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Adding and Subtracting Fractions with Unlike Denominators

By John Cabardo 2 min read Math Grade 5

Why you can’t just add the bottom numbers, how to find a common denominator, and worked examples for the fraction skills taught in grade 5.

Circles divided into fraction pieces

In grade 5, children move from adding fractions with the same denominator, like 2/7 + 3/7, to fractions with different ones, like 1/2 + 1/3. This is where many children (and parents) get stuck, usually because the steps are memorized without understanding why they work. This guide explains the idea first, then the method.

The most common mistake

Asked to work out 1/2 + 1/3, many children write 2/5. They add the tops and add the bottoms. It looks reasonable, but a quick check shows it can’t be right: 1/2 on its own is already bigger than 2/5. Adding something to it can’t make it smaller.

Encourage this kind of “does that make sense?” check. Estimating before calculating catches most fraction errors.

Why the denominators must match

The denominator tells you the size of the pieces. Halves and thirds are different sizes, so adding them is like adding 1 apple and 1 orange and calling the answer “2 apples”. Before you can add, you need to cut both fractions into pieces of the same size.

Draw two identical rectangles. Split one into halves and one into thirds. Now split both into sixths: the half becomes 3/6 and the third becomes 2/6. With pieces the same size, the addition is easy: 3/6 + 2/6 = 5/6.

The method, step by step

  1. Find a common denominator. This is a number both denominators divide into. Listing multiples works well: multiples of 4 are 4, 8, 12, 16; multiples of 6 are 6, 12, 18. The first one they share, 12, is the least common denominator.
  2. Make equivalent fractions. Whatever you multiply the bottom by, multiply the top by the same number. For 3/4 → twelfths, multiply both by 3: 9/12. For 1/6 → twelfths, multiply both by 2: 2/12.
  3. Add or subtract the numerators. 9/12 + 2/12 = 11/12. The denominator stays the same, because the size of the pieces doesn’t change.
  4. Simplify if possible. 11/12 can’t be simplified, but an answer like 6/8 should become 3/4.

Worked examples

2/3 + 1/4. Common denominator: 12. 2/3 = 8/12, and 1/4 = 3/12. 8/12 + 3/12 = 11/12.

5/6 − 1/4. Common denominator: 12. 5/6 = 10/12, and 1/4 = 3/12. 10/12 − 3/12 = 7/12.

3/4 + 2/3. Common denominator: 12. 9/12 + 8/12 = 17/12, which is an improper fraction. Write it as a mixed number: 1 5/12.

2 1/2 − 1 2/3. Convert to sixths: 2 3/6 − 1 4/6. You can’t take 4/6 from 3/6, so regroup one whole: 2 3/6 becomes 1 9/6. Then 1 9/6 − 1 4/6 = 5/6.

A shortcut that always works

If finding the smallest common denominator is hard, multiplying the two denominators together always gives a common one. For 3/4 + 1/6, that gives 24ths: 18/24 + 4/24 = 22/24, which simplifies to 11/12. It is more work to simplify at the end, but it is a reliable fallback.

What helps children succeed

  • Times tables. Finding common denominators and simplifying both depend on knowing multiplication facts well. If your child hesitates on facts, a few minutes a day with our times table quiz or multiplication worksheets will make fraction work much smoother.
  • Drawings and fraction strips. Keep using pictures until the method feels obvious. Paper strips folded into halves, quarters and eighths are cheap and effective.
  • Estimate first. Is the answer more or less than 1? More or less than 1/2? This catches most mistakes.
  • Real life. Recipes are full of fractions. “We need 3/4 cup of milk and we’ve used 1/3 cup. How much more?”

Fractions take time. Expect some confusion, keep sessions short, and come back to the drawings whenever the rules stop making sense.

Put it into practice