The best explanation of what the number 2 at the top represents is C. There are 20 groups of 32 in 8456.
Here's why:
- In long division, the numbers written above the division symbol represent the **quotient**, which is the result of the division.
- The first digit of the quotient (2 in this case) signifies how many times the divisor (32) can be fully subtracted from the first few digits of the dividend (8456).
- Sharon found that 32 can be subtracted a maximum of 20 times from 8456 without going below zero. This means there are 20 groups of 32 in 8456.
- She then subtracted 20 * 32 = 6400 from 8456, resulting in the first step shown in the calculation.
Incorrect options:
- A is incorrect because it only considers the first two digits of the dividend (84).
- B is incorrect because it suggests there are only 2 groups of 32 in the entire number, which is too few.
- D is incorrect because it suggests there are 200 groups of 32, which is too many.