EVALUATE NUMERICAL EXPRESSIONS INVOLVING INTEGERS

Evaluate numerical expressions involving integers :

Here we are going to learn, how to evaluate linear expressions. To evaluate a linear expression we have to replace each variable by the given value. Then we have to simplify this.

Linear expression means we have the highest power 1 for all the variables that we have in the question.

Let us see some examples problems based on the above topic.

Evaluate numerical expressions involving integers -Examples

Example 1 :

Evaluate the following using the given values.

y ÷ 2 + x, use x = 1 and y = 2

Solution :

Now we have to use order of operation to simplify this further.

According to "BODMAS", we have to perform division and then we can use addition.

   =  4 + 1

   = 5

So, value of the given expression is 5.

Example 2 :

Evaluate the following using the given values.

x + y + y; use x = 9, and y = 10

Solution :

  =  x + y + y

  =  9 + 10 + 10

  = 29

So, value of the given expression is 29.

Example 3 :

Evaluate the following using the given values.

 z(x + y); use x = 6, y = 8, and z = 6

Solution :

  =  z(x + y)

  =  6(6 + 8)

According to "BODMAS", we have to simplify the terms which is inside the bracket. 

  =  6(14)

Now we have to multiply 6 and 14.

  =  84

So, value of the given expression is 84.

Example 4 :

Evaluate the following using the given values.

(y + x) ÷ 2 + x; use x = 1, and y = 1

Solution :

  =  (y + x) ÷ 2 + x

=  (1 + 1) ÷ 2 + 1

Simplify the numbers which are inside the bracket first 

=  2 ÷ 2 + 1

Now we have to divide

  =  1 + 1

  =  2

So, value of the given expression is 2.

Example 5 :

Evaluate the following using the given values.

z − (y ÷ 3 − 1); use y = 3, and z = 7

Solution :

  =  z − (y ÷ 3 − 1)

=  7 − (3 ÷ 3 − 1)

Simplify the numbers which are inside the bracket first 

=  7 − (1 − 1)

=  7 − 0 ==> 7

So, the value of the given expression is 7.

Example 6 :

Evaluate the following using the given values.

 p − (9 − (m + q)); use m = 4, p = 5, and q = 3

Solution :

  =   p − (9 − (m + q))

=  5 − (9 - (4 + 3))

Perform simplification in the inner most bracket.

=  5 − (9 - 7)

=  5 − 2 ==> 3

So,  value of the given expression is 3.

Example 7 :

Evaluate the following using the given values.

 y − (4 − x − y ÷ 2); use x = 3, and y = 2

Solution :

  =    y − (4 − x − y ÷ 2)

 =  2 − (4 − 3 − 2 ÷ 2)

 =  2 − (4 − 3 − 1)

 =  2 − (4 − 4)

 =  2 − 0 ==> 2

So, value of the given expression is 2.

Example 8 :

Evaluate the following using the given values.

y ÷ 5 + 1 + x ÷ 6; use x = 6, and y = 5

Solution :

  =    y ÷ 5 + 1 + x ÷ 6

 =  5 ÷ 5 + 1 + 6 ÷ 6

 =  1 + 1 + 1 ==> 3

So,  value of the given expression is 3.

Example 9 :

Evaluate the following using the given values.

p − (9 − (m + q)); use m = 4, p = 5, and q = 3

Solution :

  =   p − (9 − (m + q))

 =  5  − (9 − (4 + 3))

=  5  − (9 − 7)

=  5  − 2 ==> 3

So, value of the given expression is 3.

Example 10 :

Evaluate the following using the given values.

6q + m − m; use m = 8, and q = 3 

Solution :

  =   6q + m − m

 =  6(3)  + 8 - 8

=  18 + 0 ==> 18

So, value of the given expression is 18.

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