In this section, we study problems like
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$\,-3 - (-5)\,$; that is, problems of the
form
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$\,x - y\,$.
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:
[beautiful math coming... please be patient] $3 - 5$ | the number being subtracted is
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$\,5\,$; read aloud as three minus five |
[beautiful math coming... please be patient] $2 - (-3)$ | the number being subtracted is
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$\,-3\,$; read aloud as two minus negative three |
[beautiful math coming... please be patient] $-1 - 6$ | the number being subtracted is
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$\,6\,$; read aloud as negative one minus six |
[beautiful math coming... please be patient] $-2 - (-7)$ | the number being subtracted is
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$\,-7\,$; read aloud as negative two minus negative seven |
To subtract a number, you add its opposite.
To subtract
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$\,3\,$, you add
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$\,-3\,$.
To subtract
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$\,-3\,$, you add
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$\,3\,$.
That is,
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$\,x - y = x + (-y)\,$, for
all real numbers
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$\,x\,$ and
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$\,y\,$.
(A good way to read this is:
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$\,x\,$ minus
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$\,y\,$ equals
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$\,x\,$ plus the opposite of
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$\,y\,$)
There are three steps in a subtraction problem.
These steps are illustrated using this example:
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$\,-3 - (-5)$
Here is a problem with more than two numbers.
Notice that every subtraction is turned into an addition in the first step.
Here, you will practice subtraction problems of the form
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$\,x - y\,$’
where
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$\,x\,$ and
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$\,y\,$ can be any of these numbers:
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$\,-10, -9, -8, \ldots, -1, 0, 1, \ldots, 8, 9, 10\,$.
About half of the problems will involve variables!
Jump to the concept questions exercise