Answer/explanation: To calculate this expression, we'll first change the mixed numbers to improper fractions:
-3 3/4 = -15/4
2 1/3 = 7/3
Now, we can rearrange the expression and solve it step by step:
-15/4 x 5/6 - 7/3
To multiply fractions, we multiply the numerators together and the denominators together:
((-15) x (5)) / ((4) x (6)) - 7/3
Simplifying:
(-75) / (24) - 7/3
To find a common denominator for these fractions, we multiply the denominators together:
(-75) / (24) - (7) * (8) / (3) * (8)
-75/24 - 56/24
Now that the fractions have the same denominator, we can simply subtract the numerators:
(-75 - 56) / 24
-131/24
The final answer is -131/24.