minus * minus: Why minus multply by minus equall to plus? Why: - x - = +?

shahar

shahar

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Why minus multply by minus equall to plus?
Why: - x - = +?
 
How do you think of multiplication to begin with? In particular, how are you defining multiplication of signed numbers?

If you look at numbers as points on a number line, then multiplying a number, "a", say, by a positive number, "b", stretches (if b> 1) or contracts (if b< 1) the position of "a". If b is negative, then it also "reverses" the direction. If you multiply by two negative numbers then the two "reversals" brings us back to the original position.
 
shahar said:
Why minus multply by minus equall to plus?
Why: - x - = +?
Click to expand...

There are many different ways to look at it, depending on the level of proof you want, and what you already know. For several answers, see here.

If you want, you might tell us your own thoughts (perhaps about one of the answers given there, or elsewhere), which will give us more to discuss.
 
Reading Comprehension

HallsofIvy said:
How do you think of multiplication to begin with? In particular, how are you defining multiplication of signed numbers?

If you look at numbers as points on a number line, then multiplying a number, "a", say, by a positive number, "b", stretches (if b> 1) or contracts (if b< 1) the position of "a". If b is negative, then it also "reverses" the direction. If you multiply by two negative numbers then the two "reversals" brings us back to the original position.
Click to expand...
I don't understand what the meaning of the streteches in:
...multiplying a number, "a", say, by a positive number, "b", stretches (if b> 1) or contracts (if b< 1) the position of "a"...
?
 
shahar said:
… meaning of the stretches …
Click to expand...
In that explanation, stretches … the position of "a" means that number "a" shifts to the right.

And contracts … the position of "a" means that number "a" shifts to the left.

The stretching/contracting explanation may not be appropriate, at your level of study. Are you in a beginning algebra class?
 
shahar said:
Why minus multply by minus equall to plus?
Why: - x - = +?
Click to expand...
If you multiply 6 by 4 (note that 4 is bigger than 1), the result is 24 (it stretched as it got bigger)
Now If you multiply 6 by 1/2 (note that 1/2 is smaller than 1), the result is 3 (it got smaller)
This is not exactly what I think the other posters were really getting at but what I said above gives the same results.
 
shahar said:
Why minus multply by minus equall to plus?
Why: - x - = +?
Click to expand...
As far as I know -

(-1) * (-1) = 1 ...................... by definition (axiom).

This is required to maintain the properties of multiplication across positive and negative domains of the number line.
 
shahar said:
Why minus multply by minus equall to plus?
Why: - x - = +?
Click to expand...
Building on what Khan said, (-1)*(-1)=1, we have the following (from example)

(-7)*(-3) = {(-1)*(7)}*{(-1)*(3)}= {(-1)*(-1)}*{(7)*(3)} = {+1}*{21}= +21 or 21
 
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