Why can't you just add the denominators?

The denominator names the size of the pieces, not how many you have. Adding halves and thirds gives a mix of piece sizes, so you first rename both as sixths: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Do you have to use the least common denominator?

No. Any common multiple works, for example 24 for 1/4 + 1/6. The least common denominator just keeps the numbers small and saves simplifying at the end.

How do you subtract fractions with unlike denominators?

Exactly as you add them: rename both fractions with a common denominator, subtract the numerators, keep the denominator and simplify. For example, 5/6 − 1/4 = 10/12 − 3/12 = 7/12.

How do you add mixed numbers with unlike denominators?

Add the whole numbers, then add the fractions using a common denominator. If the fractions make more than 1, carry a whole. For example, 1 1/2 + 2 1/3 = 3 + 3/6 + 2/6 = 3 5/6.

What grade learns adding fractions with unlike denominators?

In the US Common Core, grade 5 (standard 5.NF.A.1). In England, Year 5 covers denominators that are multiples of the same number, and Year 6 covers any different denominators and mixed numbers.

Is there a free adding fractions with unlike denominators worksheet with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 5 and 6 (Years 6 and 7 in England)

Adding fractions with unlike denominators

Here is how to add and subtract fractions with unlike denominators, step by step, with a fully worked example and a short section on mixed numbers. Try the free practice set below, then print a fresh worksheet with an answer key.

The method, step by step

Find a common denominator: the least common multiple of the two denominators is the easiest choice.
Work out what each denominator must be multiplied by to reach the common denominator.
Multiply the numerator and the denominator of each fraction by that number.
Add or subtract the new numerators and keep the common denominator.
Simplify the answer, and write it as a mixed number if the question asks for one.

CCSS 5.NF.A.1CCSS 5.NF.A.2CCSS 4.NF.B.3.CEngland: Y5 FractionsEngland: Y6 Fractions

Worked example

2/3 + 3/4 = ?

The denominators are 3 and 4. The least common multiple of 3 and 4 is 12.
Multiply the top and bottom of 2/3 by 4: 2/3 = 8/12.
Multiply the top and bottom of 3/4 by 3: 3/4 = 9/12.
Add the numerators: 8/12 + 9/12 = 17/12.
17 and 12 share no common factor except 1, so 17/12 is in simplest form.
As a mixed number, 17/12 = 1 5/12.

Practice now

Question 1 of 100 correct

1/5 + 1/2 = ? Give your answer in simplest form.

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Why you need a common denominator

The denominator tells you the size of each piece, and the numerator counts the pieces. You can only add counts of pieces that are the same size. 3 eighths plus 2 eighths is 5 eighths, just as 3 apples plus 2 apples is 5 apples. But 1 half plus 1 third is not 2 of anything until both are cut into pieces of the same size.

Picture two bars of the same length. One is cut into thirds, the other into quarters. Cut every third into 4 equal pieces and every quarter into 3, and both bars are now in twelfths. Now 2/3 is 8 of those small pieces and 3/4 is 9 of them, so together they make 17 twelfths. That is all a common denominator is: a piece size both fractions can be measured in.

Subtracting and adding fractions with unlike denominators

Subtraction uses exactly the same steps as addition: rename both fractions with a common denominator, then subtract the numerators. These examples get a little harder each time.

One denominator is a multiple of the other: 1/2 + 3/8. Since 8 is a multiple of 2, rename only the half: 1/2 = 4/8, so 4/8 + 3/8 = 7/8.
Neither is a multiple of the other: 5/6 − 1/4. The least common multiple of 6 and 4 is 12, so 10/12 − 3/12 = 7/12.
The answer simplifies: 1/6 + 1/3 = 1/6 + 2/6 = 3/6, which simplifies to 1/2.
The answer is more than 1: 4/5 + 1/2 = 8/10 + 5/10 = 13/10, which is 1 3/10 as a mixed number.
Subtracting and simplifying: 7/10 − 1/5 = 7/10 − 2/10 = 5/10 = 1/2.

Choosing the common denominator

Multiplying the two denominators always gives a common denominator, but not always the smallest one. For 1/4 + 1/6, using 4 × 6 = 24 gives 6/24 + 4/24 = 10/24, which you then simplify to 5/12. Using the least common multiple, 12, gives 3/12 + 2/12 = 5/12 straight away. Both answers are right; the smaller denominator just means smaller numbers and less simplifying.

