Two Division Questions

Date: 1 Feb 1995 22:47:25 -0500
From: Pat Couch
Subject: Math Challenge

Dear Dr. Math,
        I have a real math challenge for you. The question is:
There are 9 men. How many cookies would each man get if there 
were 113 cookies? Brodie 

Dear Dr. Math,
      What is the answer to 1,623,341 divided by 1.632 x 963.2389? 
I'm not allowed to use a calculator. Chris

Pat Couch
Learning Assistance Teacher
Lavington Elementary School

Date: 3 Feb 1995 18:44:07 GMT
From: Dr. Math
Subject: Re: Math Challenge

Dear Brodie and Chris:

Hello there!  We are glad you wrote to Dr. Math!   

Brodie, let me answer your question first.  If there are 113 cookies 
and 9 men want to share the cookies equally there are a couple of ways 
to figure out how many cookies each man gets.  The easiest way to do 
this is divide 113 by 9.  You  won't get an whole number, so either 
the men will have to divide some of the individual cookies so they can 
all have an equal amount, or some men will get more cookies than 
other men.  113/9   =  12  and 5/9 or 12 remainder 5.  

So, each man can have 12 whole cookies, and then  either all 9 men 
can have an additional 5/9 of a cookie or 5 men can have 13 cookies 
while the remaining 4 men have only 12 cookies.  Either way, I think, 
these 9 men might start feeling a little sick, what do you think? 

I have a question for you!   What if all 9 men decided they wanted to 
eat only 5 cookies.  How many cookies would be left?

I hope this helps!  Write back if you have any  other questions, Brodie!

Okay, Chris, on to your question.  This is a pretty difficult division
problem to be doing without a calculator!  The first thing to do in this
problem is to put the denominator (the bottom of the fraction) in terms 
of fractions instead of decimals . 1.632 = 1632/1000, right?  
And, 963.2389 = 9632389/10000, so our problem is now to simplify 
the following:

         1623341
       --------------------------------------
      (1632)(9632389)/(1000)(10000)

When we have fractions in the denominator, we can simplify by 
multiplying the numerator by the inverse of the fraction in the 
denominator.  The inverse of a fraction is the number you get when you 
switch the numbers in the numerator and denominator.  So, for instance, 
the inverse of 2/3 is 3/2.  So, we can simplify the above to:

         (1623341)(1000)(10000)
         ------------------------------
            (1632)(9632389)

WHOA!!! This looks like it is going to be a lot of work with multiplying
and dividing.  Your next step  would be to simplify the numerator and
denominator.   Multiply the numbers in the numerator together, and then
multiply the numbers in the denominator together and divide (using long
division).  Phew!  This may take a while!  I wish you good luck on this
endeavor!  If you have any more questions or want to check your answer,
feel free to write us back!

--Sydney, "dr. math"