Explanations:The modulo operation, represented by the symbol %, is a fundamental arithmetic operation that calculates the remainder of a division operation. In the expression 22 % 3, we are asked to find the remainder when 22 is divided by 3.
To understand this, let's break down the division process. When we divide 22 by 3, we can perform the division step-by-step:
1. First, determine how many times 3 can fit into 22 without exceeding it. This is the quotient. In this case, 3 fits into 22 a total of 7 times because \(3 \times 7 = 21\).
2. Next, calculate the product of the quotient and the divisor: \(7 \times 3 = 21\).
3. Subtract this product from the original number (22) to find the remainder: \(22 - 21 = 1\).
Therefore, the remainder when 22 is divided by 3 is 1. This is why the expression 22 % 3 evaluates to 1.
It is important to note that the remainder in a modulo operation is always a non-negative integer that is less than the divisor. In this case, the divisor is 3, and the remainder 1 is indeed less than 3.
Understanding the modulo operation is crucial in various fields, including computer science, cryptography, and number theory. It is often used in algorithms for tasks such as determining if a number is even or odd, implementing hash functions, and managing circular buffers.
In summary, the modulo operation 22 % 3 yields a remainder of 1, which is the correct answer to the given expression.