller pieces.

  3. 3

    Multiply the denominator by the same number

    Use exactly the same multiplier on the bottom number: 4 × 2 = 8. Now you can write 3/4 = 6/8.

Make more names for the same amount

How to make equivalent fractions by multiplying

Multiply the top and bottom by the same number when you need a fraction with more equal parts. One half can be renamed as two fourths, three sixths, or four eighths. The denominator grows because every original part is split into smaller equal parts.

Original fraction

1/2

One of two equal parts is shaded.

1/2 × 2/2

2/4

Each half is split into two fourths.

1/2 × 3/3

3/6

Each half is split into three sixths.

1/2 × 4/4

4/8

Each half is split into four eighths.

Notice what did not happen: 1/2 was not multiplied by 2, 3, or 4. It was multiplied by 2/2, 3/3, or 4/4. Each of those fractions equals one, so the value remains one half.

The reverse method

How to simplify equivalent fractions by dividing

Dividing by a common factor gives the same amount a shorter name. This is the reverse of multiplying to make more pieces.

8/12 ÷ 4/4 = 2/3

8/12

÷ 4/4

2/3

Both 8 and 12 divide by 4. Group the twelfths into four equal sets: eight shaded twelfths become two shaded thirds, and twelve total twelfths become three total thirds. The shaded length stays the same.

Check your answer

How to check if fractions are equivalent

Use a picture first while learning, then use a number method when you need a quick homework check. Each method asks whether the two fractions still describe the same point between zero and one.

Compare fraction bars

Draw bars of the same length. If the shaded parts stop at the same point, the fractions name the same amount.

Simplify both fractions

Reduce each fraction by common factors. If both simplify to the same fraction, they are equivalent.

Cross-multiply

For a fast number check, compare diagonal products. With 3/4 and 6/8, 3 × 8 and 4 × 6 both equal 24.

Try it yourself

Practice finding equivalent fractions

Work out the multiplier before opening an answer. When you reveal it, compare the two fraction bars and say what changed: the number of pieces, the size of each piece, or the total shaded amount.

Try this one

1/3 × 2/2 = ?

Try this one

2/5 × 3/3 = ?

Try this one

6/8 ÷ 2/2 = ?

Common mistakes

What can go wrong with equivalent fractions?

Changing only one number

1/2 → 1/4 is not equivalent

The pieces became smaller, but you did not count more of them. Change the numerator and denominator by the same factor.

Thinking a larger denominator means a larger value

1/8 is less than 1/4

When the same whole is split into more equal parts, every part is smaller. The denominator tells you the size of one part, not the total value by itself.

Counting pieces that are not equal

Fourth means four equal parts

A fraction bar only proves an idea when every piece represents the same-sized share of the whole.

Explain it to a child

Use the picture before the rule

Let the child point to the end of the shaded part on both bars. Seeing the matching endpoint makes the multiplication rule mean something instead of feeling like a trick.

“Each part was split into smaller equal parts, so we count more pieces. But the shaded amount did not change.”Then ask: “What changed—the number of pieces, the size of each piece, or the shaded amount?”

Common questions

How to Find Equivalent Fractions FAQ

Multiply the numerator and denominator by the same non-zero whole number. For example, 2/5 multiplied by 3/3 becomes 6/15. You can also divide both numbers by the same common factor to write a simpler equivalent fraction.