**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.

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.

**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

**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.

m^{2} + 2mn^{2}

**Answer :**

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

m^{2} + 2mn^{2 }= 5^{2} + 2(5)(2)^{2}

m^{2} + 2mn^{2 }= 25 + 40

m^{2} + 2mn^{2 }= 65

**Question 3 :**

Evaluate the given expression for s = 5.

s^{2} + 7s - 2

**Answer :**

Substitute 5 for s into the given expression.

s^{2} + 7s - 2 = 5^{2} + 7(5) - 2

s^{2} + 7s - 2 = 25 + 35 - 2

s^{2} + 7s - 2 = 58

**Question 4 :**

Evaluate the given expression for m = 1/3.

18m^{2} + 3m + 7

**Answer :**

Substitute 1/3 for m into the given expression.

18m^{2} + 3m + 7 = 18(1/3)^{2} + 3(1/3) + 7

18m^{2} + 3m + 7 = 2 + 1 + 7

18m^{2} + 3m + 7 = 10

**Question 5 :**

Evaluate the given expression for m = 13.

m^{2} + m - 54

**Answer :**

Substitute 13 for s into the given expression.

m^{2} + m - 54 = 13^{2} + 13 -54

m^{2} + m - 54 = 169 + 13 - 54

m^{2} + m - 54 = 128

**Question 6 :**

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

x^{2} + y^{2}

**Answer :**

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

x^{2} + y^{2 }= 3^{2} + 5^{2}

x^{2} + y^{2 }= 9 + 25

x^{2} + y^{2 }= 34

**Question 7 :**

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

5m^{2} + 2m^{2}n

**Answer :**

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

5m^{2} + 2m^{2}n = 5(5)^{2} + 2(5)^{2}(2)

5m^{2} + 2m^{2}n = 5(25) + 2(25)(2)

5m^{2} + 2m^{2}n = 125 + 100

5m^{2} + 2m^{2}n = 225

**Question 8 :**

Evaluate the given expression for s = 6.

s^{2} - 3s + 10

**Answer :**

Substitute 6 for s into the given expression.

s^{2} - 3s + 10 = 6^{2} - 3(6) + 10

s^{2} - 3s + 10 = 36 - 18 + 10

s^{2} - 3s + 10 = 28

**Question 9 :**

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

x^{2} - 3y^{2}

**Answer :**

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

x^{2} - 3y^{2 }= 2(2)^{2} - 3(-5)^{2}

x^{2} - 3y^{2 }= 2(4) - 3(25)

x^{2} - 3y^{2 }= 8 - 75

x^{2} - 3y^{2 }= -77

**Question 10 :**

Evaluate the given expression for m = 3.

(2m^{2} + 5m - 7) / 2

**Answer :**

Substitute 3 for m into the given expression.

(2m^{2} + 5m - 7) / 2 = [2(3)^{2} + 5(3) - 7] / 2

(2m^{2} + 5m - 7) / 2 = [2(9) + 15 - 7 ] / 2

(2m^{2} + 5m - 7) / 2 = (18 + 15 - 7) / 2

(2m^{2} + 5m - 7) / 2 = 26 / 2

(2m^{2} + 5m - 7) / 2 = 13

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