Dividing Fractions

Date: 7/5/96 at 14:31:15
From: kcl
Subject: Dividing Fractions

Dr.Math

Hi! I'm in grade 6 going on to grade 7 next year. I always get 
stuck on dividing fractions. Please help me!

                           Karen

Date: 7/5/96 at 16:48:4
From: Doctor Anthony
Subject: Re: Dividing Fractions

A simple rule to remember when dividing fractions is that you take the 
fraction on the bottom line (denominator), turn it upside down and 
multiply.

So 5/(1/2) is the same as 5*(2/1) = 10

You will notice that the (1/2) on the bottom line has been turned 
upside down to 2/1, or simply 2, and then multiplied.

The reason why this method works is that multiplying both top line and 
bottom line by the bottom line turned upside down causes the bottom 
line to become 1, and we need only then consider what happens on the 
top line.

Example   Simplify   5/8     (5/8)(4/3)    5/6
                     ---  =  ---------- = ----- =  5/6
                     3/4     (3/4)(4/3)     1 

In practice we don't need to carry out all the steps shown above. We 
just do the 'invert and multiply' that I described at the start.

    5/8
    --- =   5/8 * 4/3 = 5/6
    3/4

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 7/5/96 at 17:36:30
From: kcl
Subject: More on Dividing Fractions

Dr.Math,

     Hi, again! I still don't understand what you meant. Please send 
me more details about dividing fractions.
                
               Karen

Date: 7/19/96 at 17:10:31
From: Doctor Robert
Subject: Re: More on Dividing Fractions

If you know how to multiply fractions, dividing is pretty easy.  You 
multiply fractions by multiplying the numerators together to get the 
numerator of the answer, and multiplying the denominators together to 
get the denominator of the answer.  

For example 2/3 times 4/5 = 8/15.  

To divide one fraction by another, you simply invert the divisor 
(invert means make the numerator the denominator and make the 
denominator the numerator) and multiply. 

For example 2/3 divided by 4/5 is the same as 2/3 times 5/4 
which is 10/12 or 5/6 when reduced. 

Good luck.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/