In order to add those fractions, we need to write them using a commom denominator. We can do so by finding a common multiple for the original denominators:
6, 4 and 3
Since 12 is a multiple of those three numbers, we can use 12 as a new denominator for each of the fractions:
5/6 = (5 * 2)/(6 * 2) = 10/12
3/4 = (3 * 3)/(4 * 3) = 9/12
2/3 = (2 * 4)/(3 * 4) = 8/12
Notice that 10/12 is equivalent to the the original fraction 5/6, because we obtained 10/12 by multiplying both the numerator and the denominator by the same factor. The same applies to the other pairs of fractions.
Now, we can add:
5/6 + 3/4 + 2/3 = 10/12 + 9/12 + 8/12
= (10 + 9 + 8)/12
= 27/12
Now, we can simplify the result by dividing both the numerator and the denominator by the same factor. Since both 27 and 12 are multiples of 3, we can write:
27/12 = (27 : 3)/(12 : 3)
= 9/4
Now, since 9 is greater than 4, we can write the fraction 9/4 as a mixed number:
9 = 8 + 1
= 2*4 + 1
9/4 = (2*4 + 1)/4
= 2*4/4 + 1/4
= 2 + 1/4
= 2 1/4 (using the notation of mixed number)