Question

Wally knows that in order to add or subtract rational expressions, he has to find the least common denominator first. Unfortunately, he can not remember how to do that. Using complete sentences, explain to Wally how to find least common denominators. Make sure you clearly explain any important items to consider.

Answer 1

@jim_thompson5910

Answer 2

@zepdrix

Answer 3

hep me pwease!

Answer 4

So wally knows that they need the same denominator.
In order to get a `common denominator` we would just multiply the denominators together to get the value we need.

But if we want the `least common denominator` we need to do a little bit more work.
Each denominator needs to have the same `factors`.

Example:\[\Large \color{#CC0033 }{\frac{1}{6}}+\frac{1}{4}\]If we break these denominators into their factors:\[\Large \color{#CC0033 }{\frac{1}{3\cdot2}}+\frac{1}{2\cdot2}\]
We can see that they share a 2 as a factor, right?

Answer 5

The second fraction is missing a factor of 3, while the first fraction is missing a second factor of 2.

Answer 6

oh i see

Answer 7

To fix this, we'll multiply the first denominator by 2.
But we can't just multiply by 2 willy nilly.

We can however multiply the numerator AND denominator of the first fraction by 2.
Since: \(\Large \dfrac{2}{2}=1\)
Which would not affect the `value` of our fraction, which is important.

Answer 8

\[\Large \color{royalblue}{\frac{2}{2}}\cdot\color{#CC0033 }{\frac{1}{3\cdot2}}+\frac{1}{2\cdot2}\]Which turns our first fraction into:\[\Large \color{#CC0033 }{\frac{2}{3\cdot2\cdot2}}+\frac{1}{2\cdot2}\]

Answer 9

you could simplify this correct?

Answer 10

Yes, we don't `need` to write out the factors the way I explicitly did, I just feel it helps to show what factor's we're missing.

If you already know how to find the least common multiple of 4 and 6, then it saves a little bit of time.

Answer 11

ok

Answer 12

With least common multiple, we would say "If we make stacks of 4's and 6's, when will the stacks first be equal."

It turns out the LCM of 4 and 6 is 12.
So maybe that method makes more sense... I dunno :p

\[\Large \frac{1}{6}+\frac{1}{4}\]So to get from 6 to 12, we multiply by 2,\[\Large \frac{2}{12}+\frac{1}{4}\]And to get from 4 to 12, we multiply by 3,\[\Large \frac{2}{12}+\frac{3}{12}\]

Answer 13

So maybe those are the words you would want to use.
We start by finding the `Least Common Multiple` of the denominators of our rational expressions.

Then we ummmm.... multiply the numerator and denominator of each rational expression by whatever factor gets us to that LCM.

Answer 14

I dunno, this stuff is a little tricky to get into words :) lol

Answer 15

haha so my answer would be :

to find the LCD Wally would have to find the LCM of the denominators of the expressions. Then he would multiply the numerator and denominator of each expression by whichever factor gets him to that LCM