Divide numbers up to 4 digits 2 - Reasoning

When delving into the concepts of division in mathematics, a particular problem can challenge students to understand the relationship between the dividend, divisor, quotient, and remainder. In this scenario, the question revolves around the division of the number 3,786 by 15, which results in a remainder of 6. The task is to determine the largest number that can be added to the dividend—3,786—without altering the quotient that results from the division.

The key to solving this problem lies in recognising that the largest possible remainder when dividing by 15 is 14, since adding one more would equal the divisor and increase the quotient. Given that the current remainder is 6, one can add the difference between the largest possible remainder and the current remainder to the dividend. In this case, that difference is 14 - 6, which equals 8. Therefore, adding 8 to the dividend will yield the same quotient but with the largest possible remainder of 14. This exercise not only tests the student's understanding of division but also their reasoning and problem-solving skills.