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 

If there is any unknown value in the given verbal phrase, replace it by some English alphabet.

Writing Expressions

In each case, write the given verbal phrase as mathematical expression.

Example 1 :

The sum of 5 times a number and 8

Solution :

5x + 8

Example 2 :

2 times the sum of 7 times a number and 4

Solution :

2(7x + 4)

Example 3 :

7 less than 4 times a number

Solution :

4x - 7

Example 4 :

One fifth of sum of 3 times a number and 9

Solution :

(3x + 9) / 5

Example 5 :

One seventh of 3 less than 4 times a number

Solution :

(4x - 3) / 7

Example 6 :

5 times of a number is decreased by 8

Solution :

5x - 8

Example 7 :

6 times of a number is increased by 15

Solution :

6x + 15

Example 8 :

7 less than 3 times the sum of a number and 6

Solution :

3(x + 6) - 7

Example 9 :

3 times the difference between a number and 8

Solution :

3(x - 8)

Example 10 :

One fourth of 3 times the difference between a number and 6

Solution :

3(x - 6) / 4

Evaluating Expressions

Example 1 :

Evaluate the following expression for x = 3 and y = 5.

3x + 2y

Solution :

Substitute 3 for x and 5 for y into the given expression.

3x + 2y = 3(3) + 2(5)

= 9 + 10

= 19

Example 2 :

Evaluate the following expression for m = 5 and n = 2.

m2 + 2mn2

Solution :

Substitute 5 for m and 2 for n into the given expression.

m2 + 2mn= 52 + 2(5)(2)2

= 25 + 40

= 65

Example 3 :

Evaluate the following expression for s = 5.

s2 + 7s - 2

Solution :

Substitute 5 for s into the given expression.

s2 + 7s - 2 = 52 + 7(5) - 2

= 25 + 35 - 2

= 58

Example 4 :

Evaluate the following expression for m = 1/3.

18m2 + 3m + 7

Solution :

Substitute 1/3 for m into the given expression.

18m2 + 3m + 7 = 18(1/3)2 + 3(1/3) + 7

= 2 + 1 + 7

= 10

Example 5 :

Evaluate the following expression for m = 13.

m2 + m - 54

Solution :

Substitute 13 for s into the given expression.

m2 + m - 54 = 132 + 13 -54

= 169 + 13 - 54

= 128

Example 6 :

Evaluate the following expression for x = 3 and y = 5.

x2 + y2

Solution :

Substitute 3 for x and 5 for y into the given expression.

x2 + y= 32 + 52

= 9 + 25

= 34

Example 7 :

Evaluate the following expression for m = 5 and n = 2.

5m2 + 2m2n

Solution :

Substitute 5 for m and 2 for n into the given expression.

5m2 + 2m2n = 5(5)2 + 2(5)2(2)

5(25) + 2(25)(2)

= 125 + 100

= 225

Example 8 :

Evaluate the following expression for s = 6.

s2 - 3s + 10

Solution :

Substitute 6 for s into the given expression.

s2 - 3s + 10 = 62 - 3(6) + 10

= 36 - 18 + 10

= 28

Example 9 :

Evaluate the following expression for x = 2 and y = -5.

x2 - 3y2

Solution :

Substitute 2 for x and -5 for y into the given expression.

x2 - 3y2  =  2(2)2 - 3(-5)2

=  2(4) - 3(25)

= 8 - 75

= -77

Example 10 :

Evaluate the following expression for m = 3.

(2m2 + 5m - 7)/2

Solution :

Substitute 3 for m into the given expression.

(2m2 + 5m - 7)/2 = [2(3)2 + 5(3) - 7]/2

= [2(9) + 15 - 7]/2

= (18 + 15 - 7)/2

= 26/2

= 13

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