To find the least common multiple quickly, count up in multiples of the bigger denominator until you reach one the smaller denominator divides into. For 4 and 6: 6, 12. Since 4 goes into 12, the least common multiple is 12.

Adding and subtracting mixed numbers

With mixed numbers, add the whole numbers and the fractions separately, then tidy up. For 2 3/5 + 1 4/5, the wholes make 3 and the fractions make 7/5, which is 1 2/5, so the answer is 4 2/5. If the denominators differ, rename the fractions first: 1 1/2 + 2 1/3 = 3 + 3/6 + 2/6 = 3 5/6.

Subtraction sometimes needs an exchange. In 5 1/4 − 2 3/4 you cannot take 3/4 from 1/4, so exchange one whole for 4/4: 5 1/4 becomes 4 5/4, and 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2. Changing both numbers to improper fractions also works: 21/4 − 11/4 = 10/4 = 2 1/2. The mixed-number questions in the practice set below share a denominator, so you can focus on carrying and exchanging wholes.

Word problems and sense checks

Some questions in the practice set are short word problems. Find the whole first. If a fence is painted 1/3 on Saturday and 1/4 on Sunday, the painted part is 4/12 + 3/12 = 7/12. The whole fence is 1, so 1 − 7/12 = 5/12 is still unpainted.

Estimate before you calculate. 1/2 + 1/3 must be more than 1/2 and less than 1, so an answer of 2/5 is wrong before you even check the working. Comparing with 0, 1/2 and 1 like this is part of the grade 5 standard.

How it is taught in school

In the US, Common Core introduces adding and subtracting fractions with like denominators in grade 4 (4.NF.B.3). Unlike denominators, including mixed numbers, come in grade 5 (5.NF.A.1), along with word problems and using benchmark fractions to judge whether an answer is reasonable (5.NF.A.2).

In England, Year 5 pupils add and subtract fractions whose denominators are multiples of the same number, such as 1/3 + 1/6. In Year 6 they add and subtract fractions with any different denominators, and mixed numbers, using equivalent fractions.

How parents can help

Make sure equivalent fractions are solid first. If your child can't rename 2/3 as 8/12, adding will feel like a trick to memorize.
Use measuring cups. A 1/2 cup and a 1/4 cup together fill a 3/4 cup measure, which shows 2/4 + 1/4 = 3/4 in the kitchen.
Ask for an estimate before every answer: more or less than 1/2? More or less than 1?
Ask your child to explain why 1/2 + 1/3 is not 2/5. Explaining a wrong answer builds more understanding than repeating a right one.
Keep sessions short. Print a fresh worksheet, let your child mark it with the answer key, and read the worked steps together for any they missed.

Common mistakes

Adding the tops and the bottoms: 1/2 + 1/3 = 2/5. A quick check shows it can't be right, because 2/5 is less than 1/2. The real answer is 3/6 + 2/6 = 5/6.
Changing the denominator but not the numerator, for example writing 2/3 as 2/12 instead of 8/12. Whatever you multiply the bottom by, multiply the top by too.
Picking a common denominator that only one denominator goes into, such as 8 for 1/3 + 1/4. Check that both denominators divide into it exactly.
Forgetting to simplify. If the question asks for simplest form, 3/6 must be written as 1/2.
Subtracting the smaller fraction from the bigger one inside a mixed number. In 5 1/4 − 2 3/4, working out 3/4 − 1/4 gives the wrong answer; exchange a whole instead.

Questions people ask

Why can't you just add the denominators?: The denominator names the size of the pieces, not how many you have. Adding halves and thirds gives a mix of piece sizes, so you first rename both as sixths: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Do you have to use the least common denominator?: No. Any common multiple works, for example 24 for 1/4 + 1/6. The least common denominator just keeps the numbers small and saves simplifying at the end.
How do you subtract fractions with unlike denominators?: Exactly as you add them: rename both fractions with a common denominator, subtract the numerators, keep the denominator and simplify. For example, 5/6 − 1/4 = 10/12 − 3/12 = 7/12.
How do you add mixed numbers with unlike denominators?: Add the whole numbers, then add the fractions using a common denominator. If the fractions make more than 1, carry a whole. For example, 1 1/2 + 2 1/3 = 3 + 3/6 + 2/6 = 3 5/6.
What grade learns adding fractions with unlike denominators?: In the US Common Core, grade 5 (standard 5.NF.A.1). In England, Year 5 covers denominators that are multiples of the same number, and Year 6 covers any different denominators and mixed numbers.
Is there a free adding fractions with unlike denominators worksheet with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 1, 2026.

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