**Gemdas order of operations :**

A rule is needed to let us know which operation to perform first. This rule is called GEMDAS.

**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 ÷ 3 ⋅ 5 - 4²

**Solution :**

= 15 ÷ 3 ⋅ 5 - **4²
(Evaluate powers) **

**
= **15 ÷ 3 ⋅ 5 - **16**

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

**
= ****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
+ **5**²] (Evaluate the power)

= 2 [**5
+ 25**] (Grouping)

= 2 [30]

= 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 [**6²** - 21] ÷ 8 + 3

= 8 [**36 - 21**] ÷ 8 + 3

= **8 [15] **÷ 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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