Question

Determine which of the expressions could be used to represent the following calculation divide the difference between 96 and 72 by 12 select all that apply A (96 - 72) ÷ 12 B 96 - (72 ÷ 12) C (96 ÷ 12) - 72 D 24 ÷ 12 E 96 ÷ 6

Answer 1

To determine which expressions represent the calculation "divide the difference between 96 and 72 by 12," we need to look for the expression that accurately represents this operation step-by-step:

1. Calculate the difference between 96 and 72:
\( 96 - 72 = 24 \)

2. Divide that difference by 12:
\( 24 ÷ 12 = 2 \)

Now we will analyze each option to see if it matches this process:

A: \( (96 - 72) ÷ 12 \)
- This expression calculates the difference first and then divides by 12.
- Result: \( 24 ÷ 12 = 2 \) (This is correct)

B: \( 96 - (72 ÷ 12) \)
- This computes \( 72 ÷ 12 = 6 \) first, and then subtracts it from 96: \( 96 - 6 = 90 \)
- Result: 90 (This is incorrect)

C: \( (96 ÷ 12) - 72 \)
- This computes \( 96 ÷ 12 = 8 \) first, and then subtracts 72: \( 8 - 72 = -64 \)
- Result: -64 (This is incorrect)

D: \( 24 ÷ 12 \)
- This calculates \( 24 ÷ 12 = 2 \) (This is correct but does not explicitly represent the difference between 96 and 72)
- Result: 2 (This is technically correct but does not show the full operation)

E: \( 96 ÷ 6 \)
- This computes \( 96 ÷ 6 = 16 \)
- Result: 16 (This is incorrect)

In conclusion, the expressions that represent the calculation are:

- **A: \( (96 - 72) ÷ 12 \)**
- **D: \( 24 ÷ 12 \)** (though it's less descriptive)

Therefore, the correct choices are **A and D.**