**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.

**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

Hence the 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

Hence the 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

Hence the 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

Hence the 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

Hence 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

Hence the 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

Hence the 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

Hence the 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

Hence the 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

Hence the value of the given expression is 18.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate numerical expressions involving integers".

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