Question

can you show me how to get the least coomon multilple of the denominator for 2/3+1/6

Answer 1

When you add fractions with the same denominator, it's very easy.

1/4 + 2/4 = 3/4.
3/9 +4/9 = 7/9.
8/10213 + 11/10213 = 19/10213.

You'd add the numerators normally, and the denominators would be the same.
And it makes sense that a quarter slice of pizza plus 2 quarter slices give you 3 quarter slices of the pizza.

But sometimes, you need to add fractions that don't have common denominators.
Like 1/4 + 1/2. Or 1/3 + 4/9.

What you can do then is to "common denomintorize" them.
What is the least common multiple of 2 and 4?
Multiples of 2 are 2, 4, 6, 8, 10, ...
Multiples of 4 are 4, 8, 12, 16, ...

What is the smallest number that's in both lists?
Well that'd be 4.
Or the LCM(2, 4) = 4.

That means we want to make the fractions in 1/4 + 1/2 have a denominator of 4.
So we'd like to express 1/2 as a fraction with a denominator of 4.

We can multiply 1/2 on the numerator and denominator by 2 to get a denominator 4.
giving us that 1/2 = 2/4.

So now 1/4 + 1/2 = 1/4 + 2/4.

And that's just 3/4.

So in your problem what's the least common multiple of 3 and 6?