How To Add Subtract Fractions With Different Denominators

let's add 19 and3/18 to 18 and 2/3. so i like to separate outthe whole number parts from the fraction parts. so 19 and 3/18 is the samething as 19 plus 3/18. and to that, we aregoing to add 18 and 2/3,

How To Add Subtract Fractions With Different Denominators, which is the samething as 18 plus 2/3. now we can separately addthe whole number parts. so we could addthe 19 to the 18. so we could do 19 plus 18.

and then we can addthe fraction parts-- let me do this in green--plus 3/18 plus 2/3. now 19/18, prettystraightforward. that is what? let's see. 19 plus 19 would be 38. so this is going tobe 1 less than that. it's going to be 37. so that gives me 37.

and then 3/18 plus2/3, to add them, i need to have thesame denominator. and the least commonmultiple of 18 and 3 is 18. so let's convert 2/3to something over 18. so 2/3, if i want to writeit as something over 18, well, i multipliedthe denominator by 6, so i'd also have tomultiply the numerator by 6. so it's the same thing as 12/18. so i can rewrite 2/3 as 12/18.

and now i can add thesetwo things together. that's going to be-- soi have 37 plus-- it's going to be something over18-- plus something over 18. 3 plus 12 is 15, plus 15/18. and so expressing thisas a mixed number, i get 37 and 15/18. and that's the right number. but we can simplifyit even more. we can simplify the 15/18.

both the numerator and thedenominator are divisible by 3. so let's divide them both by 3. and we're not changingthe value because we're doing the same thing to thenumerator and the denominator. and so this gives us,we still have our 37, but the numerator is now 5,and the denominator is now 6. so we get 37 and 5/6. and we're done.