Session 4: Working with Numbers and Math

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January 4, 2025 - 5 minutes read - 916 words

Session 4: Working with Numbers and Math

Weekend Session 1.5 hours Phase 1: Programming Foundations

Master arithmetic operations, understand operator precedence, and work with different number types to create calculation programs.

🎯 Key Skills You'll Learn:

Arithmetic operators
Math functions
Assignment shortcuts
Integer vs decimal division

🚀 Session Project:

Compound Interest Calculator

Learning Objectives

Master arithmetic operations in C++
Understand operator precedence
Work with different number types
Create calculation programs

Warm-up (10 minutes)

Quick Review Exercise: Create a program that asks for two numbers and displays them. Make one an integer and one a decimal number.

New Concept Introduction (30 minutes)

Arithmetic Operators

C++ uses these symbols for math:

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int a = 10, b = 3;
double x = 10.0, y = 3.0;

cout << a + b << endl;    // Addition: 13
cout << a - b << endl;    // Subtraction: 7
cout << a * b << endl;    // Multiplication: 30
cout << a / b << endl;    // Division: 3 (integer division!)
cout << x / y << endl;    // Division: 3.33333 (decimal division)
cout << a % b << endl;    // Remainder (modulo): 1

Important: Integer vs Decimal Division

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int result1 = 10 / 3;        // result1 = 3 (loses decimal part)
double result2 = 10 / 3;     // result2 = 3 (still integer division!)
double result3 = 10.0 / 3;   // result3 = 3.33333 (decimal division)
double result4 = 10 / 3.0;   // result4 = 3.33333 (decimal division)

Operator Precedence (Order of Operations)

C++ follows math rules: PEMDAS/BODMAS

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int result = 2 + 3 * 4;      // result = 14 (not 20!)
int result2 = (2 + 3) * 4;   // result2 = 20

Useful Math Operations

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#include <cmath>  // Add this for advanced math

sqrt(25)         // Square root: 5
pow(2, 3)        // Power: 2^3 = 8
abs(-5)          // Absolute value: 5

Assignment Operators (Shortcuts)

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int score = 100;
score = score + 10;    // Long way
score += 10;           // Shortcut: same as above
score -= 5;            // score = score - 5
score *= 2;            // score = score * 2
score /= 4;            // score = score / 4

// Increment and Decrement
score++;               // Add 1 to score
score--;               // Subtract 1 from score

Hands-on Practice (40 minutes)

Exercise 1: Calculator Upgrade (15 minutes)

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#include <iostream>
using namespace std;

int main() {
    double num1, num2;
    
    cout << "Enter first number: ";
    cin >> num1;
    cout << "Enter second number: ";
    cin >> num2;
    
    cout << "Addition: " << num1 + num2 << endl;
    cout << "Subtraction: " << num1 - num2 << endl;
    cout << "Multiplication: " << num1 * num2 << endl;
    
    if (num2 != 0) {  // Don't worry about 'if' yet, just use it
        cout << "Division: " << num1 / num2 << endl;
    }
    
    return 0;
}

Exercise 2: Temperature Converter (15 minutes)

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#include <iostream>
using namespace std;

int main() {
    double celsius, fahrenheit;
    
    cout << "Enter temperature in Celsius: ";
    cin >> celsius;
    
    fahrenheit = (celsius * 9.0 / 5.0) + 32;
    
    cout << celsius << "°C = " << fahrenheit << "°F" << endl;
    
    return 0;
}

Exercise 3: Circle Calculator (10 minutes)

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#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double radius;
    const double PI = 3.14159;
    
    cout << "Enter circle radius: ";
    cin >> radius;
    
    double area = PI * pow(radius, 2);
    double circumference = 2 * PI * radius;
    
    cout << "Area: " << area << endl;
    cout << "Circumference: " << circumference << endl;
    
    return 0;
}

Challenge/Quiz (10 minutes)

Challenge: Compound Interest Calculator Create a program that calculates compound interest using the formula: Final Amount = Principal × (1 + rate/100)^time

Ask the user for:

Initial amount (principal)
Interest rate (as percentage, like 5 for 5%)
Number of years

Display the final amount and how much interest was earned.

Validation Prompt

🤖 AI Validation Prompt

Copy this prompt and your code to ChatGPT or Claude for instant feedback:


```
I'm learning C++ and just completed Session 4. Here's my solution to the Compound Interest Calculator challenge:

[PASTE YOUR CODE HERE]

The challenge was: Create a program that calculates compound interest using the formula: Final Amount = Principal × (1 + rate/100)^time

Please check if my solution:
1. Uses the correct compound interest formula
2. Handles decimal numbers appropriately
3. Uses the pow() function correctly
4. Displays both final amount and interest earned
5. Has good variable names and clear output

If there are issues, please explain what's wrong and give me a hint to fix it (don't give me the complete solution).
```

What You Learned

✅ Arithmetic operators (+, -, *, /, %)
✅ Integer vs decimal division
✅ Operator precedence and parentheses
✅ Assignment shortcuts (+=, -=, etc.)
✅ Math functions (sqrt, pow, abs)

Next Session Preview

In Session 5, you’ll learn to work with text and strings, including handling spaces and manipulating text data!