Find the quotient and the remainder when –433 is divided by –17.

To find the quotient and remainder when \(-433\) is divided by \(-17\), we can follow the division process:

1. **Perform division:**

   \[
   \frac{-433}{-17} = 25.47
   \]

2. The quotient must be an integer, so we round it down to the nearest whole number. In this case, the quotient is \(25\).

3. **Find the remainder:**

   To get the remainder, we can use the following relationship:
   
   \[
   \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}
   \]

   Substituting the known values:

   \[
   -433 = (-17 \times 25) + \text{Remainder}
   \]

   \[
   -433 = -425 + \text{Remainder}
   \]

   \[
   \text{Remainder} = -433 - (-425) = -8
   \]

Thus, when \(-433\) is divided by \(-17\), the quotient is \(25\) and the remainder is \(-8\).

Would you like a more detailed explanation, or do you have any other questions?

Here are 5 related questions:
1. What happens if you divide a positive number by a negative one?
2. How do we determine the remainder in non-exact division cases?
3. What is the difference between a quotient and a remainder?
4. Can the remainder ever be larger than the divisor?
5. How do we apply the remainder theorem in algebraic divisions?

**Tip:** Always check if the quotient and remainder satisfy the original equation!

Learn how to find the quotient and remainder when dividing -433 by -17. This problem covers integer division concepts, including the Division Algorithm, with a detailed step-by-step explanation. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation