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# Example of adding fractions with unlike denominators

To add these fractions we need to find a common denominator. The answer can be expressed as a mixed number. Let's try together. Created by Sal Khan.

Video transcript

Let's add 4/11 to 9/13. So in order to add
these two fractions, we need to find a
common denominator. And that common
denominator needs to be the least common
multiple of 11 and 13. And these 2 numbers, they
don't share any common factors. So their least common
multiple is literally just going to be the
product of 11 and 13. So we could say 13 times 11. 13 times 1 is 13. 13 times another 1 is 13, or you
could say 13 times 10 is 130. And we get 3, 4, 1-- 143. So that's going to be
our common denominator. So I'll write it over here. So something over 143 plus
something else over 143. And to go from 4/11
to something over 143, we multiplied the
11 times 13, or we multiplied the
denominator times 13. So we're going have to multiply
the numerator times 13, as well. And 4 times 13, let's see. 4 times 10 is 40. 4 times 3 is 12. So it gives us 52. And you can work that
out by hand if you like. 4 times 13 is 52. And then to go from 13 to
143, we multiplied by 11. So if we multiplied
the denominator by 11, if we don't want to change
the value of the fraction, we have to multiply
the numerator by 11. 9 times 11 is 99. And now we're ready to add. This is equal to our
common denominator is 143. And 52 plus 99-- 52
plus 100 would be 152, and this is going to
be 1 less than that. So it's going to be 151. 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 151 and 143. So we just get 151/143. We can write this
as a mixed number because 143 goes
into 151 one time. 1 times 143 is 143. When you subtract, let's see. This can become an 11. This is a 4. 11 minus 3 is 8. You have a remainder of 8. So this is the same thing. 151/143 is the same
thing as 1 and 8/143. And now it becomes
even more clear that these can't be
simplified anymore. And we are done. This is the same thing as
1-- I'll write the 1 a little bit bigger-- 1 and 8/143.