PEMDAS Overview and explanation

PEMDAS Overview

When you simplify a maths expression, don’t automatically perform operations from left to right, even though that’s how you read English or HIndi. Instead, follow PEMDAS:

Parentheses Do P first
Exponents Then E
Multiplication  or Division Then either M or D
Addition or Subtraction Then either A or S


For 3 + 2 x 4, you do the M first (multiply 2 and 4), then the A (add 3 to the result).
3 + 2 x 4 = 3 + 8 = 11

If you want to force the addition to go first, add parentheses. P always goes first:
(3 + 2) x 4 =5 x 4 = 20

Multiplication and Division are at the same level of importance in PEMDAS , because any Multiplication can be expressed as a Division, and vice versa.
In a sense, Multiplication and Division are two sides of the same coin.
Likewise, Addition and Subtraction are at the same level of importance. Any Addition can be expressed as a Subtraction, and vice versa.


If you have two operations of equal importance, do them left to right.
3 - 2 + 3 =1+3 = 4
Of course, override this order if you have parentheses:
3 - (2 + 3) =3-5 = -2
Now let’s consider a more complicated expression:
3 + 4(5 - 1) - 32 x 2 = ?
Here is the correct order of steps to simplify :  3 + 4(5 - 1) - 32 x 2

First Parentheses 3 + 4(4) —  32 x 2
then Exponents 3 + 4(4) — 9 x 2
then Multiplication or Division 3+16-18
Addition or Subtraction 3 + 16 - 18 = 19 - 18 = 1

Evaluate the following expressions.

1 )   39  - (25 -17 ) =
2)  3 (4 -2 )  ÷ 2 =
3) 15 x 3  ÷ 9 =
4)  (9 - 5) - (4 - 2) =
5)  14 -3 (4 -6 ) =
6) -5 x 1 ÷ 5 =
7)  (4)(—3)(2)(— 1) =
8) 5 - (4 - (3 - (2 - 1))) =
9)  -4 (5) - 12 /(2 + 4) =

10) 17(6)+ 3(6)

Answer 1) 31
39 - (25 - 17) = 39 - 8 = 31

Answer 2) 3
3 x (4 - 2) ÷ 2 = 3 x (2) ÷ 2 = 6 ÷ 2 = 3

Answer 3)  5
15 x 3 ÷ 9 = 45 ÷ 9 = 5

Answer 4)  2
(9 - 5) - (4 - 2) = (4) - (2) = 2

Answer 5)  20
14 - 3 (4 - 6 ) = 14 - 3(-2) = 14 + 6 = 20

Answer 6)  - 1
-5 x 1 ÷ 5 = -5 ÷ 5 = - 1

Answer 7) 24
( 4 ) (-3 )( 2 )(- l) = 24

Answer 8)  3
5 - (4 - (3 - (2 - 1))) = 5 - (4 - (3 - 1)) =  5 - ( 4 - 2 ) = 5 - (2) = 3
Answer 9)  - 22
- 4 ( 5 ) - 12 ÷ ( 2 + 4) = -20 - 12 ÷ (6) = -20 - 2 = -22
Answer 10)  120:
17 (6 ) + 3 (6 ) = 102 + 18 = 120



Tip: To determine whether a product will be positive or negative, count the number of negative terms being multiplied. An even number of negative terms will give you a positive product; an odd number of negative terms will give you
Tip: Start with the inner-most parentheses and be careful about the signs!
Tip: For same level operation take action from left to right.

Now consider some awkward cases like 12/2*3, 12*3/2 and 12/3/2 and 12 – 2 – 3
The real rule is that when the operations are of the same precedence, like ( * and / ) or ( + and - ) you do the operations from left to right. Hence 12/2*3 = (12/2) * 3 = 6 * 3 = 18
 and 12 * 3 / 2 = (12 * 3) / 2 = 26 / 2 = 18
 and 12/3/2 = (12/3)/2 = 4/2 = 2.
The same happens with + and –. So 12 – 2 – 3 = (12 – 2) – 3 = 7

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