Using Improper Fractions in a Word Problem

Date: 12/6/95 at 15:42:2
From: John Tong and Rajat Shamrma, SMARTER THAN JOHN TONG 
Subject: MATH, LOGIC

Mr. Smith owns 1/4 of the stock of a business.  Mrs. Smith owns 5/6 as 
much as Mr.Smith.  How much do they not own of the stock?

Date: 3/9/96 at 1:2:25
From: Doctor Jodi
Subject: Re: MATH, LOGIC

Hi John and Rajat!

To find out how much stock the Smiths DON'T own, we need to take the 
total amount of stock and subtract the amount that Mr. Smith has and 
subtract the amount that Mrs. Smith has.

First let's calculate how much stock Mrs. Smith has, then add that to 
the amount of stock that Mr. Smith has.  We'll subtract the Smiths' 
total from one, the total amount of stock.

(For word problems like this, the word of means that you need to 
multiply.)

So to find out how much stock Mrs. Smith owns, we multiply 1/4 times 
5/6.  So Mrs. Smith owns 5/24ths of the stock.

In order to add 5/24ths + 1/4th, we need a common denominator.

Since 24 times 1 is 24 and 4 times 6 is 24, we can use 24 as the common 
denominator.

5 * 1            5
_           =    _
            
24 * 1           24


1*6       =     6
_               _

4*6       =    24

5/24 + 6/24 = 11/24

Now we can also write 1 as 24/24ths  so if we subtract 24/24 - 11/24,
we get 13/24, the amount of stock that the Smiths do not own.

I hope this makes sense. If not, write back and we'll try to do a 
better job explaining.

--Doctor Jodi,  The Math Forum