# Thread: I need some help

1. ## I need some help

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

2. Originally Posted by Sandra14
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
You first need a common denominator. This will be the lcm of the two denominators. If you don't like finding them, however, all you need to do is multiply the denominators together. Warning: the resulting answer you get doing it this way usually takes more effort to simplify, so if you CAN find the lcm, I'd recommend doing it that way.

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

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

We do the same kind of thing to the 9/20:
$\frac{9}{20}=\frac{9}{20}\frac{4}{4}=\frac{9*4}{20 *4}=\frac{36}{80}$

Now that we've got a common denominator in each fraction we can go ahead and add them:
$\frac{3}{16}+\frac{9}{20}=\frac{15}{80}+\frac{36}{ 80}$
$=\frac{15+36}{80}=\frac{51}{80}$

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:
$\frac{3}{16}+\frac{9}{20}=\frac{3}{16}\frac{5}{5}+ \frac{9}{20}\frac{4}{4}$
$=\frac{15}{80}+\frac{36}{80}=\frac{51}{80}$

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

-Dan

3. thanks. what would i do if there is no lcm for the denominators

4. Originally Posted by Sandra14
thanks. what would i do if there is no lcm for the denominators
Hello,

that's the easiest case: Multiply bot denominators.

Greetings

EB

5. Originally Posted by Sandra14
thanks. what would i do if there is no lcm for the denominators
Two numbers A and B always have a least common multiple.

If A and B have no common factores the lcm is AB.

RonL