Let’s add 4/11 to 9/13. So in order to add these two fractions, we need to find a common denominator.

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## Example of adding fractions with unlike denominators

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.

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