SUBTRACTING INTEGERS

We can see from the number lines shown below, the expressions '5 - 4' and '5 + (-4)' have the same value 1.   

These equivalent expressions suggest the following rule for subtracting integers. 

Words : 

To subtract an integer, add its opposite. 

Numbers : 

5 - 8  =  5 + (-8)  =  -3

Algebra : 

a - b  =  a + (-b)

Subtracting Integers

Example 1 : 

Evaluate :

5 - 11

Solution : 

=  5 - 11

To subtract 11, add its opposite, -11.

=  5 + (-11)

Add 5 and -11.

=  -6

Example 2 : 

Evaluate :

9 - (-5)

Solution : 

=  9 - (-5)

To subtract -5, add its opposite, 5.

=  9 + 5

Add 9 and 5.

=  11

Example 3 : 

Evaluate :

- 3 - (-7)

Solution : 

=  -3 - (-7)

To subtract -7, add its opposite, 7.

=  - 3 + 7

Add -3 and 7.

=  4

Evaluating Variable Expressions

Example 4 : 

Evaluate the following expression when x = -8.

x - (-38)

Solution : 

=  x - (-38)

Substitute -8 for x.

=  - 8 - (-38)

To subtract -38, add its opposite, 38.

=  -8 + 38

Add -8 and 38.

=  30

Example 5 : 

Evaluate the following expression when x = -7.

6 - x

Solution : 

=  6 - x

Substitute -7 for x.

=  6 - (-7)

To subtract -7, add its opposite, 7.

=  6 + 7

Add 6 and 7.

=  13

Evaluating Change

Example 6 :

Mr. John had $2225 account balance in a deposit in 2015 and $3725 in 2020. Find the change in his account balance from 2015 to 2020. 

Solution : 

Substitute values. 

Change in account balance : 

=  3725 - 2225

To subtract 2225, add its opposite, -2225

=  3725 + (-2225)

=  1500

The change in John's account balance from 2015 to 2020 is $1500.

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