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alternap18 · Sep 21, 2010, 10:04 AM

like for example this one

3
_ = _
7 21

I tried my best to put it up

donf · Sep 21, 2010, 10:10 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 · Sep 21, 2010, 10:26 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 · Sep 22, 2010, 04:59 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 · Sep 22, 2010, 05:19 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 · Sep 22, 2010, 05:46 AM

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

Take your fraction:

$\frac{8}{32}$

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 · Sep 22, 2010, 06:22 AM

Hey, thanks,

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

Thanks for helping me out.

Tensyk · Sep 22, 2011, 07:34 AM

Reduce 7/21 to lowest terms

Unknown008 · Sep 22, 2011, 08:16 AM

Divide the numerator and the denominator by 7.