Question

Write a method isMultiple that determines, for a pair of integers, whether the second integer is a multiple of the first. The method should take two integer arguments and return true if the second is a multiple of the first and false otherwise. [Hint: Use the remainder operator.] Incorporate this method into an application that inputs a series of pairs of integers (one pair at a time) and determines whether the second value in each pair is a multiple of the first.

Short answer

The isMultiple method checks if the second integer is a multiple of the first by returning true if the remainder operation (second % first) is 0, otherwise false. The main application loops user input for integer pairs and utilizes this method to display results.

Step-by-step solution

Define the Method

Start by defining a method called isMultiple that takes two integer parameters. Use the signature 'public static boolean isMultiple(int a, int b)' where 'a' is the first integer and 'b' is the second.

Implement the Logic to Check Multiples

Within the method, use the remainder operator '%' to determine if 'b' is a multiple of 'a'. If 'b % a' equals 0, return true, indicating 'b' is a multiple of 'a'. Otherwise, return false.

Create the Application

Create the main application where you'll input pairs of integers and use the isMultiple method to check for multiples. You can use a Scanner to read input from the user in a loop and check each pair with the method you defined.

Input Handling and Method Invocation

Within the main application's loop, prompt the user to enter a pair of integers, read the inputs, and invoke the isMultiple method with the provided pair. Output the result after each invocation.

Terminate the Application

Define a condition to break out of the loop, such as entering a specific pair like (0, 0), or another quit command. This will stop the application from running and cease accepting new input pairs.

Key concepts

isMultiple Method

In Java, a method is a block of code designed to perform a specific task. When working with integer pairs, the isMultiple method is pivotal in determining the mathematical relationship between two numbers. This method functions by accepting two integers as parameters and returns a boolean value.

The method adheres to a simple yet vital logic: if the second integer is a multiple of the first, it returns true, otherwise, it returns false. In the context of method implementation, it's essential to define this method using proper syntax that aligns with its intended operation.

The signature 'public static boolean isMultiple(int a, int b)' initiates the method's declaration, clearly indicating that it is accessible throughout the application (public), does not require an instance to be invoked (static), will return a boolean value, and accepts two integer parameters. When such a method is executed, it enhances the code's reusability and offers clarity, as its purpose is stated directly in its name.

Remainder Operator Usage

Understanding the remainder operator (often referred to as the modulo operator) is key to implementing the isMultiple method effectively. In Java, the remainder operator is represented by '%', and it calculates the remainder of dividing the first operand by the second.

The crux of its usefulness in this scenario lies in a fundamental property of multiples: if integer 'b' is a multiple of integer 'a', then the division of 'b' by 'a' yields no remainder. Thus, in the expression 'b % a', if the result is 0, we conclude that 'b' is indeed a multiple of 'a'.

This operator is particularly useful for integer pair processing, as it allows efficient evaluation of divisibility, enabling conditional logic within methods to ascertain whether one number is a multiple of another. Its proper application within the isMultiple method directly impacts the accuracy of the method's return value.

Integer Pair Processing

When processing pairs of integers, especially in applications where comparisons between the two are necessary, structured logic and systematic input handling are crucial. The given exercise requires an application that processes user-inputted pairs and assesses their multiplicative relationship.

In practical terms, designing a loop that continuously prompts for and accepts user input—the pairs of integers—is a cornerstone of this process. This loop works in tandem with the isMultiple method, invoking it with the provided pair of integers. It's also paramount to include a clear exit condition that allows the user to terminate the loop, ensuring that the application doesn't run indefinitely.

By integrating the isMultiple method into this loop, we can achieve a seamless integer pair processing mechanism where, upon each input pair, an immediate determination of the multiplicative relationship is given. This feedback loop not only facilitates user interaction but also showcases the practical application of method implementation in processing and responding to user-provided data.