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re: el fractions etc
Posted:
Aug 9, 1995 5:48 AM


Hi Tonna and NCTM
>Karen, typing fractions on this machine will be a challenge but might be >worth it if others can follow my way of showing students why the algorithm >is to invert the divisor and multiply to divide fractions. Here goes: etc
I use a similar method to teach division of fractions in grade 8. The kids need the same background as Tonna stated, as well as having multiplied enough fractions by their recipricals to know that the product is 1.
> 1 > 1 3 ___ > ___ divided by ___ 2 > 2 5 ...is the same as _______ > > 3 > ___ > 5 > > ...a complicated > fraction!
Here I multiply by 5/3 (the reciprical of the denominator) instead of just 5, as Tonna does...
1 5 1 5 1 5 ___ x ___ ___ x ___ ___ x ___ 2 3 2 3 2 3 ____________ = ____________ = 3 5 ___ x ___ 1 ...as the 1 5 3 in the denominator drops out
And thats it 
1 3 1 5 ___ divided by ___ becomes ___ x ___ 2 5 2 3
the reciprocalandmultiply algorithm we all use.
A further issue, while we are on the topic, is _why_ do we divide fractions? (I'll use '/' for the divide symbol) I can see a reason for 1/4 / 2, as this could arise from the question 'How much of a whole pizza does each person get if 2 people share the remaining 1/4 of a pizza?'.
But what question can you pose where the necessary operation is dividing, say, 1/4 by 3/5? I used to think there weren't any such questions, until I read a good response last year (somewhere on the Net..)
Think of division of fractions another way  first think of 3 divide 6 = 1/2 as meaning that 3 is 1/2 of 6. Also, 1/4 divide 2 = 1/8 means that 1/4 is 1/8 of 2, So 1/4 divide 3/5 becomes ' 1/4 is what part of 3/5?' and the answer is that 1/4 is 5/12 of 3/5.
I haven't come across anything better than that.
Cheers
Rex
Rex Boggs  High above the hushed crowd, rex@cqpan.cqu.edu.au  Rex tried to remain focused.  Still, he couldn't shake one Glenmore High School  nagging thought: He was an Rockhampton, Quensland  old dog and this was a new Australia  trick  Gary Larson



