Re: Multiplcation Not Repeated Addition- Explain
Posted by: Juliana on 6/28/09
On 6/28/09, Rich/CA/Math wrote:
> On 6/27/09, Juliana wrote:
>> On 6/25/09, Rich/CA/Math wrote:
>>
>>>
>>> Operations should be extensible. And they are. We can not only
>>> multiply 2*3 we can multiply (1/2)*(1/3). Now explain how the
>>> latter can ever make sense if multiplication is repeated addition.
>>>
>> By seeing it as two multiplication problems, one in the numerator and
>> one in the denominator.
>>
>> 1 x 1 = 1 = 1
>> _ _ _____ _
>> 2 x 3 = 2+2+2 = 6
>
> But where does the repeated addition concept lead to a multiplication as
> 2 multiplications and a division? In other words, how do you get from a
> definition of multiplication is repeated addition to this is what you do
> with fractions.
Well, obviously you also have to learn the definition of division and the
definition of a fraction. The whole point is that it IS complicated if you
don't use these shortcuts -- you're supposed to turn from the repeated
addition to multiplication with relief, because multiplication is so much
easier, and same with division and fractions. But in the back of your head
you should retain the concept of repeated addition, because that's how it
all makes sense, just as later on you retain the concept of exponents
meaning repeated multiplication, even though you don't want to write out
two to the fifth as 2x2x2x2x2, and it may well behoove you to memorize "two
to the fifth equals thirty-two."
