Problem 6 - Discrete Mathematics with Applications

Question

Find the quotient and the remainder when the first integer is divided by the second. $$-37,73$$

Step-by-Step Solution

Answer

When dividing -37 by 73, the quotient (q) is -1 and the remainder (r) is 36. In other words, \(-37 = 73 \times (-1) + 36\).

Step 1: Understing The Problem

We are asked to divide -37 by 73 and find both the quotient and remainder. We will use the division algorithm formula to achieve this: -37 = 73 * q + r

Step 2: Calculating the Quotient

To find the quotient (q), we need to divide -37 by 73. Since the quotient should be an integer, we can look for the greatest integer (-1 in this case) that, when multiplied by 73, gives a result close to -37. q = -1 (since 73 * (-1) = -73, which is the closest result to -37)

Step 3: Calculating the Remainder

To find the remainder (r), we can plug the value of q into the division algorithm formula: -37 = 73 * (-1) + r Now, solve for r: r = -37 - 73 * (-1) r = -37 + 73 r = 36

Step 4: Final Results

When -37 is divided by 73, the quotient (q) is -1 and the remainder (r) is 36. So, in other words: \[-37 = 73 \times (-1) + 36\]