Subtracting Integers

Concept sheet | Mathematics

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
  • The opposite of |-5| is |5|.

  • |30| is the opposite of |-30|.

Use the following method to subtract two numbers.

Rule
  1. First, change the subtraction into an addition where the |2^{nd}| term is the opposite of the |2^{nd}| term of the subtraction.

  2. 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

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

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

The number line
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Answer: |-4-(-8)=-4+8=4|