SUBTRACTION OF SIGNED NUMBERS

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
 

In this section, we study problems like $\,-3 - (-5)\,$; that is, problems of the form $\,x - y\,$.
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:
$3 - 5$ the number being subtracted is $\,5\,$;
read aloud as three minus five
$2 - (-3)$ the number being subtracted is $\,-3\,$;
read aloud as two minus negative three
$-1 - 6$ the number being subtracted is $\,6\,$;
read aloud as negative one minus six
$-2 - (-7)$ the number being subtracted is $\,-7\,$;
read aloud as negative two minus negative seven
HOW TO SUBTRACT A NUMBER:

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

THREE STEPS IN A SUBTRACTION PROBLEM:

There are three steps in a subtraction problem.
These steps are illustrated using this example: $\,-3 - (-5)$

  1. identify the number being subtracted
    Answer: $\,-5\,$
  2. find the opposite of the number being subtracted
    Answer: the opposite of $\,-5\,$ is $\,5\,$
  3. rewrite the subtraction problem as addition of the opposite
    Answer: $-3 - (-5) = -3 \ {\bf\color{green}{+}}\ \color{red}{5} = 2$

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

$-3 - 5 + (-2) - (-7) + 4$
$= -3 + (-5) + (-2) + 7 + 4$
$= -10 + 11$
$= 1$

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!

    
(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.
PROBLEM TYPES:
1 2 3 4 5 6
AVAILABLE MASTERED IN PROGRESS

(MAX is 6; there are 6 different problem types.)