Dividing a Whole Number by a Fraction

Date: 04/02/97 at 18:27:09
From: Adam Thomas
Subject: Divide Whole Number by Fraction

What are the steps to divide a whole number by a fraction?

Date: 04/02/97 at 19:07:51
From: Doctor Wallace
Subject: Re: Divide Whole Number by Fraction

Hi Adam!

To divide whole numbers by a fraction, we use the same procedure we 
use when we divide a fraction by a fraction:  we invert (flip) the 
denominator (bottom number) and multiply.

To do this for whole numbers, we remember that a whole number can be 
written as a fraction by making the denominator a 1.

So 3 is the same as 3/1, 4 is 4/1, and so on.

Suppose we want to divide 2 by 1/3.  We would have this:


                        2
                     -------
                        1
                        -
                        3


We write the 2 as a fraction, so we have this:

                        2
                        -
                        1
                  -------------
                        1
                        -
                        3


Now, we flip over the bottom and multiply it by the top:


                 2     3        6
                 -  x  -   =    -    =    6
                 1     1        1 


We may have to reduce the final product.  Let's look at one more 
example:


             How about 4 divided by 5/6?


                4
                -
                1          4     6        24
           ---------- =    -  x  -   =   ---- =  4 and 4/5
                5          1     5         5
                -
                6


Remember that to multiply fractions, you just multiply the top numbers 
and put the answer on the top, and then multiply the bottom numbers 
and put the answer on the bottom.  Then reduce your final answer if 
necessary.

So this problem actually turns division problems into multiplication 
problems.

Thanks for writing! 

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