VALUE OF AN ALGEBRAIC EXPRESSION

Sometimes you may assign a definite value to a variable in an algebraic expression to find the value of that expression. This situation arises in many real life problems.

For example, a teacher wants to select 15 students from her class for a competition and she can choose any number of boys and girls.

If x represents the number of boys and y represents the number of grils selected for the competition, then the required algebraic expression to find the total number of participants is (x + y).

Here, the total number of students to be selected is 15 and if only seven girls are interested to participate in the competition, then how many boys should be selected?

Obviously, if y = 7 then

x + 7 = 15

Subtract 8 from both sides.

x = 8

The value x = 8 satisfies the equation. So, the number of boys to be selected is 8.

Follow the steps to obtain the value.

Step 1 :

Study the problem, assign a variable and write the algebraic expression.

Step 2 :

Replace each variable by the given numerical value to obtain an arithmetical expression.

Step 3 :

Simplify the arithmetical expression by PEMDAS Rule.

Step 4 :

The value so obtained is the required value of the expression.

Solved Examples

Examples 1-5 : If p = 5 and q = 6, find the value of the given expression.

Example 1 :

p + q

Solution :

= p + q

Substitute p = 5 and q = 6.

= 5 + 6

= 11

Example 2 :

q - p

Solution :

= q - p

Substitute p = 5 and q = 6.

= 6 - 5

= 1

Example 3 :

2p + 3q

Solution :

= 2p + 3q

Substitute p = 5 and q = 6.

= 2(5) + 3(6)

= 10 + 18

= 28

Example 4 :

pq - p - q

Solution :

= pq - p - q

Substitute p = 5 and q = 6.

= (5)(6) - 5 - 6

= 30 - 5 - 6

= 30 - 11

= 19

Example 5 :

5pq - 1

Solution :

= 5pq - 1

Substitute p = 5 and q = 6.

= 5(5)(6) - 1

= 150 - 1

= 149

Examples 6-8 : If m = 2 and n = -1, find the value of the given expression.

Example 6 :

3m + 2n

Solution :

= 3m + 2n

Substitute m = 2 and n = -1.

= 3(2) + 2(-1)

= 6 - 2

= 4

Example 7 :

2m - n

Solution :

= 2m - n

Substitute m = 2 and n = -1.

= 2(2) - (-1)

= 4 + 1

= 5

Example 8 :

mn - 1

Solution :

= mn - 1

Substitute m = 2 and n = -1.

= 2(-1) - 1

= -2 - 1

= -3

Examples 9-12 : If x = 3 and y = 2, find the value of the given expression.

Example 9 :

4x + 7y

Solution :

= 4x + 7y

Substitute x = 3 and y = 2.

= 4(3) + 7(2)

= 12 + 14

= 26

Example 10 :

3x + 2y - 5

Solution :

= 3x + 2y - 5

Substitute x = 3 and y = 2.

= 3(3) + 2(2) - 5

= 9 + 4 - 5

= 8

Example 11 :

x - y

Solution :

= x - y

Substitute x = 3 and y = 2.

= 3 - 2

= 1

Example 12 :

2x² + 3y²

Solution :

= 2x² + 3y²

Substitute x = 3 and y = 2.

= 2(3²) + 3(2²)

= 2(9) + 3(4)

= 18 + 12

= 30

Examples 13-14 : Write the given verbal statement as algebraic expression and find the value of the expression, if x = -2 and y = 1.

Example 13 :

"Three times the sum of x and y"

Solution :

Three times the sum of x and y :

= 3(x + y)

Substitute x = -2 and y = 1.

= 3(-2 + 1)

= 3(-1)

= -3

Example 14 :

"x is taken away from three times y"

Solution :

x is taken away from three times y :

= 3y - x

Substitute x = -2 and y = 1.

= 3(1) - (-2)

= 3 + 2

= 5

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