Equivalent fractions: how to help your child practice

What are equivalent fractions?

Equivalent fractions are fractions that look different but stand for the same amount. Half a pizza is the same as 2 slices out of 4, or 4 slices out of 8, so 1/2, 2/4 and 4/8 are equivalent.

The idea behind it: if you cut every piece into the same number of smaller pieces, you get more pieces, but each one is smaller, so the amount doesn't change. That's why you can multiply (or divide) the top and bottom of a fraction by the same number and get an equivalent fraction.

In most US schools, kids explain equivalent fractions with pictures and number lines in 3rd grade, find them by multiplying and dividing in 4th grade, and rely on them to add and subtract fractions with different denominators in 5th grade. See the fractions topic guide for the bigger picture.

How do you find an equivalent fraction, step by step?

Use the same three steps every time, so your child has a routine to fall back on:

1. Pick a number to multiply by. For 2/3, try 2.
2. Multiply the top and the bottom by that same number. 2 × 2 = 4 and 3 × 2 = 6, so 2/3 = 4/6.
3. Check with a picture. Draw a bar split into 3 parts with 2 shaded, then split each part in half. Now there are 6 parts and 4 are shaded, the same amount of the bar.

For a missing-number problem like 3/4 = ?/12, ask "What did 4 get multiplied by to make 12?" (3), then do the same to the top: 3 × 3 = 9, so 3/4 = 9/12.

To simplify, go the other way and divide the top and bottom by the same number: 6/8 ÷ 2 = 3/4.

What equivalent fractions mistakes do kids make most?

Adding the same number to the top and bottom

A child turns 1/2 into 2/3 by adding 1 to each number. Adding doesn't keep the amount the same; multiplying does. Show it with a drawing: 1/2 of a bar is clearly not the same as 2/3 of it.

Changing only one number

For 3/4 = ?/8, a child doubles the bottom to 8 but leaves the top as 3. Have them say the rule out loud each time: "whatever I do to the bottom, I do to the top."

Thinking bigger numbers mean a bigger fraction

Kids often think 4/8 is more than 1/2 because 4 and 8 are bigger numbers. Line up two equal paper strips, one cut into halves and one into eighths, and compare the shaded parts side by side.

How can you practice equivalent fractions at home in 10 minutes?

Short, mixed practice works better than a long session on one kind of problem.

• Minutes 1–3: fold it. Fold a strip of paper in half, shade one half, then fold it again. Ask how many pieces are shaded now (2 of 4) and whether the shaded amount changed.
• Minutes 4–8: five mixed problems. One "which fraction is equal" question, two missing numbers (1/3 = ?/6, 4/5 = ?/10), one simplify (5/10), and one "are these equal?" question (3/6 and 1/2).
• Minutes 9–10: explain one. Have your child tell you why 2/4 = 1/2 using the paper strip. Explaining it is the best check that they understand it, not just the rule.

Repeat a few times over the week with new numbers, so your child practices the skill rather than remembering last night's answers.

How can Easy Twin help with equivalent fractions?

Scan your child's fractions worksheet and Easy Twin makes a twin with the same kinds of questions and new fractions, so practice stays on exactly what the class is learning. Every question comes with two hints and worked steps, number lines are redrawn with new data, and your child can play the twin as a quest or you can print it with an answer key.

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