Question

Do a walk-through to find the value assigned to e. Assume that all variables are properly declared. a = 3; b = 4; c = (a % b) * 6; d = c / b; e = (a + b + c + d) / 4;

Short answer

The value assigned to \(e\) is 7.375.

Step-by-step solution

Assign Initial Values

First, assign the initial values given in the problem. We have variable \(a\) set to 3 and variable \(b\) set to 4.

Calculate Variable c

The expression for \(c\) is given by \(c = (a \% b) \times 6\). Calculate \(a \% b\), which is the remainder of 3 divided by 4. This operation results in 3 because 3 divided by 4 gives a remainder of 3. Multiply this result by 6: \(3 \times 6 = 18\). So \(c = 18\).

Calculate Variable d

Substitute the value of \(c\) from Step 2 into the expression for \(d\), which is \(d = c / b\). Therefore, \(d = 18 / 4 = 4.5\).

Calculate Variable e

Now plug the values of \(a, b, c,\) and \(d\) into the expression for \(e\): \(e = (a + b + c + d) / 4\). Substitute the values: \(e = (3 + 4 + 18 + 4.5) / 4\). First, add \(3 + 4 + 18 + 4.5 = 29.5\). Then, divide by 4 to find \(e = 29.5 / 4 = 7.375\).

Key concepts

Arithmetic Operations

In C++ programming and many other languages, arithmetic operations are fundamental. They include basic mathematical calculations such as addition, subtraction, multiplication, division, and modulus. These operations are essential in performing calculations and manipulating data in a program. In the given exercise, we use several arithmetic operators:

• Addition (+): This operator is used to sum the values of two or more operands. For example, in the calculation of 'e', the values of 'a', 'b', 'c', and 'd' are summed up.
• Multiplication (*): This operation involves multiplying two operands. It is used to find the product of a number, as demonstrated in calculating 'c = (a % b) * 6'.
• Division (/): This splits one operand by another, returning the quotient. As seen in 'd = c / b', where the value of 'c' is divided by 'b' to find 'd'.

Understanding how these operations work helps in solving equations and manipulating variables in programming tasks.

Variable Assignment

Variable assignment in C++ is the process of setting a name (variable) to store data, which can then be manipulated within the program. When we assign a value to a variable, we are storing the data in the computer's memory. In the provided exercise, several variables are assigned:

• a = 3 : This assigns the value 3 to the variable 'a'.
• b = 4 : Similarly, 'b' is assigned the value 4.
• c = (a % b) * 6 : Here, 'c' is computed by performing the modulo operation between 'a' and 'b', and then multiplying by 6. This value is then assigned to 'c'.

Assigning variables correctly ensures that each has the intended value for calculations to proceed correctly. Programming often involves changing and using these values as needed to solve different problems.

Modulo Operation

The modulo operation is a key component in programming, especially when you want to find the remainder of a division between two integers. It is denoted by the percent symbol (%) and is particularly useful in problems requiring cyclical sequences or checks.

• Usage Example: In the exercise, 'a % b' is computed where 'a' is 3 and 'b' is 4. Normally, 3 divided by 4 is 0 with a remainder of 3 because 3 can't completely divide into 4. Thus, 'a % b' results in 3.
• Real-world applications: Modulo is often used in scenarios like determining if a number is even or odd, handling periodic events, and more.

Understanding the modulo operation helps in efficiently solving problems that involve divisions where results need to be processed based on the remainder.