What is the quotient when 1359 is divided by 48?

Introduction / Context:
This question assesses basic division skills with three and two digit numbers. You are asked to find the quotient when 1359 is divided by 48. The focus is on performing integer division accurately, identifying how many full groups of 48 fit into 1359 and disregarding the remainder for the final answer.

Given Data / Assumptions:

- Dividend = 1359. - Divisor = 48. - We are asked for the quotient only, not the remainder.

Concept / Approach:
To find the quotient, we can estimate how many times 48 goes into 1359 by using nearby multiples. Multiplying 48 by convenient integers such as 20, 25 and 30 provides a range for the quotient. We then refine our guess by checking exact products until we find the largest multiple of 48 that does not exceed 1359. This multiple corresponds to the quotient, and the difference between 1359 and that multiple is the remainder (which is not required here but helps confirm the calculation).

Step-by-Step Solution:
Step 1: Start with an estimate. 50 * 20 = 1000, so 48 * 20 will be slightly less than 1000. This tells us that the quotient is greater than 20. Step 2: Compute 48 * 25 = 48 * (20 + 5) = 960 + 240 = 1200. Step 3: Since 1200 is still less than 1359, the quotient is greater than 25. Step 4: Compute 48 * 30 = 1440, which is larger than 1359, so the quotient must be less than 30. Step 5: Narrow the search between 25 and 29. Compute 48 * 28 = 48 * (20 + 8) = 960 + 384 = 1344. Step 6: Compute 48 * 29 = 48 * (30 - 1) = 1440 - 48 = 1392, which is greater than 1359. Step 7: Therefore the largest multiple of 48 that does not exceed 1359 is 1344, which is 48 * 28. Step 8: The quotient is 28 and the remainder is 1359 - 1344 = 15, though only the quotient is required.

Verification / Alternative check:
As a quick check, use approximate division. 1359 ÷ 48 is close to 1360 ÷ 50, which equals 27.2. This suggests the actual quotient should be slightly higher than 27 but less than 30, consistent with 28. The exact product calculations confirm that 28 is correct and 29 would overshoot the dividend.

Why Other Options Are Wrong:
Option A (29) corresponds to a product 1392, which is greater than 1359, so it cannot be the quotient. Option B (31) and option C (30) give even larger products and are clearly too big. Only 28 yields a product less than or equal to 1359 while 29 surpasses it, so 28 is the correct quotient.

Common Pitfalls:
Common mistakes include approximating too loosely and rounding to the nearest integer without checking the exact multiples. Another error is to ignore the fact that the quotient must give a product not exceeding the dividend. Always compute at least two nearby products to verify your chosen quotient in such questions.

Final Answer:
The quotient when 1359 is divided by 48 is 28, which corresponds to option D.