More fractions
Calculating with fractions
Fractions are numbers too, so you can add and subtract them. When they have the same denominator, it is easy!
Adding same-denominator fractions
When two fractions have the same bottom number, add the top numbers and keep the bottom number the same. For 1/5 + 3/5, add 1 + 3 = 4 and keep the 5, giving 4/5.
The denominator stays the same
Be careful — you do NOT add the bottom numbers. 2/10 + 3/10 = 5/10, not 5/20. The bottom number tells you the size of each piece and it does not change.
Subtracting same-denominator fractions
To subtract, take the top numbers away and keep the bottom the same. For 4/5 - 1/5, do 4 - 1 = 3 and keep the 5, giving 3/5.
Taking a fraction from one whole
One whole can be written as a fraction with equal top and bottom. To work out 1 - 3/10, write 1 as 10/10, then 10/10 - 3/10 = 7/10.
Fractions that make one whole
When the top numbers add up to the bottom number, you get one whole. 1/4 + 3/4 = 4/4 = 1, and 1/3 + 2/3 = 3/3 = 1.
Worked examples
Adding fifths
- Look at 1/5 + 3/5.
- The bottoms are the same, so add the tops: 1 + 3 = 4.
- Keep the bottom number 5.
Answer: 1/5 + 3/5 = 4/5
Subtracting fifths
- Look at 4/5 - 1/5.
- Subtract the tops: 4 - 1 = 3.
- Keep the bottom number 5.
Answer: 4/5 - 1/5 = 3/5
One whole take away a fraction
- Look at 1 - 3/10.
- Write 1 as 10/10.
- Subtract: 10/10 - 3/10 = 7/10.
Answer: 1 - 3/10 = 7/10
Making one whole
- Start with 1/4.
- To reach one whole (4/4), you need 3 more quarters.
- 1/4 + 3/4 = 4/4 = 1.
Answer: 1/4 + 3/4 = 1 whole
Where you see this in real life
- Adding up slices of a pizza that has ten equal slices.
- Working out how much of a chocolate bar is left after eating some.
- Combining fractions of a strip to see if they make one whole.
Key words
- Numerator
- The top number — how many parts you have.
- Denominator
- The bottom number — how many equal parts in the whole.
- Same denominator
- Fractions that have the same bottom number.
- One whole
- A complete shape or amount, like 4/4 or 10/10.
- Estimate
- A sensible guess about the size of the answer before you calculate.