Answer:4 7/12.
Step-by-step explanation: To solve the expression 3 1/3 + (-2 1/4) + 1 5/6, we need to add the fractions with a common denominator.
First, let's convert all the mixed numbers to improper fractions:
3 1/3 = 10/3
-2 1/4 = -9/4
1 5/6 = 13/6
Next, we can add the improper fractions:
10/3 + (-9/4) + 13/6 = 10/3 + -9/4 + 26/6
To add the fractions, we need to find a common denominator. In this case, the least common multiple of the denominators (3, 4, and 6) is 12.
So, we need to convert each fraction to an equivalent fraction with a denominator of 12:
10/3 = 40/12
-9/4 = -27/12
26/6 = 52/12
Finally, we can add the fractions:
40/12 + (-27/12) + 52/12 = 55/12
So, the answer is 55/12, which can be simplified to 4 7/12.