Final answer:
By following the order of operations, simplifying inside the parentheses, and then multiplying, dividing, and adding as required, Judy correctly simplified the expression to 16/23, which corresponds to answer choice D.
Step-by-step explanation:
To simplify the expression -5 ÷ [ 1/2 ( 8 - 1/3 ) ] +2, we need to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). First, we handle the expression inside the parentheses (8 - 1/3). Next, we multiply the result by 1/2 as indicated by the brackets. After simplifying the multiplication, we'll divide -5 by the result we obtained thereby. Finally, we will add 2 to find the simplified expression.
- Calculate inside parentheses: 8 - 1/3 = 24/3 - 1/3 = 23/3.
- Multiply by 1/2: (1/2) × (23/3) = 23/6.
- Divide -5 by 23/6: -5 ÷ (23/6) = -5 × (6/23) = -30/23.
- Add 2: -30/23 + 2 = -30/23 + 46/23 = 16/23.
Judy should choose answer D. 16/23.