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Integer Operations - Number Line

Suzanne Alejandre

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Back to Negative x Negative = Positive
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How can a negative times a negative equal a positive?

When doing number operations, how about thinking of a number line?
Let's take the problems:

   (1)   3 x 2
   (2)  -3 x 2
   (3)   3 x -2
   (4)  -3 x -2


Here's our number line with "|" representing 0 and each
minus sign representing one unit, some going to the left 
of "|" representing "negative" and others going to the 
right representing "positive".

  - - - - - - - - - - -|- - - - - - - - - -


(1) If I represent 3 x 2 using the number line, it will mean 
    going three spaces to the right two times.

                       |- - - - - -

    and so 3 x 2 = 6.


(2) If I represent -3 x 2 using the number line, I will go 
    three spaces to the left two times.

            - - - - - -|

    and so -3 x 2 = -6.


(3) If I represent 3 x -2 using the number line, it means 
    going three spaces, but the minus sign before the 2 
    tells me that I have to be going the opposite direction. 
    This means that instead of going three spaces two times 
    to the right, I have to go three spaces two times on the 
    left, in other words, on the negative side of the
    number line.

            - - - - - -|

    and so 3 x -2 = -6.


(4) If I represent -3 x -2 using the number line, I will 
    start on the negative side of the number line the way 
    I did with -3 x 2, but because the direction is changed 
    (indicated by -2) I am going to switch to the other side, 
    which gives me

                       |- - - - - -

    and so -3 x -2 = 6.

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