Reducing Fractions

Date: 3/7/96 at 19:6:17
From: Mrs. Carmen C. Medina
Subject: Fractions

How do you bring a fraction to its lowest term:

Example:  What's the lowest for  5
                               -----
                                 8    

and please explain the procedure.

Yasmin Medina
St. Peter and Paul School, Mt. Vernon
4 grade  

Date: 3/24/96 at 23:53:5
From: Doctor Jodi
Subject: Re: Fractions

Hi Yasmin!  

Having a fraction in lowest terms means that the numerator 
(the top) and the denominator (the bottom) don't have any 
factors in common.  

(Factors are numbers that divide into another number without a 
remainder. Six, for example, has the factors: 1, 2, 3, 6.  Does 
this make sense?)

Do you know about prime numbers?  Prime numbers have no factors 
other than 1 and themselves.  2, 3, 5, 7, 11... are all prime.

In order to make sure that a fraction is in lowest terms, we need 
to know the factors of the numerator and the denominator.  The 
best thing to know, I think, are the PRIME factors, since the 
PRIMES don't have any factors themselves.

for example, if you looked at 12 
                              ---
                              15

you might (mistakenly) think it was in lowest terms.

There are a few things that you can do

- Learn to count by various numbers (2, 3, 4, 5, etc).  If the 
numerator and denominator are both on one "list," then they have a 
common factor. You can divide by the common factor to reduce the 
fraction.

- Learn some divisibility tricks - see 

  http://mathforum.org/dr.math/problems/7divisible.html    

for some, and for division by 7, look at 

  http://mathforum.org/dr.math/problems/divide_by_7.html   

There's also a foolproof method (well, I THINK it's fool-proof, at 
least), in the sense that it always works - it might take a bit 
more time than the other methods, though:

   - Finding all the prime factors

   1. choose any two factors
   2. if they are NOT prime, find their prime factors. if they ARE 
      prime, write them in your list of prime factors. 
   3. continue until you have used up all of the non-prime 
      factors. Now your list of prime factors is complete 
   NOTE: remember that duplicates count: the prime factors of 4 
         are 2 and 2

Okay. So, for 12, let's choose 6 and 2.  2 is prime, so that goes 
on our list.  6 is not prime, so we need to find its factors.  
Let's choose 3 and 2. Now we've found all the prime factors of 12.  
They are:  3, 2, and 2.

(Note that you can multiply all of these together, 3*2*2, and get 
twelve.  This is a good check.)

Now let's do the same for 15.  15 = 3*5. These are both prime, so 
there is our list of prime factors.

Since we know that 12 and 15 both have 3 as a factor, we can 
divide both by 3 to get 4/5.

Can you find the lowest terms for 5/8 using this method?

Write back if you have more questions or want to know more...

-Doctor Jodi,  The Math Forum