AAP-2.B Algorithm - The evaluation of expressions follows a set order of operations defined by the programming language

Understanding Order of Operations in Java

What is Order of Operations?

When you solve a math problem, you need to follow a specific order to get the correct result. For example, in the expression 2+3×4, you first multiply 3 and 4, and then add 2. This rule is called the "order of operations."

In programming, we also follow a specific order of operations to evaluate expressions. These rules are similar to those in math but can have some differences depending on the programming language.

Order of Operations in Java

Java follows the same basic order of operations as mathematics. Here is the order Java uses to evaluate expressions:

Parentheses ( ): Expressions inside parentheses are evaluated first.
Multiplication (*), Division (/), and Modulus (%): These operations are evaluated next, from left to right.
Addition (+) and Subtraction (-): These operations are evaluated last, from left to right.

Let's break it down with some simple examples.

Examples

Without Parentheses:

int result = 2 + 3 * 4; // Multiplication first, then addition
System.out.println(result); // Output will be 14

With Parentheses:

int result = (2 + 3) * 4; // Parentheses first, then multiplication
System.out.println(result); // Output will be 20

Real-World Example

Imagine you are going shopping and you need to calculate the total cost of items with a discount and tax applied. Here's a breakdown:

You bought items worth $50.
There is a 10% discount.
You need to add 5% tax on the discounted price.

How would you calculate the total cost?

double itemsCost = 50.0;
double discount = 0.10; // 10%
double tax = 0.05; // 5%

// Calculate discounted price
double discountedPrice = itemsCost * (1 - discount);
// Calculate tax on discounted price
double totalCost = discountedPrice * (1 + tax);

System.out.println("Total cost after discount and tax: $" + totalCost);

So, the total cost after the discount and tax is $47.25.

Full Program Example

Here is a complete Java program that demonstrates the order of operations with comments explaining each step:

public class OrderOfOperations {
    public static void main(String[] args) {
        // Example 1: Simple arithmetic without parentheses
        int result1 = 2 + 3 * 4; // Multiplication first, then addition
        System.out.println("Result of 2 + 3 * 4: " + result1); // Output will be 14
        
        // Example 2: Using parentheses to change the order
        int result2 = (2 + 3) * 4; // Parentheses first, then multiplication
        System.out.println("Result of (2 + 3) * 4: " + result2); // Output will be 20
        
        // Real-World Example: Shopping calculation
        double itemsCost = 50.0;
        double discount = 0.10; // 10%
        double tax = 0.05; // 5%

        // Calculate discounted price
        double discountedPrice = itemsCost * (1 - discount);
        // Calculate tax on discounted price
        double totalCost = discountedPrice * (1 + tax);

        System.out.println("Total cost after discount and tax: $" + totalCost); // Output will be 47.25
    }
}

Programming Problem

Problem: Calculate the Total Price

Write a Java program to calculate the total price of three items bought from a store. Each item has a different price, and you need to apply a discount and tax to the total price.

Item 1 costs $30.
Item 2 costs $20.
Item 3 costs $50.
Apply a 15% discount to the total price.
Then add 8% tax to the discounted price.

Your program should:

Calculate the total price of the items.
Apply the discount.
Add the tax to the discounted price.
Print the final total price.

Hint: Follow the order of operations carefully to get the correct result.

Expected Output:

Total price after discount and tax: $86.7

Here's a template to get you started:

public class ShoppingCalculation {
    public static void main(String[] args) {
        // Prices of the items
        double item1 = 30.0;
        double item2 = 20.0;
        double item3 = 50.0;

        // Discount and tax rates
        double discount = 0.15; // 15%
        double tax = 0.08; // 8%

        // Step 1: Calculate the total price of the items
        double totalPrice = item1 + item2 + item3;

        // Step 2: Apply the discount
        double discountedPrice = totalPrice * (1 - discount);

        // Step 3: Add the tax to the discounted price
        double finalPrice = discountedPrice * (1 + tax);

        // Step 4: Print the final total price
        System.out.println("Total price after discount and tax: $" + finalPrice);
    }
}

Conclusion

Understanding the order of operations is crucial for writing correct and efficient programs. Always remember to use parentheses to make your expressions clear and ensure they evaluate in the order you intend. Practice with different expressions and scenarios to become comfortable with these concepts. Happy coding!

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