I don't see why you think she didn't multiply straight across? Because she
did. The only difference between your way and hers is she divided the
numerator 3 and denominator 6 by 3 before she multiplied.
Also; you can multiply straight across much like you can multiply whole
numbers:
ex) 2 x 2 = 4 or (2/1) x (2/1) = (4/1)
ex) 4/3 x 5/8 = 20/24 or 5/6 (i did the reverse of you; multiply across
then divide out)
ex) 4/3 x 5/8 or 1/3 x 5/2 = 5/6 (which is the way you did it; divided out
before multiplying across)
The diagram you drew proves why you can multiply straight across. Remember,
denominator represents how many parts equal a whole (whole = 1), and the
numerator represents the number of given parts. When adding or subtracting
fractions, the ratio size of the denom. and the numer. is not changed, you
are still working within the confines of that original ratio. When
multiplying, the ratio of parts to whole is being increased. 1/2->2
'parts'=whole; 1/2x1/3->each 'part' is divided into thirds->1/6
Haiying, you do realise that with fractions you can multiply straight
across? i.e. the two top numbers and two bottom numbers multiply to give
you the top and bottom numbers of the new fraction? (So 5/6 x 3/4 would be
15/24, which cancels down (divides by 3 on top and bottom) to 5/8.) Unless
you just prefer your way, which is fine of course :>
Did I need to watch more than about 5 minutes to see that something that
could have taken maybe 20 seconds, instead took 5 minutes? I was only
talking about that part anyway...
I don't know, that's just what we were taught at school. When multiplying
fractions you can multiply the tops with the bottoms, and it will give you
the right answer :)
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