Adding and subtracting fractions with unlike denominators
I can add and subtract fractions with different denominators by first rewriting them with a common denominator.
Learn
You drink 1/2 a bottle of water in the morning and 1/3 in the afternoon. How much is gone?
You can only add parts directly when they are the same size. Halves and thirds are different sizes.
Find a common denominator — a number both denominators divide into. For 2 and 3, use 6.
Rewrite each fraction: 1/2 = 3/6 and 1/3 = 2/6. Then add: 3/6 + 2/6 = 5/6.
Subtraction works the same way: 3/4 − 1/6 = 9/12 − 2/12 = 7/12. Simplify your answer if you can.
Worked examples
1/2 + 1/3
- Common denominator: 6.
- 1/2 = 3/6, 1/3 = 2/6.
- 3/6 + 2/6 = 5/6.
3/4 − 1/6
- Multiples of 4: 4, 8, 12. Multiples of 6: 6, 12. Use 12.
- 3/4 = 9/12, 1/6 = 2/12.
- 9/12 − 2/12 = 7/12.
Explore
Show 1/2 with denominator 6 (3/6), then 1/3 with denominator 6 (2/6). Now show their total: 5/6.
Guided practice
Use the hints as much as you like. You can try each question as many times as you need.
0 of 2 solved
What common denominator would you use for 1/4 + 1/6? (Use the smallest.)
1/2 + 1/3 = ?
Independent practice
Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.
0 of 4 solved
3/4 − 1/6 = ?
2/5 + 1/10 in simplest form.
5/6 − 1/4 = ?
2/3 + 3/4 = ? (any form)
Common mistakes
Adding tops and bottoms: 1/2 + 1/3 = 2/5.
Why it happens: 2/5 is less than 1/2, which cannot be right when you added more.
What to do: Rewrite with a common denominator first, then add numerators only.
Changing the denominator but not the numerator: 1/2 = 1/6.
Why it happens: Changing only the denominator changes the size of the fraction.
What to do: Multiply the numerator by the same factor you used for the denominator.
Lesson check
Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.
0 of 3 solved
1/3 + 1/6 in simplest form.
7/8 − 1/2 = ?
3/5 + 2/3 = ? (any form)
Show mastery on your own
Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.
Start mastery check