8.1 Order of operations
The order in which you carry out operations can make a big difference to the final answer. When doing any calculation that involves doing more than one operation, you must follow the rules of BIDMAS in order to arrive at the correct answer.
Case study _unit2.8.1 B: Brackets
Any calculation that is in brackets must be done first.
Example:
Extract _unit2.8.1
2 × (3 + 5)
2 × 8 = 16
Note that this could also be written as 2 (3 + 5) because if a number is next to a bracket, it means you need to multiply
Case study _unit2.8.2 I: Indices
After any calculations in brackets have been done, you must deal with any calculations involving indices or powers i.e.
Extract _unit2.8.2
32 = 3 × 3
or
43 = 4 × 4 × 4
Example:
Extract _unit2.8.3
3 × 42
3 × (4 × 4)
3 × 16 = 48
Case study _unit2.8.3 D: Divide
Next come any division or multiplication calculations. Of these two calculations, it does not matter which you do first.
Example:
Extract _unit2.8.4
16 − 10 ÷ 5
16 − 2 = 14
Case study _unit2.8.4 M: Multiply
Example:
Extract _unit2.8.5
5 + 6 × 2
5 + 12 = 17
Case study _unit2.8.5 A: Add
Finally, any calculations involving addition or subtraction are done. Again, it does not matter which of these two are done first.
Case study _unit2.8.6 S: Subtract
Example:
Extract _unit2.8.6
24 + 10 − 2
34 − 2 = 32
or
24 + 8 = 32
Activity _unit2.8.1 Activity 18: Using BIDMAS
Now have a go at carrying out the following calculations yourself. Make sure you apply BIDMAS!
4 + 3 × 2
5 (4 − 1)
36 ÷ 32
7 + 15 ÷ 3 − 4
Answer
4 + 6 = 10
5 × 3 = 15
36 ÷ 9 = 4
7 + 5 − 4 = 8
Now that you have learned the rules of BIDMAS you are ready to apply them when using formulas.