Adding fractions with unlike denominators: a parent's guide

Why do fractions need a common denominator before you add them?

You can only add pieces that are the same size. 1/2 and 1/3 are pieces of different sizes, so "1 piece + 1 piece" doesn't tell you how much you have. Cut both into sixths, though, and 1/2 becomes 3/6 and 1/3 becomes 2/6. Now the pieces match, and 3 sixths + 2 sixths = 5/6.

The denominator names the size of the pieces, and the numerator counts them. That's why you add the numerators but keep the denominator: you're counting same-size pieces, not making new ones.

In most US schools, 4th graders add fractions that already share a denominator, and 5th graders add and subtract fractions and mixed numbers with unlike denominators. A child who is solid on equivalent fractions will find this much easier. The fractions topic guide has the bigger picture, and fractions practice by grade shows how the skill builds from 3rd to 6th grade.

How do you add fractions with unlike denominators, step by step?

Use the same four steps every time. Here is 2/5 + 1/3:

1. Find a common denominator. Look for a number both denominators divide into. Listing multiples works: 5, 10, 15 and 3, 6, 9, 12, 15. The smallest shared one is 15.
2. Rename each fraction. 2/5 = 6/15 (multiply top and bottom by 3). 1/3 = 5/15 (multiply top and bottom by 5).
3. Add the numerators, keep the denominator. 6/15 + 5/15 = 11/15.
4. Simplify if you can. 11/15 is already in simplest form.

If one denominator divides into the other, it's quicker: for 3/4 + 1/8, only 3/4 needs renaming, to 6/8, so the sum is 7/8.

When the answer is more than 1, turn it into a mixed number: 2/3 + 3/4 = 8/12 + 9/12 = 17/12, which is 1 5/12. Subtraction works the same way, subtracting the numerators in step 3.

What adding fractions with unlike denominators mistakes do kids make most?

Adding the tops and the bottoms

A child writes 1/2 + 1/3 = 2/5. But 2/5 is less than 1/2, so it can't be the sum of 1/2 and something more. Ask your child to estimate first, then rename to sixths: 3/6 + 2/6 = 5/6.

Changing the denominator but not the numerator

For 3/4 + 1/8, a child turns 3/4 into 3/8 and gets 4/8. Changing only the bottom changes the amount. Whatever you multiply the bottom by, multiply the top by too: 3/4 = 6/8, so the sum is 7/8.

Stopping before the answer is finished

A child works out 1/6 + 1/3 = 1/6 + 2/6 = 3/6 and stops, when the question asks for simplest form. 3/6 simplifies to 1/2. In the same way, 17/12 should become 1 5/12 when a mixed number is asked for. Make "Can I simplify?" the last step every time.

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

Mix estimating with exact answers, so your child can catch their own mistakes.

• Minutes 1–3: estimate first. Ask "Is 1/2 + 2/5 more or less than 1?" (less, since 2/5 is less than 1/2) and "Is 5/6 + 1/4 more or less than 1?" (more).
• Minutes 4–8: five mixed problems. One where one denominator divides the other (1/2 + 1/4), two that need a new denominator (1/2 + 2/5, 3/4 − 1/3), one that needs simplifying (1/6 + 1/2 = 4/6, which simplifies to 2/3), and one that goes past 1 (5/6 + 1/4).
• Minutes 9–10: compare to the estimate. For each answer, check it against the estimate. 5/6 + 1/4 = 13/12 = 1 1/12, which is just over 1, as predicted.

Repeat a few times over the week with new denominators.

How can Easy Twin help with adding 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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