Final answer:
To determine the number of blocks Ollie used, the total height of the stack (10 1/2 inches) is divided by the height of one block (3/4 inch), resulting in 14 blocks. This was found by multiplying 21/2 by the reciprocal of 3/4, yielding 14 as the final result.
Step-by-step explanation:
The student is performing an operation related to volume of stack and block height to find out how many blocks make up a certain total height. To find the number of blocks used by Ollie, we have to divide the total height of the stack by the height of one block. Since each block is 3/4 inch tall and the total height is 10 1/2 inches, we first convert 10 1/2 inches to a improper fraction (21/2) to make the division easier.
Next, we divide 21/2 by 3/4. We achieve this by multiplying 21/2 by the reciprocal of 3/4, which is 4/3.
21/2 × 4/3 = 21/2 × 4 × 1/3 = (21 × 4)/(2 × 3) = 84/6 = 14.
Ollie used 14 blocks to reach a height of 10 1/2 inches. Therefore, the correct answer is 14, which is none of the options provided (A, B, C, or D).