Divide Numbers up to 4 Digits by a Two-Digit Whole Number Using the Formal Written Method of Long Division 3 - Reasoning

In the context of teaching mathematical operations, particularly the formal written method of long division, students are often presented with reasoning tasks to deepen their understanding. In one such task, Rosie has attempted to use long division to divide numbers up to four digits by a two-digit whole number. However, she has made an error in her calculations that needs to be identified and explained. The task at hand is to pinpoint Rosie's mistake and provide a clear explanation of where she went wrong in the process.

The error in Rosie's long division method lies in her multiplication steps. She incorrectly used the multipliers 20 and 55 when she should have used 200 and 50 respectively. To be precise, instead of calculating 16 x 200, Rosie wrote 16 x 20, and instead of 16 x 50, she wrote 16 x 55. This mistake affects the entire division process, leading to an incorrect result. By understanding and correcting these multipliers, students will learn the importance of accuracy in each step of the long division method, ensuring that they apply the correct values when multiplying to subtract from the dividend in the division process.