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SUBTRACTION OF SIGNED NUMBERS

Jump right to the exercises!
See the best ALGEBRA PINBALL time for this exercise

The concepts for this exercise are summarized below. For a complete discussion, read the text.

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.

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

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 .

There are three steps in a subtraction problem.
These steps are illustrated using the example  -3 - (-5) :
  1. identify the number being subtracted
    Answer: -5
  2. find the opposite of the number being subtracted
    Answer: 5
  3. rewrite the subtraction problem as addition of the opposite
    Answer: -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.

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

Here, you will practice subtraction problems of the form "x - y"
where  x  and  y  can be any of these numbers: -10, -9, -8, ..., -1, 0, 1, ..., 8, 9, 10 .
About half of the problems will involve variables!

Click on "new problem" to get started!


Subtract:


Put your answer here:


Click here or press "tab" to check your answer:


When you're ready to time yourself, use these buttons.
When you "end timing," you'll get a summary sheet of your results. Good luck!
     


   (press the "BACK" key to return to this page after printing)


CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

Click on "new problem" to get started!
            Want to practice a particular problem type?