What is the quotient and reminder when 37 is divided by -5?

Give detailed solution and reason where required....

To find the quotient and remainder when 37 is divided by -5, we use the division algorithm, which states:

Dividend = (Divisor × Quotient) + Remainder, where the remainder should satisfy 0 ≤ |Remainder| < |Divisor|.

Step 1: Perform the Division
We divide 37 by -5:

37 ÷ (-5) = -7.4

Since we need an integer quotient, we take the floor of -7.4, which is -8 (the greatest integer less than or equal to -7.4).

Step 2: Compute the Remainder
Using the division algorithm:

37 = (-5 × Quotient) + Remainder

Substituting Quotient = -8:

37 = (-5 × -8) + R

37 = 40 + R

Solving for R:

R = 37 - 40 = -3

Step 3: Verify Remainder Condition
The remainder must satisfy 0 ≤ |Remainder| < |Divisor|.

Here, |R| = |-3| = 3, which is less than |Divisor| = 5, so the remainder condition is satisfied.

Final Answer:
Quotient = -8, Remainder = -3.