Evaluate 4 1/2 - 2 - 5 2/3
A: - 3 1/6
B: 12 1/6
C: 2 1/6
To evaluate the expression 4 1/2 - 2 - 5 2/3, we first need to convert all the mixed numbers to improper fractions.
4 1/2 can be written as (4 * 2 + 1) / 2 = 9/2.
5 2/3 can be written as (5 * 3 + 2) / 3 = 17/3.
So, the expression becomes:
9/2 - 2 - 17/3.
To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 2 * 3 = 6.
Converting 9/2 to have a denominator of 6: (9/2) * (3/3) = 27/6.
Converting 17/3 to have a denominator of 6: (17/3) * (2/2) = 34/6.
Now, the expression becomes:
27/6 - 12/6 - 34/6.
Subtracting the fractions, we get:
(27 - 12 - 34) / 6 = -19 / 6.
Converting the improper fraction to a mixed number:
-19 / 6 = -3 1/6.
Therefore, the answer is A: - 3 1/6.