To check if your answer is correct, let's go step by step:
Starting with the expression:
7/8 - 3/4(2-1/6) - 2/3
First, let's simplify the expression inside the parentheses:
2 - 1/6 = 12/6 - 1/6 = 11/6
Now let's distribute the fraction 3/4 to the expression inside the parentheses:
3/4 * (11/6) = (3 * 11) / (4 * 6) = 33/24 = 11/8
Now let's substitute this back into the original expression:
7/8 - 11/8 - 2/3
To add or subtract fractions, we need a common denominator. You correctly found the common denominator as 24. Now let's continue:
(7 - 11 - 2 * 8) / 8 * 3
Simplifying the numerators first:
(-4 - 16) / 24
Now, combining the terms in the numerator:
-20 / 24
Dividing both the numerator and denominator by their greatest common divisor of 4:
-5 / 6
So, the correct answer is -5/6, not -7/6 as you calculated.
Hope this helps!