Let's add four elevenths to nine over thirteen
In order to add these two fractions we need to find a common denominator
And that common denominator used to be the least common multiple of eleven and thirteen
And these two numbers don't share any common factors
So their least common multiple is really just going to be the product of eleven and thirteen
So we could say thirteen times eleven
Thirteen times one is thirteen
Thirteen times another one is thirteen
Or you could say thirteen times ten is a hundred and thirty
And we get: three, four, one - one hundred and forty-three
So that's going to be our common denominator
So I'll write it over here:
Something over one hundred and forty-three plus
Something else over one hundred and forty-three
And to go from four elevenths to something over one forty-three
We multiply the eleven times thirteen
--Or we multiply the denominator times thirteen--
So we're going to have to multiply the numerator times thirteen as well
And four times thirteen--let's see: four times ten is forty
Four times three is twelve, so it gives us fifty-two
And you can work that out by hand if you like
Four times thirteen is fifty-two
And then to go from thirteen to one forty-three we multiply by eleven
So if we multiply the denominator by eleven
(if we don't want to change the value of the fraction)
We have to multiply the numerator by eleven
Nine times eleven is ninety-nine
And now we're ready to add: this is equal to--our common denominator is one hundred and forty-three
And fifty-two plus ninety-nine
--Fifty-two plus a hundred would be one hundred and fifty two
And this is going to be one less than that
So it's going to be one hundred and fifty-one
And I think that's about as simplified as we can get
As far as I know, it doesn't look like there are any common factors between one fifty-one and one forty-three
So we just get one fifty-one over one forty-three
--We can write this as a mixed number
Because one forty-three goes into one fifty-one one time
One times one forty-three is one forty-three
When you subtract--let's see, this can become an eleven
This is a four
Eleven minus three is eight
You have a remainder of eight
So one fifty-one over one forty-three is the same thing as one and eight one forty-thirds
And now it becomes even more clear that these can't be simplified anymore
And we are done--this is the same thing as one and eight one forty-thirds