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-and-evaluating-expressions.png

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 11-12 : Evaluate the numerical expression.

Example 11 :

12 + 7 x 10

Solution :

= 12 + 7 x 10

In the numerical expression above, we have two operations : addition and multiplication. According to PEMDAS Rule, we have to do multiplication first, then addition.

= 12 + 70

= 82

Example 12 :

92 - 48 ÷ 12

Solution :

In the given numerical  expression, we have more than two operations. Using PEMDAS Rule, we can carry out the operations one by one as shown below and evaluate.

Evaluation

= 92 - 48 ÷ 12

= 81 - 48 ÷ 12

= 81 - 4

= 77

Operation

Exponent

Divide

Subtract

Result

Example 13-15 : Write a numerical expression for the given verbal phrase and evaluate.

Example 13 :

"The sum of 5 times 9 and 8"

Solution :

= 5x9 + 8

Using PEMDAS Rule,

= 45 + 8

= 53

Example 14 :

"1.5 times the sum of 7 times 4 and 2"

Solution :

= 1.5[7(4) + 2]

Using PEMDAS Rule,

= 1.5[28 + 2]

= 1.5 x 30

= 45

Example 15 :

"12 is multiplied by 3, the result is divided by 18 and 5 is added to the final answer"

Solution :

= [(12 x 3)/18] + 5

Using PEMDAS Rule,

= [36/18] + 5

= 2 + 5

= 7

Example 16 :

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 17 :

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 18 :

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 19 :

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 20 :

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 21 :

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 22 :

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 23 :

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 24 :

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 25 :

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


Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. SAT Math Resources (Videos, Concepts, Worksheets and More)

    Jul 11, 24 05:20 PM

    SAT Math Resources (Videos, Concepts, Worksheets and More)

    Read More

  2. SAT Math Videos (Part - 21)

    Jul 11, 24 05:14 PM

    satmath18.png
    SAT Math Videos (Part - 21)

    Read More

  3. Best Way to Learn Mathematics

    Jul 11, 24 11:59 AM

    Best Way to Learn Mathematics

    Read More