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### Reducing Fractions

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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

Yasmin Medina
St. Peter and Paul School, Mt. Vernon
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```
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

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Associated Topics:
Elementary Fractions

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