Order of operations
Some calculations involve more than one operation (for example adding, subtracting, multiplying or dividing).
The order you carry out these operations in will produce different answers, so the order in which a calculation is carried out is important.
One way to remember the correct order is with the word BODMAS. BODMAS stands for:
- Brackets - take brackets off before doing anything else
- Of - this can mean 'power of', 'square root of' etc
- Division
- Multiplication
- Addition
- Subtraction
Example
What is \(2 + 3 \times 4\) ?
If we calculate the \(2 + 3\) part first, we get:
\((2 + 3) \times 4\)
\(= 5 \times 4 = 20\)
If we calculate the \(3 \times 4\) part first, we get:
\(2 + (3 \times 4)\)
\(= 2 + 12 = 14\)
These are obviously two different answers - but which one is correct?
BODMAS tells us that 'multiplication' comes before 'addition', so the second answer is correct:
\(2 + 3 \times 4 = 2 + 12 = 14\)
Question
What is \(4+(2+3)^2\)?
This calculation involves 'addition', 'brackets' and 'power of'.
BODMAS tells us the order of operation is Brackets then Of then Addition:
- \(4+(2+3)^2\) (remove brackets first)
- \(4+5^2\) (work out power of, in this case 'squared' or 'to the power of \(2\)')
- \(4+25\) (finally, work out the addition)
- \(=29\)