More addition & subtraction
Adding and subtracting fractions with the same denominator
When fractions have the same denominator (the same bottom number), we can add or subtract them by working only with the numerators (the top numbers). The denominator stays the same.
Adding fractions
Check the denominators are the same. Then add the numerators and keep the denominator the same. For example, 3/5 + 1/5 = 4/5. The bottom number never changes when the denominators match.
Subtracting fractions
Again the denominators must be the same. Subtract the numerators and keep the denominator. For example, 5/6 − 2/6 = 3/6. To find what is left of a whole, write 1 as a fraction: 1 = 5/5, so 1 − 3/5 = 2/5.
Proper and improper fractions
A proper fraction has a numerator smaller than its denominator (less than 1), like 3/5. An improper fraction has a numerator bigger than its denominator (more than 1), like 7/5. When the numerator equals the denominator, the fraction equals 1 whole, like 9/9 = 1.
Worked examples
Adding fractions
- Check the denominators are the same: both are 5.
- Add the numerators: 3 + 1 = 4.
- Keep the denominator the same: 5.
Answer: 3/5 + 1/5 = 4/5
Subtracting from a whole
- A cake in 5 pieces is 5/5 (1 whole).
- 2 pieces are eaten, so subtract 2/5.
- 5/5 − 2/5 = 3/5.
Answer: 3/5 of the cake is left.
Making an improper fraction
- Check the denominators match: both are 9.
- Add the numerators: 5 + 5 = 10.
- Keep the denominator: 10/9. The numerator is bigger than the denominator, so it is improper.
Answer: 5/9 + 5/9 = 10/9 (an improper fraction).
Two fractions that make 1
- The denominators are both 10, and 10/10 = 1.
- Look for two numerators that add to 10.
- 7 + 3 = 10, so 7/10 + 3/10 = 10/10 = 1.
Answer: 7/10 + 3/10 = 1 whole.
Where you see this in real life
- Working out how much of a cake or pizza is left after some slices are eaten.
- Adding two portions of an apple pie that a chef has served.
- Sharing a chocolate bar split into equal pieces.
- Combining fractions of an hour that add up to a whole hour.
Key words
- Numerator
- The top number of a fraction — how many parts you have.
- Denominator
- The bottom number of a fraction — how many equal parts the whole is split into.
- Proper fraction
- A fraction less than 1, where the numerator is smaller than the denominator.
- Improper fraction
- A fraction more than 1, where the numerator is bigger than the denominator.