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Adding and Subtracting Fractions with Unlike Denominators (Grade 5)
The common-denominator method step by step, worked examples, an online practice with instant checking and printable worksheets with an answer key.
Fractions with different denominators are pieces of different sizes, so you cannot add or subtract the numerators directly. A half and a third are both single pieces, but a half is bigger than a third, so "1 piece + 1 piece" means nothing until the pieces are cut to the same size.
To make the pieces the same size, rewrite both fractions using a common denominator — a number that both denominators divide into evenly. The smallest one is called the least common denominator (LCD). For 1/2 and 1/3, the LCD is 6, because 6 is the smallest number that both 2 and 3 divide into evenly.
Multiply each fraction's numerator and denominator by the same number so its denominator becomes the LCD, then add or subtract the numerators and keep the common denominator. For example, 7/12 - 1/2 becomes 7/12 - 6/12 = 1/12. If the numerator ends up bigger than the denominator, change the answer to a mixed number, and simplify it if the numerator and denominator share a common factor.
To check your answer, estimate first: 3/5 is a bit more than a half and 11/12 is almost a whole, so the sum should be close to one and a half, and 1 31/60 fits. You can also change both fractions to decimals and add those — the decimal sum should match your fraction answer.
Worked examples
56 + 38 = 1524
56 - 12 = 13
17 + 310 = 3170
Practice: solve 10 problems
Examples with answers
| Problem | Answer |
|---|---|
| 16 + 310 | 715 |
| 78 + 79 | 14772 |
| 12 - 110 | 25 |
| 25 + 38 | 3140 |
| 34 + 23 | 1512 |
| 23 - 14 | 512 |
| 13 + 38 | 1724 |
| 12 - 310 | 15 |
| 710 - 13 | 1130 |
| 910 + 1011 | 189110 |
| 38 + 1011 | 12588 |
| 710 - 311 | 47110 |
Common mistakes
Adding the numerators and the denominators without a common denominator gives a wrong answer: 1/2 + 1/3 is not 2/5. Both fractions need the same denominator first: 3/6 + 2/6 = 5/6.
When you multiply to get a common denominator, you must multiply the numerator by the same number. To turn 1/2 into sixths, multiply both parts by 3: 1/2 = 3/6, not 1/6.
If the numerator ends up bigger than the denominator, write it as a mixed number. 7/6 should be written as 1 1/6, not left as 7/6.
Practice in the game
Each right answer builds a tower that defends the fortress. Free, no sign-up, phone or computer.
For parents: practising at home
Practice 5 to 10 problems a day instead of one long session. Ask your child to say each step out loud: find a common denominator, rewrite both fractions, then add or subtract the numerators. If a problem feels hard, go back to multiplication tables and simple equivalent fractions, because finding a common denominator depends on both.
Assign fractions with unlike denominators to a student in ZnayQuest: they practice at home in the game, and you see every mistake, what they answered and the correct answer, so you know which step they get wrong.
FAQ
How do you add fractions with unlike denominators?
Rewrite each fraction with a common denominator, then add or subtract the numerators and keep that denominator. Simplify the answer and change it to a mixed number if needed.
What if the two denominators don't share a common factor?
Multiply the two denominators together — that product is always a common denominator, even if it isn't the smallest one. You can simplify the final answer afterward.
Is it free?
Yes. The lesson, the practice and the worksheets are free, with no sign-up.