Fractions in Simplest Form

Date: 01/15/98 at 22:44:36
From: Kristi
Subject: Simplest form 

Hi, 

I don't understand how you would write a fraction in simplest 
form. For instance, how would you write 99/6 in simplest form?

Thank you,
Kristi

Date: 01/20/98 at 11:04:07
From: Doctor Trone
Subject: Re: Simplest form 

Hi Kristi,

Simplest form means lowest terms. For example, 5/6 is a fraction in 
lowest terms or simplest form.  

When a fraction is in lowest terms, the only common factor of the 
numerator and denominator is 1. What does this mean? Take, for 
example, the fraction 5/6. The only whole number that both 5 and 6 
can be divided by is 1. There is no other whole number.  

To reduce a fraction to lowest terms (that is, to simplify a 
fraction), you need to divide out the Greatest Common Factor (GCF).  
The GCF is the largest whole number that both the numerator and 
denominator can be divided by. It has to be the same number.  

For example, take the fraction 5/20. What is the largest number that 
5 and 20 can be divided by without leaving a remainder? Right, it's 5.  
Thus 5/20 can be simplified (reduced) by dividing both the top and the 
bottom by 5: 5/20 simplifies to 1/4. The fraction 1/4, which is 
another name for 5/20, is said to be in lowest terms.  

In the fraction 99/6, you need to find the greatest common factor 
(GCF) of 99 and 6, which is the largest number both 99 and 6 can be 
divided by without leaving a remainder. In this case, the GCF is 3, 
which means you need to divide both top and bottom by 3.  

Thus, what would 99/6 simplify to? That's right, divide by 3 and you 
get 33/2. 33/2 is simplest form. 

You might ask, "How do I know a fraction like 33/2 is in simplest 
form" This is a good question.

A fraction is in lowest terms only when the GCF of both the numerator 
and denominator is equal to 1. 
 
Is 12/20 in lowest terms?  No, I can divide both the numerator and 
the denominator by 4. (12/20 = 3/5)

Is 17/51 in lowest terms? No, I can divide by 17. (17/51 = 1/3)
 
Is 7/11 in lowest terms?  Yes, I can divide only by 1. There is no 
other number I can divide by to simplify the fraction. GCF = 1.
 
Is 16/19 in lowest terms? Yes, I can only divide by 1. There is no 
other number I can divide by to simplify the fraction. GCF = 1.
 
Is 33/2 in lowest terms?

Sometimes students are asked to change improper fractions like 33/2 
into mixed numbers. A mixed number is a combination (sum) of a whole 
number and a fraction, such as 3 5/6, which is read three and five-
sixths. It means 3 + 5/6. What would 33/2 be as a mixed number?

If you need more help of if you do not understand the explanation, 
please let us know. Best of luck and thank you for writing Dr. Math.   

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