-   -   How to reduce fractions to the lowest terms? (https://www.askmehelpdesk.com/mathematics/how-reduce-fractions-lowest-terms-509524.html)

• Sep 21, 2010, 10:04 AM
alternap18
how to reduce fractions to the lowest terms??
like for example this one

3
_ = _
7 21

I tried my best to put it up
• Sep 21, 2010, 10:10 AM
donf

3/7 is at it's lowest terms.

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.
• Sep 21, 2010, 10:26 AM
wowwy

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.
• Sep 22, 2010, 04:59 AM
galactus

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 $\frac{7}{11}$
• Sep 22, 2010, 05:19 AM
donf

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.
• Sep 22, 2010, 05:46 AM
Unknown008

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.

$\frac{150}{875} = \frac{\cancel{25}.6}{\cancel{25}.35} = \frac{6}{35}$
• Sep 22, 2010, 06:22 AM
donf

Hey, thanks,

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

Thanks for helping me out.
• Sep 22, 2011, 07:34 AM
Tensyk
Reduce 7/21 to lowest terms
• Sep 22, 2011, 08:16 AM
Unknown008
Divide the numerator and the denominator by 7.

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