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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:
- when a negative number is being subtracted, it goes inside parentheses
- the subtraction sign is read as minus
- a negative number like -3 is read as negative three
- even though the same symbol " - " is used both for subtraction and for finding the opposite of a number,
it is read in different ways
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) :
- identify the number being subtracted
Answer: -5
- find the opposite of the number being subtracted
Answer: 5
- 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!
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.