Order of Operations
BODMAS
Operations:
"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.
But, when you see something like...
7 + (6 × 52 + 3)
... what part should you calculate first?
Start at the left and go to the right?
Or go from right to left?
Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you can get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:
Order of Operations
Do things in Brackets First
 | 6 × (5 + 3) | = | 6 × 8 | = |
48
| ||
 | 6 × (5 + 3) | = | 30 + 3 | = |
33
| (wrong) |
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract
| 5 × 22 | = | 5 × 4 | = |
20
| ||
| 5 × 22 | = | 102 | = |
100
| (wrong) |
Multiply or Divide before you Add or Subtract
| 2 + 5 × 3 | = | 2 + 15 | = |
17
| ||
| 2 + 5 × 3 | = | 7 × 3 | = |
21
| (wrong) |
Otherwise just go left to right
| 30 ÷ 5 × 3 | = | 6 × 3 | = |
18
| ||
| 30 ÷ 5 × 3 | = | 30 ÷ 15 | = |
2
| (wrong) |
How Do I Remember It All ... ? BODMAS !
B
| Brackets first |
O
| Orders (i.e. Powers and Square Roots, etc.) |
DM
| Division and Multiplication (left-to-right) |
AS
| Addition and Subtraction (left-to-right) |
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