PROBLEM SOLVING USING ORDER OF OPERATIONS

When two or more operations are carried out, which can be performed first.

To avoid this confusion, our mathematicians has found some set of rules followed in order of operations.

Example 1 :

Evaluate :

35 - 10 ÷ 2 x 5 + 3

Solution :

35 - 10 ÷ 2 x 5 + 3

We don't have brackets or parenthesis in this problem.

= 35 - 10 ÷ 2 x 5 + 3 (Division)

= 35 - 5 x 5 + 3 (Multiplication)

= 35 - 25 + 3 (Subtraction)

= 10 + 3 (Addition)

= 13

Example 2 :

Evaluate :

2(3 x 6 - 4) + 7

Solution :

2(3 x 6 - 4) + 7

= 2(3 x 6 - 4) + 7

(Inside the bracket performing multiplication)

= 2(18 - 4) + 7 

(Inside the bracket performing subtraction)

= 2 x 14 + 7 (Multiplication)

= 28 + 7

= 35

Example 3 :

Evaluate :

5 + 4 x 7 + 27 ÷ 9

Solution :

= 5+ 4 x 7 + 27 ÷ 9 (Multiplication comes first)

= 5 + 28 + 27 ÷ 9 (Division)

= 5 + 28 + 3 (Addition)

= 36

Example 4 :

Evaluate :

4 x 3² - (3 + 2)²

Solution :

= 4 x 3² - (3 + 2)² (Bracket)

= 4 x 3²  - (5)²  (Exponents)

= 4 x 9 -  25 (Multiplication)

= 36 - 25 (Subtraction)

= 11

Example 5 :

Evaluate :

(7-3 x 2) ÷ (8 ÷ 4 - 1)

Solution :

= (7- 3 x 2) ÷(8 ÷ 4 - 1)

= (7 - 6) ÷ (8 ÷ 4 - 1)

= (7 - 6) ÷ (2 - 1)

= 1 ÷ 1

= 1

Example 6 :

Evaluate :

19 - [{3 x 7} - {9 ÷ 3}] + 14

Solution :

= 19 - [(3 x 7) - (9 ÷ 3)] + 14

= 19 - [21 - (9 ÷ 3)] + 14

= 19 - [21 - 3] + 14

= 19 - 18 + 14

= 19 - 18 + 14

= 15

Example 7 :

Evaluate :

4 x [(4 x 3) ÷ 2] x 7

Solution :

= 4 x [(4 x 3) ÷ 2] x 7

= 4 x [12 ÷ 2] x 7

= 4 x 6 x 7

= 168

Example 8 :

Evaluate :

5 + [6 + (7 x 2)] ÷ 5

Solution :

= 5 + [6 + (7 x 2)] ÷ 5

= 5 + [6 + 14] ÷ 5

= 5 + 20 ÷ 5

= 5 + 4

= 9

Example 9 :

Evaluate :

5 x 2² + 2 x 3²

Solution :

= 5 x 2² + 2 x 3²

=  5 x 4 + 2 x 9

= 20 + 18

=  38

Example 10 :

Evaluate :

3 - 2² ÷ 2 + 1

Solution :

= 3 - 2² ÷ 2 + 1

= 3 - 4 ÷ 2 + 1

= 3 - 2 + 1

= 1 + 1

= 2

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