I need some help with this math problem could you please explain how you get the answer step by step thanks

add fraction with different denominator

3/16 9/20

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- Apr 30th 2006, 01:05 AM #1

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- Apr 30th 2006, 03:49 AM #2Originally Posted by
**Sandra14**

$\displaystyle 16=2^4$ and $\displaystyle 20=2^25$ so the lcm is $\displaystyle 2^45=80$.

To change the value of the denominator in each fraction we simply multiply the fraction by 1, in the form of a/a=1. For example, we want a denominator of 80 in the fraction 3/16, so writing it out step by step:

$\displaystyle \frac{3}{16}=\frac{3}{16}\frac{5}{5}=\frac{3*5}{16 *5}=\frac{15}{80}$

We do the same kind of thing to the 9/20:

$\displaystyle \frac{9}{20}=\frac{9}{20}\frac{4}{4}=\frac{9*4}{20 *4}=\frac{36}{80}$

Now that we've got a common denominator in each fraction we can go ahead and add them:

$\displaystyle \frac{3}{16}+\frac{9}{20}=\frac{15}{80}+\frac{36}{ 80}$

$\displaystyle =\frac{15+36}{80}=\frac{51}{80}$

You should always take a moment to see if the result can be simplified. As it happens, there are no common factors between 51 and 80, so you are done.

Typically you would probably want to write out the solution in the following manner:

$\displaystyle \frac{3}{16}+\frac{9}{20}=\frac{3}{16}\frac{5}{5}+ \frac{9}{20}\frac{4}{4}$

$\displaystyle =\frac{15}{80}+\frac{36}{80}=\frac{51}{80}$

It's slightly more compact and still shows all of your work.

-Dan

- May 1st 2006, 01:21 AM #3

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- May 1st 2006, 01:31 AM #4

- May 1st 2006, 03:32 AM #5

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