# how to reduce fractions to the lowest terms??

Asked Sep 21, 2010, 11:04 AM — 8 Answers
like for example this one

3
_ = _
7 21

I tried my best to put it up

 donf Posts: 5,067, Reputation: 2798 Printers & Electronics Expert #2 Sep 21, 2010, 11:10 AM

3/7 is at it's lowest terms.

try this to see if it will help you.

8/32 = 4/16 = 2/8 =1/4.

It looks like you were trying to find the lowest common denominator. Is that what you want? You need to fractions to do that.
 wowwy Posts: 5, Reputation: 10 New Member #3 Sep 21, 2010, 11:26 AM

Simplifying (or reducing) fractions means finding out what can be evenly divided into both top and bottom.

In your example, you are actually doing the reverse... so.. if you multiply 7 x 3 you get 21. You have to multiply the top by 3 also. Your answer would be 9 over 21.
 galactus Posts: 2,272, Reputation: 1436 Ultra Member #4 Sep 22, 2010, 05:59 AM

Finding the prime factorization may help reduce a fraction when it is tough to reduce compared to, say, 8/12.

Suppose we were asked to reduce
$\frac{3913}{6149}$

$3913=43\cdot 7\cdot 13$

$6149=43\cdot 11\cdot 13$

$\frac{\not{43}\cdot 7\cdot \not{13}}{\not{43}\cdot 11\cdot \not{13}}$

The cancellations reduce it down to $\frac{7}{11}$
 donf Posts: 5,067, Reputation: 2798 Printers & Electronics Expert #5 Sep 22, 2010, 06:19 AM

Galactus,

I have never seen that process, not that that surprises me all that much.

Can you take a moment and "PM" with an explanation of how it works.
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #6 Sep 22, 2010, 06:46 AM

It's in fact the same process as you did earlier donf.

$\frac{8}{32}$

You divided both numerator and denominator by two successively to get 1/4.

It's like you did it this way:

$\frac{8}{32} = \frac{2.2.2}{2.2.2.2.2} = \frac{2.2}{2.2.2.2} = \frac{2}{2.2.2} = \frac{1}{2.2} = \frac{1}{4}$

Now, if you get multiples of prime numbers of other factors instead of strictly prime numbers as factors, they still work.

$\frac{150}{875} = \frac{\cancel{25}.6}{\cancel{25}.35} = \frac{6}{35}$
 donf Posts: 5,067, Reputation: 2798 Printers & Electronics Expert #7 Sep 22, 2010, 07:22 AM

Hey, thanks,

Now I recognize the process and yes I've used it in the past.

Thanks for helping me out.
 Tensyk Posts: 1, Reputation: 10 Junior Member #8 Sep 22, 2011, 08:34 AM
Reduce 7/21 to lowest terms
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #9 Sep 22, 2011, 09:16 AM
Divide the numerator and the denominator by 7.

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