EVALUATING NUMERICAL EXPRESSIONS
Numerical Expressions :
Numerical Expression is a mathematical statement that involves only numbers along with one or more operation symbols.
The word BEDMAS may help you to remember this order.
- 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 Bracket Bracket Division Addition Answer |
Problem 2 :
4 × [(4 × 3) ÷ 2] × 7
Solution :
|
= 4 × [(4 × 3) ÷ 2] × 7 = 4 × [12 ÷ 2] × 7 = 4 × 6 × 7 = 168 |
Inner Bracket Division 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 Addition Answer |
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 |
Division Multiplication Addition Answer |
Problem 7 :
7 × 4 – 3 × 5
Solution :
|
= 7 × 4 – 3 × 5 = 28 – 15 = 13 |
Multiplications Subtraction Answer |
Problem 8 :
8 + 6 ÷ 3 × 4
Solution :
|
= 8 + 6 ÷ 3 × 4 = 8 + 2 × 4 = 8 + 8 = 16 |
Division Multiplication Addition Answer |
Problem 9 :
3 × 4 + 52
Solution :
|
= 3 × 4 + 52 = 12 + 5 × 5 = 12 + 25 = 37 |
Multiplication Square Addition Answer |
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 bracket Exponent Multiplication Multiplication Subtraction Answer |
Problem 11 :
(5 - 2)2 – 22
Solution :
|
= (5 - 2)2 – 22 = 32 – 4 = 9 – 4 = 5 |
Subtraction Square Subtraction Answer |
Problem 12 :
(15 – 32) ÷ 3
Solution :
|
= (15 – 32) ÷ 3 = (15 – 9) ÷ 3 = 6 ÷ 3 = 2 |
Exponent Bracket Division Answer |
Problem 13 :
5 × (22 + 2) + 6
Solution :
|
= 5 × (22 + 2) + 6 = 5 × (4 + 2) + 6 = 5 × 6 + 6 = 30 + 6 = 36 |
Brackets, exponent Bracket Multiplication Addition Answer |
Problem 14 :
35 – 3 × 23 + 7
Solution :
|
= 35 – 3 × 23 + 7 = 35 – 3 × 8 + 7 = 35 – 24 + 7 = 42 – 24 = 18 |
Exponent Multiplication Addition Subtraction Answer |
Problem 15 :
(3 × 7 – 5)/2
Solution :
|
= (3 × 7 – 5)/2 =(21 – 5)/2 = 16/2 = 8 |
Multiplication Subtraction Division Answer |
Problem 16 :
[3 × (7 – 5)]/2
Solution :
|
= [3 × (7 – 5)]/2 = [3 × 2]/2 = 6/2 = 3 |
Subtraction Multiplication Division Answer |
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
Problem 19 :
Evaluate the expression −8x + 5 − 2x − 4 + 5x when x = 2 before and after simplifying. Which method do you prefer? Explain
Solution :
Simplifying the expression,
= −8x + 5 − 2x − 4 + 5x
= -8x - 2x + 5x + 5 - 4
= -10x + 5x + 1
= -5x + 1
when x = 2
= -5(2) + 1
= -10 + 1
= -9
Problem 20 :
Find the value of 2x − 1 when x + 6 = 2.
Solution :
Given that, x + 6 = 2
x = 2 - 6
x = -4
Applying the value of x in 2x - 1, we get
= 2(-4) - 1
= -8 - 1
= -9
Problem 21 :
A class of 144 students voted for a class president. Three-fourths of the students voted for you. Of the students who voted for you, 5/9 are female. How many female students voted for you?
a) 50 b) 60 c) 80 d) 108
Solution :
Number of students voted = 144
Number of students voted for you = 3/4 of 144
= 3/4 x 144
= 3 x 36
= 108
Number of female = 5/9 of 108
= 5/9 x 108
= 5 x 12
= 60
So, option b is correct.
Recent Articles
-
Finding Range of Values Inequality Problems
May 21, 24 08:51 PM
Finding Range of Values Inequality Problems -
Solving Two Step Inequality Word Problems
May 21, 24 08:51 AM
Solving Two Step Inequality Word Problems -
Exponential Function Context and Data Modeling
May 20, 24 10:45 PM
Exponential Function Context and Data Modeling