WRITING AND EVALUATING EXPRESSIONS
In this section, you will learn how to write a mathematical expression from a verbal description and evaluate expressions for the given values of the variables or unknowns.
Writing Expression from a Verbal Phrase
Let us see, how to write a verbal phrase as an expression.
If there is any unknown value in the given verbal phrase, replace it by some English alphabet.
Example 1
Example 2
Example 3
Writing Expressions - Practice Questions
Question 1 :
Write the given verbal phrase into mathematical expression
"The sum of 5 times a number and 8"
Answer :
5x + 8
Question 2 :
Write the given verbal phrase into mathematical expression
"2 times the sum of 7 times a number and 4"
Answer :
2(7x + 4)
Question 3 :
Write the given verbal phrase into mathematical expression
"7 less than 4 times a number"
Answer :
4x - 7
Question 4 :
Write the given verbal phrase into mathematical expression
"One fifth of sum of 3 times a number and 9"
Answer :
(3x + 9) / 5
Question 5 :
Write the given verbal phrase into mathematical expression
"One seventh of 3 less than 4 times a number"
Answer :
(4x - 3) / 7
Question 6 :
Write the given verbal phrase into mathematical expression
"5 times of a number is decreased by 8"
Answer :
5x - 8
Question 7 :
Write the given verbal phrase into mathematical expression
"6 times of a number is increased by 15"
Answer :
6x + 15
Question 8 :
Write the given verbal phrase into mathematical expression
"7 less than 3 times the sum of a number and 6"
Answer :
3(x + 6) - 7
Question 9 :
Write the given verbal phrase into mathematical expression
"3 times the difference between a number and 8"
Answer :
3(x - 8)
Question 10 :
Write the given verbal phrase into mathematical expression
"One fourth of 3 times the difference between a number and 6"
Answer :
3(x - 6) / 4
Evaluating Expressions - Practice Questions
Question 1 :
Evaluate the given expression for x = 3 and y = 5.
3x + 2y
Answer :
Substitute 3 for x and 5 for y into the given expression.
3x + 2y = 3(3) + 2(5)
3x + 2y = 9 + 10
3x + 2y = 19
Question 2 :
Evaluate the given expression for m = 5 and n = 2.
m2 + 2mn2
Answer :
Substitute 5 for m and 2 for n into the given expression.
m2 + 2mn2 = 52 + 2(5)(2)2
m2 + 2mn2 = 25 + 40
m2 + 2mn2 = 65
Question 3 :
Evaluate the given expression for s = 5.
s2 + 7s - 2
Answer :
Substitute 5 for s into the given expression.
s2 + 7s - 2 = 52 + 7(5) - 2
s2 + 7s - 2 = 25 + 35 - 2
s2 + 7s - 2 = 58
Question 4 :
Evaluate the given expression for m = 1/3.
18m2 + 3m + 7
Answer :
Substitute 1/3 for m into the given expression.
18m2 + 3m + 7 = 18(1/3)2 + 3(1/3) + 7
18m2 + 3m + 7 = 2 + 1 + 7
18m2 + 3m + 7 = 10
Question 5 :
Evaluate the given expression for m = 13.
m2 + m - 54
Answer :
Substitute 13 for s into the given expression.
m2 + m - 54 = 132 + 13 -54
m2 + m - 54 = 169 + 13 - 54
m2 + m - 54 = 128
Question 6 :
Evaluate the given expression for x = 3 and y = 5.
x2 + y2
Answer :
Substitute 3 for x and 5 for y into the given expression.
x2 + y2 = 32 + 52
x2 + y2 = 9 + 25
x2 + y2 = 34
Question 7 :
Evaluate the given expression for m = 5 and n = 2.
5m2 + 2m2n
Answer :
Substitute 5 for m and 2 for n into the given expression.
5m2 + 2m2n = 5(5)2 + 2(5)2(2)
5m2 + 2m2n = 5(25) + 2(25)(2)
5m2 + 2m2n = 125 + 100
5m2 + 2m2n = 225
Question 8 :
Evaluate the given expression for s = 6.
s2 - 3s + 10
Answer :
Substitute 6 for s into the given expression.
s2 - 3s + 10 = 62 - 3(6) + 10
s2 - 3s + 10 = 36 - 18 + 10
s2 - 3s + 10 = 28
Question 9 :
Evaluate the given expression for x = 2 and y = -5.
x2 - 3y2
Answer :
Substitute 2 for x and -5 for y into the given expression.
x2 - 3y2 = 2(2)2 - 3(-5)2
x2 - 3y2 = 2(4) - 3(25)
x2 - 3y2 = 8 - 75
x2 - 3y2 = -77
Question 10 :
Evaluate the given expression for m = 3.
(2m2 + 5m - 7) / 2
Answer :
Substitute 3 for m into the given expression.
(2m2 + 5m - 7) / 2 = [2(3)2 + 5(3) - 7] / 2
(2m2 + 5m - 7) / 2 = [2(9) + 15 - 7 ] / 2
(2m2 + 5m - 7) / 2 = (18 + 15 - 7) / 2
(2m2 + 5m - 7) / 2 = 26 / 2
(2m2 + 5m - 7) / 2 = 13
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