Explanation: The modulus operation, denoted by the '%' symbol, is a fundamental arithmetic operation that returns the remainder of a division operation. In the context of the expression 22 % 3, the modulus operation calculates the remainder when 22 is divided by 3.
To understand this concept, let's break down the division process:
1. **Division Process**: When 22 is divided by 3, the quotient is 7 because 3 goes into 22 seven times (3 * 7 = 21).
2. **Remainder Calculation**: After multiplying the quotient by the divisor (3 * 7 = 21), we subtract this product from the original number (22 - 21 = 1). The result, 1, is the remainder.
Thus, the expression 22 % 3 evaluates to 1, as the remainder when 22 is divided by 3 is 1.
It is important to note that the modulus operation always returns a non-negative remainder. This means that even if the dividend is negative, the result of the modulus operation will still be a non-negative number. For example, -22 % 3 would also yield 1, as the remainder of -22 divided by 3 is 1.
Understanding the modulus operation is crucial in various fields, including computer science, cryptography, and competitive programming, where it is used to solve problems involving cyclic or periodic behavior.
In summary, the modulus operation 22 % 3 correctly evaluates to 1, as it represents the remainder of the division of 22 by 3. This concept is foundational in arithmetic and is widely applicable in various mathematical and computational contexts.