Home›11+›Maths›Fractions, decimals and percentages (FDP)›Adding and subtracting fractions
Adding and subtracting fractions
Unlike denominators, mixed numbers, and borrowing from a whole.
Adding and subtracting fractions is easy once the pieces are the same size. In this lesson you will learn how to:
- add and subtract fractions with the same bottom number
- make the pieces the same size when the bottom numbers are different
- finish off an answer: simplify it, and change an improper fraction to a mixed number
- add mixed numbers, carrying a whole when you need to
- subtract mixed numbers, borrowing a whole when there are not enough pieces
1. The same bottom number
Example: 38 + 28
3 eighths and 2 eighths make 5 eighths. Taking away works the same way: 79 − 49 = 39, which simplifies to 13.
Strip adder: tap the strip to add or take away pieces
2. Different bottom numbers
Example: 13 + 14
- Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. The LCM is 12.
- 13 = 412 (multiply the top and bottom by 4) and 14 = 312 (multiply by 3).
Same-size pieces: find a number in both times tables
3. Step by step, then finish off
Example: 56 − 14
- The LCM of 6 and 4 is 12.56 = 1012, 14 = 312
- Take away the tops.1012 − 312 = 712
- 7 and 12 share no factor, so it is finished.712
Example: 34 + 23
- The LCM of 4 and 3 is 12.912 + 812
- Add the tops.1712
- More than 1 whole: 17 ÷ 12 = 1 r 5.1 512
Workshop: add and take away fractions
- Level 1 has the same bottom numbers. Levels 2 to 4 need a common denominator. Level 5 answers are more than 1 whole.
- Two in a row with no slips moves you up a level.
4. Mixed numbers: carrying and borrowing
Example: 2 34 + 1 12
- Add the wholes.2 + 1 = 3
- Add the fractions (12 = 24).34 + 24 = 54 = 1 14
- Carry the whole.3 + 1 14 = 4 14
Example: 3 14 − 1 34
You need to take away 3 quarters, but there is only 1 quarter. Cut up one of the whole pizzas:
becomes
- 3 14 = 2 wholes and 54 (4 quarters from the cut-up pizza, plus 1).
- Take away 1 whole and 3 quarters: 2 − 1 = 1, and 54 − 34 = 24.
Another way: change both to improper fractions (Lesson 3.2): 134 − 74 = 64 = 1 12.
Pizza party: are there enough slices, or do you need to cut up a whole?
5. Mixed number workshop
Levels 1 to 3 add mixed numbers (carrying a whole at level 2). Levels 4 and 5 take them away (borrowing a whole when you need to).
6. Right or wrong?
Each sum was done by a pupil. Some are right. Some have one of the mistakes from this lesson. Can you tell which?
7. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Use rough paper and write each step. Give every answer in its simplest form. Move up when you are getting most of them right.
The mistakes that cost marks
- Adding the bottom numbers. Writing 14 + 13 = 27. make the bottom numbers the same first, then add only the tops: 312 + 412 = 712.
- Changing only the bottom number. Writing 13 as 112. multiply the top and the bottom by the same number: 13 = 412.
- Using a bottom number that is not in both times tables. Using 10 for 14 + 16. 10 is not in the 4 or 6 times tables. Use the LCM, 12.
- Forgetting to carry the whole. Leaving 2 34 + 1 12 as 3 and 54. 54 = 1 14, so carry the 1: 4 14.
- Taking away the small fraction from the big one. Writing 3 14 − 1 34 = 2 24. you cannot take 3 quarters from 1 quarter. Borrow a whole first: 2 54 − 1 34 = 1 12.
- Not finishing off. Leaving 68 or 1712. simplify (34) and change improper fractions to mixed numbers (1 512).
Quick checklist
Tick each one when you can do it without help.
All ticked. Brilliant work! You have finished Lesson 3.3.
Download
Print these and work through them away from the screen.
All of this is free
Every 11+ maths resource on this site is free, with no account needed. Taught sessions are currently GCSE maths only — if you would like a group opened for this subject, join the waiting list and it helps me decide what to run next.
Join the waiting list →