SUBTRACTION OF SIGNED NUMBERS

In this section, we study problems like [beautiful math coming... please be patient] $\,-3 - (-5)\,$; that is, problems of the form [beautiful math coming... please be patient] $\,x - y\,$.
The good news is that every subtraction problem is an addition problem in disguise!
In one easy step, every subtraction problem is changed to an addition problem, which you already know how to solve.

READING SUBTRACTION PROBLEMS ALOUD:

It's important that you can recognize subtraction problems, and read them aloud correctly.
There are several things that you should notice as you study the examples below:

EXAMPLES:
[beautiful math coming... please be patient] $3 - 5$ the number being subtracted is [beautiful math coming... please be patient] $\,5\,$;
read aloud as three minus five
[beautiful math coming... please be patient] $2 - (-3)$ the number being subtracted is [beautiful math coming... please be patient] $\,-3\,$;
read aloud as two minus negative three
[beautiful math coming... please be patient] $-1 - 6$ the number being subtracted is [beautiful math coming... please be patient] $\,6\,$;
read aloud as negative one minus six
[beautiful math coming... please be patient] $-2 - (-7)$ the number being subtracted is [beautiful math coming... please be patient] $\,-7\,$;
read aloud as negative two minus negative seven
HOW TO SUBTRACT A NUMBER:

To subtract a number, you add its opposite.
To subtract [beautiful math coming... please be patient] $\,3\,$, you add [beautiful math coming... please be patient] $\,-3\,$.
To subtract [beautiful math coming... please be patient] $\,-3\,$, you add [beautiful math coming... please be patient] $\,3\,$.
That is, [beautiful math coming... please be patient] $\,x - y = x + (-y)\,$, for all real numbers [beautiful math coming... please be patient] $\,x\,$ and [beautiful math coming... please be patient] $\,y\,$.
(A good way to read this is:   [beautiful math coming... please be patient] $\,x\,$ minus [beautiful math coming... please be patient] $\,y\,$   equals   [beautiful math coming... please be patient] $\,x\,$ plus the opposite of [beautiful math coming... please be patient] $\,y\,$)

THREE STEPS IN A SUBTRACTION PROBLEM:

There are three steps in a subtraction problem.
These steps are illustrated using this example: [beautiful math coming... please be patient] $\,-3 - (-5)$

  1. identify the number being subtracted
    Answer: [beautiful math coming... please be patient] $\,-5\,$
  2. find the opposite of the number being subtracted
    Answer: the opposite of [beautiful math coming... please be patient] $\,-5\,$ is [beautiful math coming... please be patient] $\,5\,$
  3. rewrite the subtraction problem as addition of the opposite
    Answer: [beautiful math coming... please be patient] $-3 - (-5) = -3 + 5 = 2$

Here is a problem with more than two numbers.
Notice that every subtraction is turned into an addition in the first step.

[beautiful math coming... please be patient] $-3 - 5 + (-2) - (-7) + 4$
[beautiful math coming... please be patient] $= -3 + (-5) + (-2) + 7 + 4$
[beautiful math coming... please be patient] $= -10 + 11$
[beautiful math coming... please be patient] $= 1$

Master the ideas from this section
by practicing both exercises at the bottom of this page.

When you're done practicing, move on to:
Mixed Addition and Subtraction of Signed Numbers

 
 

Here, you will practice subtraction problems of the form ‘[beautiful math coming... please be patient] $\,x - y\,$’
where [beautiful math coming... please be patient] $\,x\,$ and [beautiful math coming... please be patient] $\,y\,$ can be any of these numbers: [beautiful math coming... please be patient] $\,-10, -9, -8, \ldots, -1, 0, 1, \ldots, 8, 9, 10\,$.
About half of the problems will involve variables!
Jump to the concept questions exercise

    
(an even number, please)
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
(MAX is 6; there are 6 different problem types.)