# EVALUATING NUMERICAL EXPRESSIONS

Numerical Expressions :

Numerical Expression is a mathematical statement that involves only numbers along with one or more operation symbols.

• 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)

Problem 1 :

5 + [6 + (7 × 2)] ÷ 5

Solution :

 = 5 + [6 + (7 × 2)] ÷ 5= 5 + [6 + 14] ÷ 5= 5 + 20 ÷ 5= 5 + 4= 9 Inner BracketBracketDivisionAdditionAnswer

Problem 2 :

4 × [(4 × 3) ÷ 2] × 7

Solution :

 = 4 × [(4 × 3) ÷ 2] × 7= 4 × [12 ÷ 2] × 7= 4 × 6 × 7= 168 Inner BracketDivision Multiplication Answer

Problem 3 :

[(2 × 3) + (11 – 5)] ÷ 3

Solution :

 =  [(2 × 3) + (11 – 5)] ÷ 3= [6 + 6] ÷ 3= 12 ÷ 3= 4 Inner Brackets Bracket Division Answer

Problem 4 :

19 – [{3 × 7} – {9 ÷ 3}] + 14

Solution :

 = 19 – [{3 × 7} – {9 ÷ 3}] + 14 = 19 – [21 – {9 ÷ 3}]+ 14= 19 - [21 - 3}] + 14= 19 – 18 + 14= 1 + 14= 15 Set Bracket  Division Bracket Subtraction AdditionAnswer

Problem 5 :

30 ÷ 3 ÷ 5

Solution :

 =  30 ÷ 3 ÷ 5= 10 ÷ 5= 2 From left to right Division Answer

Problem 6 :

18 ÷ 3 + 11 × 2

Solution :

 =  18 ÷ 3 + 11 × 2= 6 +  11 × 2= 6 + 22= 28 DivisionMultiplication AdditionAnswer

Problem 7 :

7 × 4 – 3 × 5

Solution :

 = 7 × 4 – 3 × 5= 28 – 15= 13 Multiplications SubtractionAnswer

Problem 8 :

8 + 6 ÷ 3 × 4

Solution :

 = 8 + 6 ÷ 3 × 4= 8 + 2 × 4= 8 + 8= 16 Division Multiplication AdditionAnswer

Problem 9 :

3 × 4 + 52

Solution :

 = 3 × 4 + 52= 12 + 5 × 5= 12 + 25= 37 MultiplicationSquareAdditionAnswer

Problem 10 :

4 × 32 – (3 + 2)2

Solution :

 = 4 × 32 – (3 + 2)2= 4 × 3 × 3 – 52= 4 × 3 × 3 – 5 × 5= 4 × 9 – 25= 36 – 25= 11 Exponent, inner bracketExponentMultiplicationMultiplicationSubtractionAnswer

Problem 11 :

(5 - 2)2 – 22

Solution :

 = (5 - 2)2 – 22= 32 – 4= 9 – 4= 5 SubtractionSquareSubtractionAnswer

Problem 12 :

(15 – 32) ÷ 3

Solution :

 = (15 – 32) ÷ 3= (15 – 9) ÷ 3= 6 ÷ 3= 2 ExponentBracketDivisionAnswer

Problem 13 :

5 × (22 + 2) + 6

Solution :

 = 5 × (22 + 2) + 6= 5 × (4 + 2) + 6= 5 × 6 + 6= 30 + 6= 36 Brackets, exponentBracketMultiplicationAdditionAnswer

Problem 14 :

35 – 3 × 23 + 7

Solution :

 = 35 – 3 × 23 + 7= 35 – 3 × 8 + 7= 35 – 24 + 7= 42 – 24 = 18 ExponentMultiplicationAdditionSubtractionAnswer

Problem 15 :

(3 × 7 – 5)/2

Solution :

 = (3 × 7 – 5)/2=(21 – 5)/2= 16/2= 8 MultiplicationSubtractionDivisionAnswer

Problem 16 :

[3 × (7 – 5)]/2

Solution :

 = [3 × (7 – 5)]/2= [3 × 2]/2= 6/2= 3 SubtractionMultiplicationDivisionAnswer

Problem 17 :

(56 ÷ 8 – 7)/(56 ÷ (8 – 7)

Solution :

= (56 ÷ 8 – 7)/(56 ÷ (8 – 7))

= (7 – 7)/(56 – 1)

= 0/ 1

= 0

Problem 18 :

[25 – (16 – 11)]/[(12 ÷ 4 + 2)]

Solution :

= [25 – (16 – 11)]/[(12 ÷ 4 + 2)]

= [(25 – 5)]/[(3 + 2)]

= 20/5

= 4

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