Maths
How do you add and subtract fractions?
Quick answer
To add or subtract fractions, first give them the same denominator. Then add or subtract only the numerators and keep the denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
In one sentence
Fractions can be added or subtracted once they have the same denominator, and then you combine only the numerators.
Explained
The denominator tells you the size of the pieces. The numerator tells you how many pieces you have. You can only add or subtract pieces that are the same size.
Same denominator. Think of pizza cut in sevenths. 2 slices plus 3 slices makes 5 slices, and each slice is still a seventh. So 2/7 + 3/7 = 5/7. The denominator stays the same.
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Different denominators. You need to change at least one fraction so that both have the same denominator. Use a common multiple of the denominators, ideally the smallest. This uses equivalent fractions.
Try 1/2 + 1/3. The smallest number that both 2 and 3 go into is 6.
Step by step
- Find a common denominator.6.
- Rewrite each fraction.1/2 = 3/6 and 1/3 = 2/6.
- Add the numerators.3 + 2 = 5, so the answer is 5/6.
- Simplify if you can.5/6 is already in its simplest form.
Subtracting works the same way. For 3/4 − 1/6, the common denominator is 12. Then 9/12 − 2/12 = 7/12.
Sometimes the answer is an improper fraction, such as 3/5 + 4/5 = 7/5. You can write that as the mixed number 1 2/5: see improper fractions and mixed numbers. Finish by checking whether the answer can be made simpler; see simplifying fractions.
Examples
| Sum | Common denominator | Answer |
|---|---|---|
| 2/7 + 3/7 | 7 | 5/7 |
| 1/2 + 1/4 | 4 | 3/4 |
| 1/2 + 1/3 | 6 | 5/6 |
| 5/6 − 1/3 | 6 | 3/6 = 1/2 |
| 3/4 − 1/6 | 12 | 7/12 |
Common mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. The denominators describe piece size, so they do not get added.
- Changing only the bottom. If you change the denominator, you must change the numerator by the same multiplication.
- Forgetting to simplify. 3/6 is correct but 1/2 is better.
Quick quiz
Adding and subtracting fractions
Check what you know with 4 quick questions.
Question 1 of 4
What is 2/7 + 3/7?
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Related topics
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Simplifying fractions
To simplify a fraction, divide the top and bottom by the same number until you cannot go any further. For example, 12/18 simplifies to 2/3 when you divide both by 6.
Comparing fractions
To compare fractions, check whether they share a denominator or a numerator, or rewrite them with a common denominator. The bigger fraction is the one with more of the whole.
Improper fractions and mixed numbers
An improper fraction has a numerator bigger than its denominator, like 7/4. A mixed number shows the same amount as a whole number plus a fraction, like 1 3/4.
The 24-hour clock
The 24-hour clock counts the hours from 00:00 at midnight to 23:59, so there is no am or pm. For afternoon times, add 12: 3 pm is 15:00.