Q&A #1493

Teachers' Lounge Discussion: Dividing fractions

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2010100216:50:27
Subject: Re: why

On 2010100211:25:43, teresa wrote:
>why are we allowed to flip the second fraction in a division problem 
When you get to algebra, you will seldom see the divide symbol that is
on the 4 function calculator.  Instead, you will use the slash or with
a pencil, you will use a horizontal line.    

For example, 6 divided by 3 is two.  which is represented as 
-- = 2.  This answers the question, "How many 3s are in 6."  

Suppose you have 3/4 div by 2/5.   In a complex fractions, you write:

The above is read as three fourths divided by two fifths. 
In that problem you want 1 in the denominator so you multiply the 2/5
by 5/2 =1 and then you multiply the numerator by 5/2 and then you get

So, we invert so we can turn that messy old denominator to one and 
then we use the same multiplier for the numerator.  

In fractions and algebra, there is a rule that if you multiply the
denominator by a number, you have to multiply the numerator by the
same thing.  

So, when the problem is presented as 3/4 div 2/5 we tell the student
to invert and divide.  He hasn't had algebra and and is not prepared
to understand complex fractions.    

Actually we are telling the student to multiply  both the 3/4 and the
2/5 by the reciprocal of 2/5.  We multiply 3/4 by 5/2 and we also at
the same time multiply the 2/5 by 5/2 and we get:

15/8 x 1.  But we don't need the 1, we we just write 15/8.  

So, there is a little disconnect between arithmetic and algebra. In
algebra, we stop using the lower grade way to say divide.  Maybe that
is because algebra builds up on rational numbers vice just integers
where both integers and fractions are rational.  In fact, each integer
is a fraction such as 1/1. 2/1, etc, but we don't teach that until we
get into elementary algebra.  So, as long as we keep using the old
fashioned divide symbol, we will have to do the best we can.  

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