The remainder when -76 is divided by 3,
96.
is (a) -1
(b) 1
(c) 2
(d) -2

To find the remainder when \(-76\) is divided by 3, follow these steps:

1. **Find the remainder when \(76\) is divided by 3**:
   \[
   76 \div 3 = 25 \text{ remainder } 1
   \]
   So, \(76 \equiv 1 \ (\text{mod} \ 3)\).

2. **Consider the negative sign**:
   Since \(-76\) is just the negative of \(76\), the remainder when \(-76\) is divided by 3 is the negative of the remainder when \(76\) is divided by 3. Thus:
   \[
   -76 \equiv -1 \ (\text{mod} \ 3)
   \]

3. **Adjust the remainder to be non-negative**:
   Since remainders are usually taken to be non-negative, we add 3 to \(-1\) to find a positive remainder:
   \[
   -1 + 3 = 2
   \]

Therefore, the remainder when \(-76\) is divided by 3 is \(2\).

So, the correct answer is **(c) 2**.

---

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What is the remainder when 96 is divided by 5?
2. How do you calculate the remainder for negative numbers in general?
3. What are modular arithmetic properties, and how are they applied?
4. How would you solve \(-50 \mod 4\)?
5. What is the significance of modular arithmetic in computer science?

**Tip**: When dealing with negative numbers in modular arithmetic, add the modulus to the negative remainder to get a positive remainder.

Discover how to find the remainder when -76 is divided by 3 with a detailed step-by-step solution. This problem covers modular arithmetic, including the adjustment of negative remainders to positive values. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation