Subtracting Integers

Concept sheet | Mathematics

Secondary

1-2

It is important to understand that subtracting a number is the same as adding its opposite.

Definition

Opposite numbers are numbers that have the same absolute value, but are of the opposite sign. The sum of two opposite numbers is always zero.

|4+(-4)=0| and |-4+4=0|

|9+(-9)=0| and |-9+9=0|

Examples

Use the following method to subtract two numbers.

Rule

First, change the subtraction into an addition where the |2^{nd}| term is the opposite of the |2^{nd}| term of the subtraction.
Then perform adding integers using one of the following methods.

Examples

Doing the following subtraction: |-15-(-8)| is equivalent to the following addition: |-15+8|.
To calculate the difference of |-3| and |6|, calculate the sum of |-3| and |-6|.
|5-20=5+(-20)|

After converting the subtraction into an addition, add the terms using any of the methods mentioned above.

Here is an example using the number line method.

Example

Subtract |-4 - (-8)|

1) Change the subtraction into an addition where the |2^e| term is the opposite of the |2^e| term of the subtraction

|-4 - (-8)| becomes |-4 + 8|.

2) Draw a number line

3) Draw a point for the first term of the operation (-4).

4) The second term of the addition is positive |(8)|, so make 8 jumps to the right.

Answer: |-4-(-8)=-4+8=4|