Pre-Algebra

LESSON 6 - Subtracting Integers

*** Attention Students ***
Use the form at the bottom of the page to submit your work.

Now this is a little more tricky at first.  You probably understand the idea of subtraction (1 - 1 = 0) but you may not understand the idea of subtracting a negative number (1 - (- 1) = 2) or the concept of subtracting and getting a negative number (1 - 2 = -1).  Be ready to use your number line from before, and that will help some.  (Two wrongs don't make a right, but two negatives do make a positive.)

Example 1

You have to think this example through as you go, or it'll seem like gibberish.  Also look to the other examples for help.

We will obtain the rule by applying a fundamental law of addition and subtraction..
        Since 9 = 7 + 2
        then 9 - 2 = 7
        and 9 - 7 = 2
or, in general terms:
        if a = b + c
        then a - b = c
        and a - c = b
We have seen that
 
        (-5) + (+3) = -2
                   or
        (-2) = (-5) + (+3)
Therefore:
        (-2) - (-5) = +3
but we know that
        (-2) + (+5) = +3
Therefore comparing the two statements
        -(-5) = (+5)
When nothing is separating the negative signs, then two negatives make a positive: -(-4) = +4. There is nothing but parentheses between the negative signs.

A similar result will clearly hold whatever the numbers.

Therefore we conclude that for any number a

          -(-a) = +a
          Similarly -(-2a) = +2a
           
             
Example 2
      5x - (-3x)
      = 5x + 3x
      = 8x

Example 3
      -2b - (-4b)
      = -2b + 4b
      = 2b

Example 4

To find (-2) - (-5)

Get your number line out to help illustrate this rule.
 
 

If we add a negative number we move to the left along the scale.

      Thus (-2) + (-5) = -7
  Consequently if we subtract a negative number we must move to the right. Starting from (-2) and moving 5 to the right we reach +3, i.e.,
      (-2) - (-5) = -3
To find (-2) - (-5)

  When adding a positive number we move to the right.

  Therefore when subtracting a positive number we move to the left.

  Therefore starting from (-2) we move 5 divisions to the left and read (-7)

  To summarize the rules for addition and subtraction we have:

        +(+a) = (+a)
        +(-a) = (-a)
        -(+a) = (-a)
        -(-a) = (+a)

 

Let's try a couple of word problems together.

Example 5

A elevator starting from the ground floor rises to the fourth floor. Then it descends to the second floor, rises to the sixth floor and finally descends to the ground floor. Express its movements by using positive and negative numbers.

We start at zero (ground), go up to the 4th floor (which is + 4), down to the 2nd floor (which is -2), up to the 6th floor (which is +4) and then down to the ground floor (which is -6)

Therefore: 0 + 4 - 2 + 4 - 6 = 0


Example 6

The movement of the mercury in a thermometer was as follows. Starting at +8 degrees it rose 2 degrees, fell 14 degrees, then rose 4 degrees and finally fell 6 degrees. Express these, using positive and negative signs, and find the final temperature.

We start at +8, go up 2 (which is +2), down 14 (which is - 14), up 4 (which is +4) and down 6 (which is -6)

8 + 2 - 14 + 4 - 6 = -6 degrees

How did you do on these?  Were you able to follow my two examples?

 

 

Pre-Algebra
Lesson 6 Assignment


Do the test below. If you get 3 or fewer wrong, it will be assumed that you understand the lesson, and you can go on immediately to the next lesson.

If you get more than 3 wrong, you will be asked to resubmit the wrong answers and show your work. The teacher will then look at your work and give you advice on what you are doing wrong.


Name:
Enter your correct email address:


Write down the values of:


1.  6 - 2
	 A  8       
	 B  -12       
	 C  -4       
	 D  4       
	 E  -8       
	 F  -6 




2.  6 - (-2)

  
	 A  -8       
	 B  8       
	 C  -12       
	 D  -16       
	 E  4       
	 F  -4 






3.  -6 - 2

  
	 A  12       
	 B  36       
	 C  -4       
	 D  4       
	 E  8       
	 F  -8






4.  -6 - (-2)

  
	 A  -12       
	 B  -8       
	 C  -10       
	 D  4       
	 E  -4       
	 F  12 






5.  0 - (-3)

  
	 A  3       
	 B  -3       
	 C  -9       
	 D  9       
	 E  6       
	 F  0 






6.  -4 - 4

  
	 A  16       
	 B  -16       
	 C  8       
	 D  0       
	 E  4       
	 F  -8






7.  -4 - (-4)

  
	 A  0       
	 B  -16       
	 C  -8       
	 D  16       
	 E  8       
	 F  -4 






8.  -4 - (+4)

  
	 A  0       
	 B  -8       
	 C  8       
	 D  16       
	 E  12       
	 F  -16 






9.  -4 - (-2)

  
	 A  -6       
	 B  6       
	 C  8       
	 D  -2       
	 E  -8       
	 F  0 






10.  5 - (-6)

  
	 A  -1       
	 B  1       
	 C  -11       
	 D  11       
	 E  30       
	 F  





  

  

Simplify the following. 

  

  


11.  2a - (-5a)

  
	 A  -10a       
	 B  10a       
	 C  7a       
	 D  -7a       
	 E  3a       
	 F  -3a 






12.  -4x - (3x)

  
	 A  12x       
	 B  -7x       
	 C  7x       
	 D  -12x^2       
	 E  -x       
	 F  x 






13.  3ab - (-7ab)

  
	 A  -4ab       
	 B  4a^2b^2       
	 C  -ab       
	 D  -4       
	 E  10ab       
	 F  ab 






14.  2x - 3y - 5y - 3x

  
	 A  5x - 8y       
	 B  -5x - 2y       
	 C  5x - y       
	 D  -x - 8y      
	 E  -x+2y       
	 F  x - 2y 






15.  3a - 2b - 2a + 5b

  
	 A  5a - b       
	 B  a^2 - 3b       
	 C  5a - 7b       
	 D  a - 7b       
	 E  a + 3b       
	 F  ab - 3 






16.  3x - y - 4x - 3y

  
	 A  -x - 4y       
	 B  2y - x       
	 C  7x - 2y       
	 D  7x - 4y       
	 E  x + 2y       
	 F  -x + 4y 






17.  3x - 3y - 4x

  
	 A  -4x       
	 B  7x - 3y       
	 C  6xy - 4       
	 D  -x - y       
	 E  x - 3y       
	 F  -x - 3y






18.  5 + x - 6 - 2x - 3x + 7

  
	 A  x - 6       
	 B  5x + 12       
	 C  -x + 1       
	 D  6 - 4x       
	 E  6       
	 F  6x - 6 






19.  18b - (-46b)

  
	 A  28b       
	 B  -28b       
	 C  64b^2       
	 D  -64b^2       
	 E  64b       
	 F  -28b^2 






20.  Ken purchased a share of stock for $30. The next day the price of the stock
       dropped 6. On the third day, the price rose by $15.
       How much was Ken's stock worth at the end of the third day? 

  
A  $46       
	 B  $18       
	 C  $23       
	 D  $39       
	 E  $7       
	 F  $9 








  


                        


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