Arithmetic Operations

Computers are fundamentally very fast calculating machines — the word “computer” itself comes from “to compute” (to calculate). So it’s only natural that C++ has strong math capabilities. In this lesson, we’ll learn the basic arithmetic operators that you’ll use in almost every program.

Basic Arithmetic Operators

C++ provides five basic arithmetic operators:

Let’s go through each one with code examples you can run.

Addition (+) and Subtraction (-)

#include <iostream>

int main() {
    int a = 15;
    int b = 7;

    int sum = a + b;
    int difference = a - b;

    std::cout << a << " + " << b << " = " << sum << std::endl;
    std::cout << a << " - " << b << " = " << difference << std::endl;

    return 0;
}

Output:

15 + 7 = 22
15 - 7 = 8

No surprises here — exactly the same as the math you already know.

Multiplication (*)

In math we use x or . for multiplication. In C++ (and almost all programming languages), we use the asterisk (*):

#include <iostream>

int main() {
    int length = 8;
    int width = 5;
    int area = length * width;

    std::cout << "Area of the rectangle: " << area << " cm2" << std::endl;

    return 0;
}

Output:

Area of the rectangle: 40 cm2

Division (/)

This is where things get interesting. Division in C++ behaves differently depending on the data types:

#include <iostream>

int main() {
    // Integer division (whole numbers)
    int a = 7;
    int b = 2;
    std::cout << "7 / 2 = " << a / b << std::endl;

    // Double division (decimal numbers)
    double c = 7.0;
    double d = 2.0;
    std::cout << "7.0 / 2.0 = " << c / d << std::endl;

    return 0;
}

Output:

7 / 2 = 3
7.0 / 2.0 = 3.5

Wait — 7 / 2 = 3? Not 3.5?

How to get a decimal result:

// Option 1: Use the double type
double result1 = 7.0 / 2.0;    // 3.5

// Option 2: Cast one of the operands to double
int x = 7, y = 2;
double result2 = (double)x / y;  // 3.5

// Option 3: At least one operand must be double
double result3 = 7.0 / 2;       // 3.5
double result4 = 7 / 2.0;       // 3.5

As long as at least one of the two numbers is a double, the result will be a double as well.

Modulo (%) — Remainder

The modulo operator returns the remainder of a division. This might sound unfamiliar, but it’s actually used very frequently in programming.

Think of it this way: you have 17 cookies and want to divide them equally among 5 people.

• Each person gets: 17 / 5 = 3 cookies (integer division)
• Cookies left over: 17 % 5 = 2 cookies

#include <iostream>

int main() {
    std::cout << "17 % 5 = " << 17 % 5 << std::endl;  // 2
    std::cout << "10 % 3 = " << 10 % 3 << std::endl;  // 1
    std::cout << "20 % 4 = " << 20 % 4 << std::endl;  // 0 (evenly divisible)
    std::cout << "7 % 10 = " << 7 % 10 << std::endl;  // 7

    return 0;
}

Output:

17 % 5 = 2
10 % 3 = 1
20 % 4 = 0
7 % 10 = 7

Common uses of modulo:

1. Check odd/even: number % 2 — if the result is 0, it’s even; if 1, it’s odd
2. Check multiples: number % 3 == 0 — true if the number is a multiple of 3
3. Limit a range: number % 12 — result is always 0-11 (useful for hours)
4. Get the last digit: number % 10 — gives the ones digit

#include <iostream>

int main() {
    int number = 17;

    if (number % 2 == 0) {
        std::cout << number << " is even" << std::endl;
    } else {
        std::cout << number << " is odd" << std::endl;
    }

    std::cout << "The last digit of " << number << " is " << number % 10 << std::endl;

    return 0;
}

Output:

17 is odd
The last digit of 17 is 7

Operator Precedence (Priority)

Just like in math, C++ has rules for the order of operations. Multiplication and division are performed before addition and subtraction:

#include <iostream>

int main() {
    int result1 = 2 + 3 * 4;     // 2 + 12 = 14 (not 20!)
    int result2 = (2 + 3) * 4;   // 5 * 4 = 20 (using parentheses)

    std::cout << "2 + 3 * 4 = " << result1 << std::endl;
    std::cout << "(2 + 3) * 4 = " << result2 << std::endl;

    return 0;
}

Output:

2 + 3 * 4 = 14
(2 + 3) * 4 = 20

Precedence Table (Simplified)

Operators with equal precedence are evaluated from left to right:

int result = 20 / 4 * 2;  // (20 / 4) * 2 = 5 * 2 = 10

Operations with Variables

Of course, arithmetic operators can be used with variables, not just literal numbers:

#include <iostream>

int main() {
    double price = 25000;
    int quantity = 3;
    double discount = 0.1;  // 10%

    double subtotal = price * quantity;
    double savings = subtotal * discount;
    double total = subtotal - savings;

    std::cout << "Unit price  : Rp " << price << std::endl;
    std::cout << "Quantity    : " << quantity << std::endl;
    std::cout << "Subtotal    : Rp " << subtotal << std::endl;
    std::cout << "Discount(10%): Rp " << savings << std::endl;
    std::cout << "Total       : Rp " << total << std::endl;

    return 0;
}

Output:

Unit price  : Rp 25000
Quantity    : 3
Subtotal    : Rp 75000
Discount(10%): Rp 7500
Total       : Rp 67500

Compound Assignment Operators

C++ has shortcuts for a common operation — modifying a variable based on its current value:

int score = 100;

score = score + 10;   // Long form
score += 10;          // Short form (same result)

score = score - 5;    // Long form
score -= 5;           // Short form

And there are two special operators that are used very frequently:

int counter = 0;

counter++;    // Increment: counter = counter + 1 (now 1)
counter++;    // Increment again (now 2)
counter--;    // Decrement: counter = counter - 1 (now 1)

++ (increment) and -- (decrement) increase or decrease a variable by 1. By the way, this is where the name C++ comes from — “C plus 1”.

Full Program: Math Formula Calculator

#include <iostream>

int main() {
    // Calculate area and circumference of a circle
    double pi = 3.14159;
    double radius;

    std::cout << "Enter the radius of the circle: ";
    std::cin >> radius;

    double area = pi * radius * radius;
    double circumference = 2 * pi * radius;

    std::cout << "\nResults:" << std::endl;
    std::cout << "Radius        : " << radius << std::endl;
    std::cout << "Area          : " << area << std::endl;
    std::cout << "Circumference : " << circumference << std::endl;

    return 0;
}

Example interaction:

Enter the radius of the circle: 7

Results:
Radius        : 7
Area          : 153.938
Circumference : 43.9823

Exercises

Exercise: Create a program that takes the length and width of a rectangle as input, then calculates and displays its area and perimeter.

Formulas:

• Area = length x width
• Perimeter = 2 x (length + width)

Expected interaction example:

Enter length: 10
Enter width: 5

Rectangle area: 50
Rectangle perimeter: 30

Bonus challenge: Modify your program to also calculate the diagonal length. Formula: diagonal = square root of (length^2 + width^2). Hint: use #include <cmath> and the sqrt() function.

Summary

• Arithmetic operators: +, -, *, /, %
• Integer division truncates the decimal: 7 / 2 = 3
• Modulo (%) returns the remainder: 17 % 5 = 2
• Precedence: parentheses > multiplication/division/modulo > addition/subtraction
• Compound operators: +=, -=, *=, /=, %=
• Increment (++) and decrement (--) add/subtract 1

In the next lesson, we’ll learn about strings in more depth — not just displaying them, but manipulating them too!