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Q&A #5962

Teachers' Lounge Discussion: Multiplying fractions

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From: ari-free <arielbhaviv@gmail.com>
To: Teacher2Teacher Public Discussion
Date: 2008070600:10:29
Subject: Re: fraction



Well, first we have to clarify what multiplication is. Let's say we
have to make dinner with a choice from 2 kinds of meat (beef or
chicken) and 3 kinds of vegetable (carrot, potato or corn). Now to
make a meal we need to pair a meat with a vegetable. So how many pairs
can we make?
beef, carrot
beef, potato
beef, corn
chicken, carrot
chicken, potato
chicken, corn
2X3=6. 

Another way is make a table:
          carrot           potato        corn

beef    (beef,carrot)  (beef,potato)  (beef,corn)

chicken (chick,carrot) (chick,potato) (chicken,corn)


We can also show 2 horizontal (meat) lines crossed by 3 vertical
(veggie) lines and we get 6 intersections. We could draw a point on
each intersection. 

What multiplication is after is the number of pairs or intersections.
You can also see with 3x1 that the answer is 3 intersections (3 horiz
lines crossed by 1 vertical) and 3x0 = 0 intersections (since 3
horizontal lines not crossed with any vertical lines won't give you
any intersections).


Now multiplying fractions:
1/2 X 2/3
I draw a box and that represents 1. I draw a horizontal line to cut it
in half. I mark the bottom half with \\\ 
Then I draw 2 vertical lines to cut it in thirds. I mark 2 out of the
3 vertical rectangles with ///
You should see that 2 out of the 6 pieces are intersected. 1/2 x 2/3=
2/6

The box should look something like this (the whole box should really
be a square):
_______________________________
|/////////|/////////|         |
|/////////|/////////|         |
|/////////|/////////|         |
|/////////|/////////|         |
-------------------------------
|XXXXXXXXX|XXXXXXXXX|\\\\\\\\\|
|XXXXXXXXX|XXXXXXXXX|\\\\\\\\\|
|XXXXXXXXX|XXXXXXXXX|\\\\\\\\\|
|XXXXXXXXX|XXXXXXXXX|\\\\\\\\\|
-------------------------------
You can see that 2 out of 6 parts are intersected with X. 

I hope this is accurate and helpful

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