Why do fractions get smaller when you multiply them?

Angela12

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If multiplication is really a form of addition and numbers get larger and larger when you add them, why do fractions get smaller and smaller when you multiply them? For instance, 3/4 + 2/3 = 1 5/12, but 3/4*2/3 = 1/2.
 
lol...

Yeah. Guess that makes perfect sense! The smaller and smaller parts are multiplying aren't they?
Thanks.
 
I feel I should point out that the term "fraction" can include things like \(\displaystyle \frac{3}{2}\) which is larger than 1. Multiplying a number by such a fraction gives you a larger result. One way of thinking about it is that if a is less than 1, we can write a= 1- b for some positive b so that ax= (1- b)x= x- bx, less than x. If a is larger than one, whether written as a fraction or not, we can write it as a= 1+ b so that ax= (1+ b)x= x+ bx, larger than x.
 
If you take two-thirds of something (that is, multiply by 2/3), you should not expect to end up with more than what you started with. After all, 2/3 is less than 1. (1 represents the whole.)

When we think about multiplication as repeated addition, we're generally talking about adding "whole" stuff.

2 × 3 = 2 + 2 + 2

3 × 2 = 3 + 3

et cetera


3/4 × 2 = 3/4 + 3/4

Here, we deal with "full" three-fourths.


3/4 × 2/3 =
(3/4)(1/3) + (3/4)(1/3)

Now, we no longer deal with "full" three-fourths. Instead, we repeatedly add only one-third of each 3/4ths.


Whether fractional factors produce a bigger or smaller product all depends upon whether the factors are bigger than the whole or smaller.

Cheers 8-)
 
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If multiplication is really a form of addition

Not really!!! Multiplication by itself is an "Operation" which has its own rules. Rudimentary multiplication like 3 * 2 = 6 can be equivalent to addition - but more complicated operation like (-3) * (-2) = 6 cannot be that easily explained. So my opinion is to "delete" the equivalence of multiplication and addition.


and numbers get larger and larger when you add them, why do fractions get smaller and smaller when you multiply them? For instance, 3/4 + 2/3 = 1 5/12, but 3/4*2/3 = 1/2.
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