# Thread: [SOLVED] Changing fractions to have their least common denominator equivalent

1. ## [SOLVED] Changing fractions to have their least common denominator equivalent

Ok, I am having a really hard time understanding this. I thought I did but the answer key has a different answer than what I thought it was.

Here's the problem:

change 2m and m+n/m-n to fractions having their least common denominator.

How do I solve this problem?

2. If I understand what you mean, you want to combine the two terms into one fraction.

2m +(m+n)/(m-n)
= [2m(m-n) +(m+n)] / (m-n)
= [2m^2 -2mn +m +n] / (m-n)

That is it.

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Or, you meant:

2m(m-n) / (m-n), and (m+n) / (m-n)
Those are two fractions having a least common denominator.

3. change 2m and m+n/m-n to fractions having their least common denominator.

SInce only one of the terms has a denom, that is the least common.

Let's start with little numbers: 3 and 5/8 Since all whole numbers are understood to have a denom of 1, we must multiply the denom by 8 to have the same denom as the fraction. When we multiply the bottom by 8, we must be sure to multiply the top by 8 also in order to keep the value equal, so we have 3 = 24/8

So in your problem, we have 2m /1 Multiply top and bottom by the other denom --> 2m(m-n) --> [2m^2 -2mn] / [m-n] is the 1st fraction. The other fraction remains the same.

Hope this is helpful to you.