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Order of operations (BIDMAS/BODMAS)
Evaluating complex calculations with nested brackets and indices.
When a calculation has more than one operation, the order you do them in changes the answer. Mathematicians all over the world use the same order, so everyone gets the same answer. In this lesson you will learn:
- the order of operations, remembered as BIDMAS
- how to work through a calculation one step at a time
- why some operations are equal partners, done from left to right
- how to handle brackets, brackets inside brackets, and indices
- how to solve missing sign and missing bracket puzzles
1. Why we need an order
The order is BIDMAS. Work down the list:
- BBrackets first. Work out whatever is inside them.
- IIndices next: powers like 42 (4 × 4) and 23 (2 × 2 × 2).
- D MDivision and Multiplication, working from left to right.
- A SAddition and Subtraction, working from left to right.
2. One step at a time
Example: 20 − 3 × 4 + 6
- There are no brackets or indices, so multiply first: 3 × 4 = 12.
- Now only − and + are left. Work from left to right: 20 − 12 = 8, then 8 + 6 = 14.
The BIDMAS machine: tap the operation to do first
- Tap the sign (or the power) that BIDMAS says to do next. That part turns into its answer.
- Two with no slips moves you up a level: level 3 brings brackets, level 4 indices, level 5 brackets inside brackets.
3. Equal partners: left to right
Example: 20 − 8 + 2
Adding first (8 + 2 = 10, then 20 − 10) gives 10, which is wrong.
Example: 24 ÷ 4 × 2
Multiplying first (4 × 2 = 8, then 24 ÷ 8) gives 3, which is wrong.
Who is right? Check their working
4. Brackets and indices
Example: 2 × (3 + (8 − 2) ÷ 3)
- The innermost brackets first: 8 − 2 = 6.
- Still inside the brackets, divide before adding: 6 ÷ 3 = 2, then 3 + 2 = 5.
- Finally 2 × 5 = 10.
| Calculation | Working | Answer |
|---|---|---|
| 3 + 42 | The index first: 42 = 16. Then 3 + 16. | 19 |
| (3 + 4)2 | The brackets first: 3 + 4 = 7. Then 72 = 49. | 49 |
Place the brackets: make the calculation true
- Tap the first number to go inside the brackets, then the last. The answer updates as you go.
- Wrong place? Tap Clear the brackets and try another.
5. Missing sign puzzles
Example: 8 ? 2 ? 3 = 19. Which signs go in the gaps?
- 19 is quite big compared with 8, 2 and 3, so try a × somewhere.
- 8 + 2 × 3 = 8 + 6 = 14. Too small.
- 8 × 2 + 3 = 16 + 3 = 19. That works.
Fill the gaps: tap a gap to change its sign
6. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Write each step on rough paper. Move up when you are getting most of them right.
The mistakes that cost marks
- Working straight from left to right. 2 + 3 × 4 = 5 × 4 = 20. multiply before adding: 2 + 12 = 14.
- Doing all the adding before the subtracting. 20 − 8 + 2 = 20 − 10 = 10. equal partners go left to right: 12 + 2 = 14.
- Doing all the multiplying before the dividing. 24 ÷ 4 × 2 = 24 ÷ 8 = 3. left to right: 6 × 2 = 12.
- Treating a power as multiplying. 3 + 42 worked out as 3 + 8 = 11. 42 = 4 × 4 = 16, so the answer is 19.
- Starting with the outside brackets. In 2 × (3 + (8 − 2) ÷ 3), adding 3 + 8 first. start with the innermost brackets: 8 − 2 = 6.
- Losing a number when you rewrite the line. write the whole line again each time, changing only the part you just worked out.
Quick checklist
Tick each one when you can do it without help.
All ticked. Brilliant work! You have finished Lesson 2.4.
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