
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 fortythree

So that's going to be our common denominator

So I'll write it over here:

Something over one hundred and fortythree plus

Something else over one hundred and fortythree

And to go from four elevenths to something over one fortythree

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 thirteenlet's see: four times ten is forty

Four times three is twelve, so it gives us fiftytwo

And you can work that out by hand if you like

Four times thirteen is fiftytwo

And then to go from thirteen to one fortythree 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 ninetynine

And now we're ready to add: this is equal toour common denominator is one hundred and fortythree

And fiftytwo plus ninetynine

Fiftytwo 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 fiftyone

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 fiftyone and one fortythree

So we just get one fiftyone over one fortythree

We can write this as a mixed number

Because one fortythree goes into one fiftyone one time

One times one fortythree is one fortythree

When you subtractlet's see, this can become an eleven

This is a four

Eleven minus three is eight

You have a remainder of eight

So one fiftyone over one fortythree is the same thing as one and eight one fortythirds

And now it becomes even more clear that these can't be simplified anymore

And we are donethis is the same thing as one and eight one fortythirds