EVALUATING NUMERICAL EXPRESSIONS

PEMDAS rule can be used to simplify or evaluate complicated numerical expressions with more than one binary operation easily.

Very simply way to remember  PEMDAS rule :

P ----> Parentheses (or Brackets)

E ----> Exponents 

M ----> Multiplication

D ----> Division

A ----> Addition

S ----> Subtraction

Important Notes :

1. In a particular simplification, if you have both  multiplication and division, do the operations one by one in the order from left to right.

2. Multiplication does not always come before division. We have to do one by one in the order from left to right.

Examples :

16 ÷ 4 x 3 = 4 x 3 = 12

In the above simplification, we have both division and multiplication.

From left to right, we have division first and multiplication next.

So we do division first and multiplication next.

Problem 1 :

Evaluate the following numerical expression.

29 - 5 x 3

Solution :

Problem 2 :

Evaluate the following numerical expression.

(14 + 12) x 3

Solution :

Problem 3 :

Evaluate the following numerical expression.

9² - 15 ÷ 3

Solution :

Problem 4 :

Evaluate the following numerical expression.

5 + 5 x (5 + 7) ÷ 4 - 6

Solution :

Problem 5 :

Evaluate the following numerical expression.

-2(12 ÷ 4 x 3) + 10

Solution :

Problem 6 :

Evaluate the following numerical expression.

6 + [(16 - 4) ÷ (2² + 2)] - 2

Solution :

Problem 7 :

Evaluate the following numerical expression.

(96 ÷ 12) + 14 x (12 + 8) ÷ 2

Solution :

Problem 8 :

Evaluate the following numerical expression.

(93 + 15) ÷ (3 x 4) - 24 + 8

Solution :

Problem 9 :

Evaluate the following numerical expression.

55 ÷ 11 + (18 - 6) x 9

Solution :

Problem 10 :

Evaluate the following numerical expression.

(7 + 18) x 3 ÷ (2 + 13) - 28

Solution :

Problem 11 :

19 - {(3 x 7) - (9 ÷ 3)} + 14

Solution :

= 19 - {(3 x 7) - (9 ÷ 3)} + 14

= 19 - (21 - 3) + 14

= 19 - 18 + 14

= 1 + 14

= 15

So, the answer is 15.

Problem 12 :

[2 x 3 + (11 - 5)] ÷ 3

Solution :

= [2 x 3 + (11 - 5)] ÷ 3

= [2 x 3 + 6] ÷ 3

= [6 + 6] ÷ 3

= 12 ÷ 3

= 4

So, the answer is 4.

Problem 13 :

{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

= 24 x 7

= 168

So, the answer is 168.

Problem 14 :

5 + [13 - (8 ÷ 4)]

Solution :

= 5 + [13 - (8 ÷ 4)]

= 5 + [13 - 2]

= 5 + 11

= 16

So, the answer is 16.

Problem 15 :

[25 - (16 - 11)]  ÷ [12 ÷ 4 + 2]

Solution :

= [25 - (16 - 11)]  ÷ [12 ÷ 4 + 2]

= [25 - 5]  ÷ [3 + 2]

= 20 ÷ 5

= 4

So, the answer is 4.

Replace * with either +, -, x or ÷ to make  a true statement :

Problem 16 :

3 + 15 * 3 = 8

Solution :

3 + 15 * 3 = 8

When * is replaced with +, we get

= 3 + 15 + 3

= 21

It is not equal to 8. So, + is not the replacement.

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