Question

Evaluate the following expressions. a. 25 / 3 b. 20 - 12 / 4 * 2 c. 32 % 7 d. 3 - 5 % 7 e. 18.0 / 4 f. 28 - 5 / 2.0 g. 17 + 5 % 2 - 3 h. 15.0 + 3.0 * 2.0 / 5.0

Short answer

a) 8.33, b) 14, c) 4, d) -2, e) 4.5, f) 25.5, g) 15, h) 16.2

Step-by-step solution

Evaluate 25 / 3

To evaluate this expression, simply divide 25 by 3. The result is:\[25 \div 3 = 8.3333... = 8.33\ ( ext{rounded to two decimal places})\]

Evaluate 20 - 12 / 4 * 2

First, follow the order of operations (parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right)). Start by dividing:\[12 \div 4 = 3\]Then multiply 3 by 2:\[3 \times 2 = 6\]Finally, subtract from 20:\[20 - 6 = 14\]

Evaluate 32 % 7

The modulus operation gives the remainder of the division of two numbers. Divide 32 by 7 and find the remainder:\[32 \div 7 ightarrow ext{remainder is } 4\]So, \(32 \% 7 = 4\).

Evaluate 3 - 5 % 7

Calculate the modulus first: \[5 \% 7 = 5\]because 5 divided by 7 leaves a remainder of 5. Then perform the subtraction:\[3 - 5 = -2\]So, \(3 - 5 \% 7 = -2\).

Evaluate 18.0 / 4

Simply divide 18.0 by 4:\[18.0 \div 4 = 4.5\]

Evaluate 28 - 5 / 2.0

First perform the division:\[5 \div 2.0 = 2.5\]Then subtract from 28:\[28 - 2.5 = 25.5\]

Evaluate 17 + 5 % 2 - 3

First find the modulus:\[5 \% 2 = 1\]Then, calculate the expression step by step:\[17 + 1 - 3 = 18 - 3 = 15\]

Evaluate 15.0 + 3.0 * 2.0 / 5.0

Follow the order of operations. First, perform the multiplication:\[3.0 \times 2.0 = 6.0\]Next, do the division:\[6.0 \div 5.0 = 1.2\]Finally, add the result to 15.0:\[15.0 + 1.2 = 16.2\]

Key concepts

Order of Operations

In programming and mathematics, evaluating expressions isn't just about calculating from left to right. Instead, there is a specific sequence of steps you need to follow, commonly known as the order of operations. This sequence ensures consistent and correct results across different platforms and languages.

When evaluating any expression, you should remember the acronym PEMDAS which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order dictates that operations enclosed in parentheses should be done first, followed by any exponents. Then, perform all multiplication and division from left to right. Lastly, handle the addition and subtraction, also from left to right.

So, by carefully following the PEMDAS rule, you can ensure your expressions are evaluated correctly and consistently every time.

Arithmetic Operators in C++

C++ provides a range of arithmetic operators that allow for various mathematical calculations. These operators help perform basic math operations easily within your programs.

• Addition (+) to add two numbers.
• Subtraction (-) to subtract one number from another.
• Multiplication (*) for multiplying numbers.
• Division (/) to divide one number by another.
• Modulus (%) to find the remainder of a division operation.

These operators function in the usual mathematical sense. However, it's crucial to understand how they work in conjunction with data types, especially division and modulus operations. For division, the result type can vary significantly if you're dividing integers versus floating-point numbers, and this nuance is handled by the data types involved, which we'll discuss further in the "Data Types in C++" section.

Data Types in C++

Understanding data types in C++ is essential because they define what kind of data a variable can hold and how operations affect this data. Some common data types include:

• int: Holds whole numbers without decimals, such as 5 or -3. Operations involving integers return integer results. For example, 5 / 2 yields 2.
• double: Holds numbers with decimals, such as 4.5 or -3.3. When used in operations, the result typically retains its decimal component.

The choice of data type can influence the results of operations. For instance, dividing two `int` variables truncates the decimal part, leading to different results compared to `double` division. Choosing the correct data type ensures precision and accuracy in calculations.

Modulus Operator

The modulus operator (%) is a unique and essential arithmetic operator in C++. It is used to find the remainder of a division between two integers. This operator can be extremely useful, especially in tasks like determining whether a number is even or odd.

Using the modulus operator is straightforward. If you write `a % b`, it divides `a` by `b`, and the result is the remainder of this division. For example, `32 % 7` equals 4 since 32 divided by 7 gives a quotient of 4 with a remainder of 4.

It's important to note that the modulus operator only works with integer values. Attempting to use it with floats will result in an error. Understanding this operator can greatly enhance your programming logic, particularly in loops and conditionals where determining conditions based on remainders can direct the flow of a program.