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

Calculate Remainder of a divided by b

First, we find the result of the operation \( a \, \% \, b \). Knowing \( a = 3 \) and \( b = 4 \), the remainder when 3 is divided by 4 is 3, because 4 goes into 3 zero times completely and there remains a 3. Hence, \( a \, \% \, b = 3 \).

Calculate Value of c

Now, substitute the remainder we calculated into the expression for \( c \). We have \( c = (a \, \% \, b) \times 6 = 3 \times 6 = 18 \). So, the value of \( c \) is 18.

Calculate Value of d

Next, we use the value of \( c \) to find \( d \). We have \( d = \frac{c}{b} = \frac{18}{4} = 4.5 \). Thus, the value of \( d \) is 4.5.

Calculate Value of e

Finally, we can determine the value of \( e \) using the formula \( e = \frac{a + b + c + d}{4} \). Substituting in the known values gives: \( e = \frac{3 + 4 + 18 + 4.5}{4} = \frac{29.5}{4} = 7.375 \). Hence, \( e \) is 7.375.

Key concepts

Variable Declaration in C++

In C++, variables act as storage locations within a program where you can store data that might change throughout the execution. To declare a variable, you need to specify its type followed by a name, and optionally initialize it with a value using the assignment operator.

For instance, in our exercise, the variables `a`, `b`, `c`, `d`, and `e` are declared possibly like this:

• `int a = 3;`
• `int b = 4;`
• `int c;`
• `double d;`
• `double e;`

Here, `int` is a data type for integer values, while `double` is used for floating-point numbers, allowing for decimal values.

Correct variable declaration is essential as it tells the compiler how much memory space is needed, and what type of data is being worked with. Understanding this concept is the first step in efficiently using variables for arithmetic operations in C++.

Modulus Operator in C++

The modulus operator in C++, represented by the symbol `%`, is used to find the remainder of the division of two numbers. It can be particularly useful when you need to determine how much is left over after division rather than how many times one number fits into another.

In the exercise, we see `c = (a % b) * 6`. Here `a % b` is calculated with `a = 3` and `b = 4`, which results in `3` because 3 goes into 4, zero times, leaving a remainder of 3.

Remember that the modulus operator only works with integer types, as it does not make sense to find a fractional remainder. This operator can often be seen in loops and algorithms where remainders play a critical role, such as finding out if a number is even or odd.

Division in C++

Division in C++ can yield different results based on the data types involved. When both operands are integers, the result is also an integer and is called integer division, which means it discards any fractional part.

For instance, `c / b` where `c = 18` and `b = 4`, calculates to 4 in integer division because the fractional part (0.5) is discarded in integer division. However, if we use floating-point types, such as `double`, the division results include the fractions.

That's why here, `d` is declared as a `double` to store the result 4.5, exemplifying how using different types can affect arithmetic operations and the accuracy of the results you require.

Arithmetic Expressions in C++

Arithmetic expressions in C++ consist of operators and operands arranged in a sequence to perform calculations. This includes basic operators like addition (+), subtraction (-), multiplication (*), division (/), and modulus (%).

An arithmetic expression must follow the operator precedence rules, which determine the order in which operations are executed. For our problem, `e = (a + b + c + d) / 4`, the expression inside the parentheses is calculated first due to precedence rules, followed by division.

Breaking down expressions into smaller parts can help in understanding the flow and the result. Using parentheses is a crucial method of controlling the order of operations, ensuring that the parts of an expression which need to be computed first, are executed accordingly, leading to correct results.