https://file.aiquickdraw.com/mathbot/file/1727493518961rvzzgryt.jpg

Let's break down the given image and work on the parts that have errors.

Here are the calculations we need to check:

1. **\(-91834 \div 425\)**:
   - Quotient: \(-217\) (this is correct)
   - To find the remainder, we use:
     \[
     \text{Remainder} = -91834 - (-217 \times 425)
     \]
     \[
     \text{Remainder} = -91834 - (-92225) = -91834 + 92225 = 391
     \]
     So, the correct answer is: \(-91834 \mod 425 = 391\).

2. **\(26487 \div 1082\)**:
   - Quotient: \(24\) (this is correct)
   - To find the remainder:
     \[
     \text{Remainder} = 26487 - (24 \times 1082)
     \]
     \[
     \text{Remainder} = 26487 - 25968 = 519
     \]
     So, the correct answer is: \(26487 \mod 1082 = 519\).

3. **\(-12867 \div 668\)**:
   - Quotient: \(-20\) (this is correct)
   - Remainder is already given correctly as 493.

4. **\(88184 \div 2772\)**:
   - Quotient: \(31\) (this is correct)
   - To find the remainder:
     \[
     \text{Remainder} = 88184 - (31 \times 2772)
     \]
     \[
     \text{Remainder} = 88184 - 85932 = 2252
     \]
     So, the correct answer is: \(88184 \mod 2772 = 2252\).

### Corrected Results:
1. \(-91834 \div 425 = -217\) and \(-91834 \mod 425 = 391\)
2. \(26487 \div 1082 = 24\) and \(26487 \mod 1082 = 519\)
3. \(-12867 \div 668 = -20\) and \(-12867 \mod 668 = 493\)
4. \(88184 \div 2772 = 31\) and \(88184 \mod 2772 = 2252\)

Would you like more details or clarifications?

### Related Questions:
1. What is the general method for finding the remainder when dividing two numbers?
2. How does integer division handle negative dividends?
3. Can you explain how to calculate the remainder using modular arithmetic?
4. What happens if we divide by zero in modular operations?
5. How can you verify if a quotient and remainder pair are correct?

**Tip**: When working with negative numbers in modular arithmetic, remember that the remainder is always non-negative, even if the dividend is negative.

Find the quotients and remainders for the given division problems.

Learn how to find quotients and remainders for various division problems involving positive and negative integers. The page explains step-by-step methods using integer division and the modulo operation. Suitable for middle and high school students.

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