Question

Suppose \(\mathbf{x}, \mathbf{y},\) and \(\mathbf{z}\) are int variables and \(\mathbf{x}=2, \mathbf{y}=5,\) and \(\mathbf{z}=6 .\) What is the output of each of the following statements? a. cout << "x = " << x << ", y = " << y << ", z = " << z << endl; b. cout << "x + y = " << x + y << endl; c. cout << "Sum of " << x << " and " << z << " is " << x + z << endl; d. cout << "z / x = " << z / x << endl; e. cout << "2 times " << x << " = " << 2 *x << endl;

Short answer

a) x = 2, y = 5, z = 6 b) x + y = 7 c) Sum of 2 and 6 is 8 d) z / x = 3 e) 2 times 2 = 4

Step-by-step solution

Statement a

The given statement is:```cppcout << "x = " << x << ", y = " << y << ", z = " << z << endl;```Substitute the values of x, y, and z into the statement. We have \(x = 2\), \(y = 5\), and \(z = 6\). Thus, the output will be:```x = 2, y = 5, z = 6```

Statement b

The given statement is:```cppcout << "x + y = " << x + y << endl;```Calculate \(x + y\) where \(x = 2\) and \(y = 5\). The sum is \(2 + 5 = 7\). Therefore, the output will be:```x + y = 7```

Statement c

The given statement is:```cppcout << "Sum of " << x << " and " << z << " is " << x + z << endl;```Calculate \(x + z\) where \(x = 2\) and \(z = 6\). The sum is \(2 + 6 = 8\). Therefore, the output will be:```Sum of 2 and 6 is 8```

Statement d

The given statement is:```cppcout << "z / x = " << z / x << endl;```Divide \(z\) by \(x\) where \(z = 6\) and \(x = 2\). Since both are integers, perform integer division: \(6 / 2 = 3\). Therefore, the output will be:```z / x = 3```

Statement e

The given statement is:```cppcout << "2 times " << x << " = " << 2 *x << endl;```Calculate \(2 \times x\) where \(x = 2\). The result is \(2 \times 2 = 4\). Therefore, the output will be:```2 times 2 = 4```

Key concepts

Integer Variables

When programming in C++, integer variables are commonly used to store whole numbers. An integer variable, denoted by the keyword `int`, is capable of storing values that don't require a fractional component. For example, if you have integer variables such as \( x \), \( y \), and \( z \) as in our exercise, you could assign them specific whole number values:

• \( x = 2 \)
• \( y = 5 \)
• \( z = 6 \)

Unlike floating-point variables, integers are precise with calculations that do not involve a decimal. Working with integer variables ensures you can execute operations like addition, subtraction, multiplication, and division, delivering exact results as long as fractional remainders are not part of the operation.

C++ Operators

Operators in C++ are symbols that perform operations on variables and values. There are several types of operators, with some of the most fundamental being arithmetic operators, which include:

• **Addition (`+`)**: Combines two numbers into their sum.
• **Subtraction (`-`)**: Subtracts one number from another.
• **Multiplication (`*`)**: Multiplies two numbers.
• **Division (`/`)**: Divides one number by another.

In the context of our exercise, these operators allow expressions like \( x + y \) and \( z / x \) to be evaluated. They are integral to performing calculations and manipulating data in your programs. Understanding these operators helps develop logical and efficient code, enabling you to manipulate integer variables effectively.

C++ Standard Output

The C++ Standard Output is used to print output to the console. This is done using the `cout` object, which is part of the iostream library. In the exercise, `cout` is paired with the insertion operator (`<<`) to direct information to the screen, like so: ```cpp cout << "x = " << x; ``` Here is how it works: - The `cout` object is followed by the insertion operator (`<<`), which funnels the data to the output. - Text or variables are passed through `cout` using the insertion operator. - `endl` is used to insert a newline character to help format the output for easier reading. Using these techniques, you can display messages and variable values effectively, enabling better interaction and information presentation in your C++ applications.

Integer Division

Integer division in C++ is a division operation performed between two integer operands, resulting in an integer quotient. When you divide two integers, any remainder that would result from division is discarded, and only the integer part of the quotient is retained. For example, in the division \( z / x \) with \( z = 6 \) and \( x = 2 \), the result is 3, with no remainder:\[z \div x = \frac{6}{2} = 3\]It's important to remember:- If the divisor doesn't evenly divide the dividend, C++ truncates the decimal values and keeps only the whole number result.- Integer division is different from floating-point division, which would preserve the decimal remainder.This concept ensures precision when working with whole numbers, but it is crucial to be cautious when a complete result including a fractional part is needed.