# EVALUATE THE NUMERICAL EXPRESSIONS

When two or more operations carried out, different answers can result depending on the order in which the operations are performed.

For example, consider the expression 16 - 10 ÷ 2

 John decided to subtract first then divide.= 6 ÷ 2= 3 Tina decided to divide first then subtract.= 16 - 5= 11

Which answer is correct 3 or 11 ?

To avoid this confusion, we use the concept order of operations.

• Perform operations within Brackets first.(B)
• Then, calculate any part involving Exponents.(E)
• Then, starting from the left, perform all Divisions and Multiplications as you come to them. (D and M)
• Finally, working from the left, perform all Additions and Subtractions. (A and S)

Note :

If an expression contains more than one set of brackets, evaluate the innermost brackets first.

The division line of fractions behaves like a set of brackets. This means that the numerator and denominator must each be found before doing the division

Evaluate the following numerical expression.

Example 1 :

6 x 8 - 18 ÷ (2 + 4)

Solution :

 = 6 x 8 - 18 ÷ (2 + 4)= 6 x 8 - 18 ÷ 6= 6 x 8 - 3= 48 - 3= 45 BracketDivisionMultiplicationSubtraction

Example 2 :

10÷5+20÷(4+1)

Solution :

 = 10÷5+20÷(4+1)= 10÷5+20÷5= 2+20÷5= 2+4= 6 BracketDivisionDivisionAddition

Example 3 :

5 + (2x10-5) - 6

Solution :

 = 5 + (2x10-5) - 6= 5 + (20-5) - 6= 5+15 - 6= 20 - 6= 14 Bracket, MultiplicationSubtractionAdditionSubtraction

Example 4 :

18 - (15÷3+4) + 1

Solution :

 = 18 - (15÷3+4) + 1= 18 - (5+4) + 1= 18 - 9 + 1= 9 +1= 10 Bracket, DivisionBracket, AdditionSubtractionAddition

Example 5 :

(2x3-4) + (33÷11+5)

Solution :

Since we have two set of terms inside the bracket, we will simplify that first.

(2x3-4) + (33÷11+5)

= (6-4) + (3+5)

= 2 + 8

= 10

Example 6 :

(18÷3+3) ÷ (4x4-7)

Solution :

 = (18÷3+3) ÷ (4x4-7)= (6+3) ÷ (16-7)= 9 ÷ 9= 1 Division, MultiplicationAddition, SubtractionDivision

Example 7 :

(50÷5+6) - (8x2-4)

Solution :

= (50÷5+6) - (8x2-4)

= (10+6) - (16-4)

= 16 - 12

= 4

Example 8 :

(10x3-20) + 3(9÷3+2)

Solution :

= (10x3-20) + 3(9÷3+2)

(30-20) + 3(3+2)

= 10+3(5)

= 10+15

= 25

Example 9 :

(7-3x2) ÷ (8÷4-1)

Solution :

= (7-3x2÷ (8÷4-1)

= (7-6÷ (2-1)

= 1 ÷ 1

= 1

Example 10 :

(5+3)x2+10 ÷ (8-3)

Solution :

= (5+3)x2+10 ÷ (8-3)

= 8x2+10÷5

= 16+10÷5

= 16+2

= 18

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