GEMDAS ORDER OF OPERATIONS

Gemdas order of operations :

A rule is needed to let us know which operation to perform first. This rule is called GEMDAS. What does GEMDAS stand for ?

Step 1 :

Evaluate expressions inside grouping symbols.

Step 2 :

Evaluate all powers.

Step 3 :

Do all multiplications and divisions from left to right.

Step 4 :

Do all additions and subtractions from left to right.

Let us see some examples to understand the above concept.

Example 1 :

Evaluate the following expression

15 ÷  5 - 4²

Solution :

=  15 ÷  5 - 4² (Evaluate powers)

=  15 ÷  5 - 16

=  15 ÷  5 - 16 (Perform division, 15/3  = 5)

=   5 - 16 (Perform multiplication, 5(5)  = 25)

=  25 - 16 (Perform subtraction)

=  9

Example 2 :

Evaluate the following expression

2 [5  + (30 ÷  6)²]

Solution :

=  2 [5  + (30 ÷ 6)²] (Evaluate inner most bracket)

=  2 [5  + 5²] (Evaluate the power)

=  2 [5  + 25] (Grouping)

=  2 

=  60

Example 3 :

Evaluate the following expression

(6 + 4²) / (3² ⋅ 4)

Solution :

=  (6 + 4²) / (3² ⋅ 4) (Evaluate the powers)

=  (6 + 16) / (9 ⋅ 4)

=  22 / 36

=  11/18

Example 4 :

Evaluate the following expression

8 [6² - 3 (2 + 5)] ÷ 8 + 3

Solution :

=  8 [6² - 3 (2 + 5)÷ 8 + 3

=  8 [6² - 3 (7)÷ 8 + 3

=  8 [ - 21] ÷ 8 + 3

=  8 [36 - 21÷ 8 + 3

=  8  ÷ 8 + 3

120 ÷ 8 + 3

=  15 + 3

=  18

Example 5 :

Evaluate the following expression Solution :

=  { [(8 + 5)(6 - 2)²] - (4⋅17 ÷  2) } / [(24 ÷  2) ÷  3)]

Evaluating the signs in the inner most bracket,

=  { [(13)(4)²] - (4⋅17 ÷  2) } / [(24 ÷  2) ÷  3)]

=  { [(13)(4)²] - (4⋅17 ÷  2) } / [12 ÷  3)]

From left to right, we have multiplication first. So we have to multiply 4 by 17 and then divide it by 2.

=  {[(13)(4)²] - (68 ÷  2) }/ [12 ÷  3)]

(4)²  =  16

=  {[(13)(16)] - 34} / [12 ÷  3)]

=  (208 - 34) / 4

=  174 / 4

Dividing both numerator and denominator by 2, we get

=  87/2 After having gone through the stuff given above, we hope that the students would have understood "Gemdas order of operations".

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