Adding & subtracting fractions
Adding & subtracting: same denominator
When the bottom numbers match, the pieces are all the same size — so you can just count them.
Add the tops, keep the bottom
When two fractions have the SAME denominator, add or subtract the numerators and leave the denominator alone. 3/10 + 4/10 = 7/10 9/10 − 4/10 = 5/10 The denominator tells you the SIZE of each piece, and that has not changed — only how many you have.
Why the denominator stays
Think of tenths as slices. Three slices plus four slices is seven slices — they are still tenths. A very common mistake is to add the bottoms too: 3/10 + 4/10 = 7/20. That is wrong. Adding two amounts cannot make each piece smaller. If your answer looks smaller than what you started with, check this first.
Simplifying the answer
Always cancel the answer if you can. 5/10 both divide by 5, giving 1/2. 4/12 both divide by 4, giving 1/3. Divide the top and the bottom by the same number until nothing else goes into both.
Answers of 1 or more
If the numerator ends up equal to the denominator, the answer is 1 whole. 4/10 + 6/10 = 10/10 = 1 If it ends up bigger, the answer is more than 1 — an IMPROPER fraction, which you can write as a mixed number. 7/5 = 1 2/5 So before you calculate, you can predict: will the answer be less than 1, exactly 1, or more?
Worked examples
3/10 + 4/10
- The denominators match, so add the numerators.
- 3 + 4 = 7.
- The denominator stays 10.
Answer: 3/10 + 4/10 = 7/10
9/10 − 4/10
- Subtract the numerators: 9 − 4 = 5.
- Keep the denominator: 5/10.
- Simplify: both divide by 5.
Answer: 9/10 − 4/10 = 1/2
The pizza left for Dad
- Eva eats 1/6 and Mia eats 3/6.
- Together they eat 1/6 + 3/6 = 4/6.
- The whole pizza is 6/6, so 6/6 − 4/6 = 2/6.
Answer: 2/6, which simplifies to 1/3
An answer of exactly 1
- 4/10 + 6/10 — add the numerators: 4 + 6 = 10.
- That gives 10/10.
- A fraction with the same top and bottom is 1 whole.
Answer: 4/10 + 6/10 = 1
Finding a missing numerator
- ▢/16 + 12/16 = 19/16.
- The numerators must add to 19.
- 19 − 12 = 7.
Answer: The missing numerator is 7
Where you see this in real life
- Two people eating slices of the same pizza — the slices are all the same size.
- Adding two measurements both given in tenths of a metre.
- Working out how much of a task is left when you have done 3/8 of it.
Key words
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Simplify
- Cancel a fraction to its smallest form.
- Improper fraction
- A fraction whose top is bigger than its bottom.
- Mixed number
- A whole number and a fraction together.
- Whole
- The complete amount, written as a fraction with equal top and bottom.