How To Add Simple Fractions With Different Denominators

let's add 4/11 to 9/13. so in order to addthese two fractions, we need to find acommon denominator. and that commondenominator needs to be the least commonmultiple of 11 and 13.

How To Add Simple Fractions With Different Denominators, and these 2 numbers, theydon't share any common factors. so their least commonmultiple is literally just going to be theproduct of 11 and 13. so we could say 13 times 11.

13 times 1 is 13. 13 times another 1 is 13, or youcould say 13 times 10 is 130. and we get 3, 4, 1-- 143. so that's going to beour common denominator. so i'll write it over here. so something over 143 plussomething else over 143. and to go from 4/11to something over 143, we multiplied the11 times 13, or we multiplied thedenominator times 13.

so we're going have to multiplythe 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 thatout by hand if you like. 4 times 13 is 52. and then to go from 13 to143, we multiplied by 11.

so if we multipliedthe denominator by 11, if we don't want to changethe value of the fraction, we have to multiplythe numerator by 11. 9 times 11 is 99. and now we're ready to add. this is equal to ourcommon denominator is 143. and 52 plus 99-- 52plus 100 would be 152, and this is going tobe 1 less than that. so it's going to be 151.

and i think that's about assimplified as we can get. as far as i know,it doesn't look like there are any commonfactors between 151 and 143. so we just get 151/143. we can write thisas a mixed number because 143 goesinto 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 samething as 1 and 8/143. and now it becomeseven more clear that these can't besimplified anymore. and we are done. this is the same thing as1-- i'll write the 1 a little

bit bigger-- 1 and 8/143.