Chapter 16: Arithmetic Operators

Part 1: What Are Arithmetic Operators?

Arithmetic operators are symbols used in programming to perform common mathematical operations on numeric values (operands). They take one or two numbers, perform a specific calculation, and return a new number as the result.

Think of them as the basic functions on a calculator: addition, subtraction, multiplication, and division. But programming gives us a few extra, incredibly useful tools as well.

Part 2: Meet the Family: Your Arithmetic Toolbox

Let’s introduce each operator with its symbol, name, and a simple example. We’ll use Python for our examples, as its syntax is clean and readable, but the concepts apply to almost every language.

Now, let’s explore each one in detail.

Part 3: The Core Four: +, -, *, /

These are the operators you’re already familiar with from basic math. They work exactly as you’d expect.

Important Note on Division: In some older languages (like Python 2), dividing two integers would perform “integer division” and truncate the result (e.g., 15 / 4 would be 3). In modern languages like Python 3, the / operator always returns a floating-point number, which is much more intuitive for beginners.

Part 4: The Specialist: Floor Division (//)

Floor division is like regular division, but it always rounds the answer down to the nearest whole number. It’s not the same as simply dropping the decimal part, especially when dealing with negative numbers.

Think of it as dividing and then taking the floor of the result (the greatest integer less than or equal to it).

Instructor’s Note: The behavior with negative numbers can be surprising at first. The key is to remember it always rounds down (towards negative infinity), not towards zero. -3.75 rounded down is -4.

Part 5: The Remainder Expert: Modulo (%)

The modulo operator gives you the remainder after division. It’s incredibly useful for a surprising number of tasks. Think of it as asking the question: “After dividing these two numbers as evenly as possible, how much is left over?”

Practical Uses of Modulo:

1. Checking if a number is even or odd: This is the most classic use case.

   python

   PHP

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   number <span class="token operator">=</span> <span class="token number">7</span> <span class="token keyword">if</span> number <span class="token operator">%</span> <span class="token number">2</span> <span class="token operator">==</span> <span class="token number">0</span><span class="token punctuation">:</span>     <span class="token keyword">print</span><span class="token punctuation">(</span><span class="token string-interpolation"><span class="token string">f"</span><span class="token interpolation"><span class="token punctuation">{</span>number<span class="token punctuation">}</span></span><span class="token string"> is even."</span></span><span class="token punctuation">)</span> <span class="token keyword">else</span><span class="token punctuation">:</span>     <span class="token keyword">print</span><span class="token punctuation">(</span><span class="token string-interpolation"><span class="token string">f"</span><span class="token interpolation"><span class="token punctuation">{</span>number<span class="token punctuation">}</span></span><span class="token string"> is odd."</span></span><span class="token punctuation">)</span>

2. Working with cycles: Imagine you have a list of 3 items and you want to cycle through them endlessly. You can use an index and the modulo operator.

   python

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   colors <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token string">"red"</span><span class="token punctuation">,</span> <span class="token string">"green"</span><span class="token punctuation">,</span> <span class="token string">"blue"</span><span class="token punctuation">]</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">10</span><span class="token punctuation">)</span><span class="token punctuation">:</span>     color_index <span class="token operator">=</span> i <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>colors<span class="token punctuation">)</span>     <span class="token keyword">print</span><span class="token punctuation">(</span><span class="token string-interpolation"><span class="token string">f"Iteration </span><span class="token interpolation"><span class="token punctuation">{</span>i<span class="token punctuation">}</span></span><span class="token string">: </span><span class="token interpolation"><span class="token punctuation">{</span>colors<span class="token punctuation">[</span>color_index<span class="token punctuation">]</span><span class="token punctuation">}</span></span><span class="token string">"</span></span><span class="token punctuation">)</span>

   This will print red, green, blue, red, green, blue, etc.

3. Checking divisibility: Is a number divisible by another? number % divisor == 0.

4. Extracting digits: Need the last digit of a number? number % 10 gives it to you.

Part 6: The Power User: Exponentiation (**)

This operator raises a number to a power. It’s much cleaner than writing x * x * x for cubes.

Part 7: Operator Precedence (Order of Operations)

Just like in mathematics, arithmetic operators follow a specific order when they appear together in an expression. You might remember PEMDAS or BODMAS from school. Programming has a similar, well-defined precedence.

1. Parentheses ()

2. Exponentiation **

3. Multiplication *, Division /, Floor Division //, Modulo % (all have the same precedence, evaluated left to right)

4. Addition +, Subtraction - (evaluated left to right)

The most important rule: When in doubt, use parentheses! They make your intention clear to both the computer and anyone reading your code.

Part 8: Practical, Real-World Examples

Let’s see how these operators come together to solve real problems.

Example 1: Building a Simple Calculator

Example 2: Temperature Converter

Example 3: Calculating a Restaurant Bill

Example 4: Time Converter

Summary: The Arithmetic Operator Philosophy

• Arithmetic operators are the tools for performing mathematical calculations in code.

• The core four (+, -, *, /) work just like basic math. Remember that / often results in a decimal (float).

• Floor division (//) divides and always rounds down to the nearest integer. This is key to remember with negative numbers.

• Modulo (%) gives you the remainder of a division. It’s a surprisingly versatile tool for checking even/odd, creating cycles, and more.

• Exponentiation (**) raises a number to a power, and can also be used for roots.

• Operator precedence matters. Use parentheses () to make your calculations clear and predictable.

Mastering these operators is like learning to use a hammer, saw, and screwdriver. They are the fundamental tools you will use in almost every program you write. Practice with them, experiment with different combinations, and soon they will become second nature.