Order of Operations - PEMDAS
Operations
"Operations" means 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?
Warning: Calculate them in the wrong order, and you will get a wrong answer !
So, long ago people agreed to always follow certain rules when doing calculations, and they are:
Order of Operations
Do things in Parentheses First. Example:
 |
|
6 × (5 + 3) |
= |
6 × 8 |
= |
48 |
|
 |
|
6 × (5 + 3) |
= |
30 + 3 |
= |
33 |
(wrong) |
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
|
|
5 × 22 |
= |
5 × 4 |
= |
20 |
|
|
|
5 × 22 |
= |
102 |
= |
100 |
(wrong) |
Multiply or Divide before you Add or Subtract. Example:
|
|
2 + 5 × 3 |
= |
2 + 15 |
= |
17 |
|
|
|
2 + 5 × 3 |
= |
7 × 3 |
= |
21 |
(wrong) |
Otherwise just go left to right. Example:
|
|
30 ÷ 5 × 3 |
= |
6 × 3 |
= |
18 |
|
|
|
30 ÷ 5 × 3 |
= |
30 ÷ 15 |
= |
2 |
(wrong) |
How Do I Remember ? PEMDAS !
|
|
|
|
P |
Parentheses first |
|
E |
Exponents (ie Powers and Square Roots, etc.) |
|
MD |
Multiplication and Division (left-to-right) |
|
AS |
Addition and Subtraction (left-to-right) |
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
|
|
|
After you have done "P" and "E", just go from left to right doing any "M" or "D" as you find them.
Then go from left to right doing any "A" or "S" as you find them. |
 |
You can remember by saying "Please Excuse My Dear Aunt
Sally". |
Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract),
and in Canada they say BEDMAS (Brackets,Exponents,Divide,Multiply,Add,Subtract). It all means the same thing!
It doesn't really matter how you remember it, just so long as you get it right.
Examples
Example: How do you work out 3 + 6 × 2 ?
Multiplication before Addition:
First 6 × 2 = 12, then 3 + 12 = 15
Example: How do you work out (3 + 6) × 2 ?
Parentheses first:
First (3 + 6) = 9, then 9 × 2 = 18
Example: How do you work out 12 / 6 × 3 ?
Multiplication and Division rank equally, so just go left to right:
First 12 / 6 = 2, then 2 × 3 = 6
Oh, yes, and what about 7 + (6 × 52 + 3) ?
| 7 + (6 × 52 + 3) |
|
| 7 + (6 × 25 + 3) |
Start inside Parentheses, and then use Exponents First |
| 7 + (150 + 3) |
Then Multiply |
| 7 + (153) |
Then Add |
| 7 + 153 |
Parentheses completed, last operation is an Add |
| 160 |
DONE ! |
|
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