Teacher2Teacher Q&A #5962

Teachers' Lounge Discussion: Multiplying fractions

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From: ari-free

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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