Lesson 5: Basic Math Operations

Course: Python Fundamentals | Duration: 2 hours | Level: Absolute Beginner

Learning Objectives

By the end of this lesson, students will be able to:

• Use all Python arithmetic operators: +, -, *, /, //, %, **
• Understand operator precedence (order of operations)
• Convert user input (text) to numbers using int() and float()
• Build programs that perform mathematical calculations
• Solve real-world math problems with Python

Prerequisites

• Lessons 1-4: Basic Python, print, input, variables

Lesson Outline

Part 1: Python as a Calculator (30 minutes)

Explanation

Python can do math - and it's very good at it. Before we do math with user input, let's learn all the math operators Python supports.

Think of Python operators like the buttons on a calculator:

• + is the plus button
• - is the minus button
• * is the multiply button (we use * instead of × because keyboards don't have ×)
• / is the divide button

But Python has some extra operators that calculators don't:

• // is floor division - divide and round DOWN to whole number
• % is modulo - the remainder after division
• ** is exponentiation - raise to a power (2**3 means 2³)

Examples

# Basic arithmetic
print(10 + 3)    # Addition:       13
print(10 - 3)    # Subtraction:    7
print(10 * 3)    # Multiplication: 30
print(10 / 3)    # Division:       3.3333333333333335
print(10 // 3)   # Floor division: 3  (drops the decimal)
print(10 % 3)    # Modulo:         1  (10 ÷ 3 = 3 remainder 1)
print(10 ** 3)   # Exponentiation: 1000  (10³)

Understanding floor division and modulo:

# Imagine you have 17 cookies to share equally among 5 people
cookies = 17
people = 5
 
each_person_gets = 17 // 5   # 3 cookies each
leftover_cookies = 17 % 5    # 2 cookies left over
 
print(f"Each person gets {each_person_gets} cookies")
print(f"Leftover cookies: {leftover_cookies}")

Understanding exponentiation:

print(2 ** 8)    # 256 - useful in computer science (bits!)
print(10 ** 6)   # 1,000,000 - one million
print(3 ** 3)    # 27 - "3 cubed"

Operator precedence (order of operations): Python follows the same order of operations as math class (PEMDAS/BODMAS):

1. ** (exponentiation) - first
2. *, /, //, % (multiplication/division) - second
3. +, - (addition/subtraction) - last

print(2 + 3 * 4)      # 14  (not 20! - multiplication first)
print((2 + 3) * 4)    # 20  (parentheses override order)
print(10 - 2 + 3)     # 11  (left to right when same precedence)
print(2 ** 3 ** 2)    # 512 (right to left for exponentiation: 2 ** (3**2) = 2**9)

Teacher's Note: The % (modulo) operator confuses many beginners. Use this analogy: "It's like asking 'after everyone gets an equal share, what's left over?'" - clock math is also good (5 hours after 10 o'clock = 10+5 = 15, and 15 % 12 = 3, so it's 3 o'clock).

Practice

Mental math challenge: Before running the code, predict the output:

print(7 + 3 * 2)
print((7 + 3) * 2)
print(20 / 4 + 1)
print(17 % 5)
print(2 ** 4)

Part 2: Numbers with User Input (30 minutes)

Explanation

Here's the problem: input() always gives us text (a string). If the user types "42", we get the text "42", not the number 42.

Why does this matter?

# This looks wrong:
number = input("Enter a number: ")  # User types: 10
doubled = number * 2
print(doubled)
# Output: 1010  ← Not what we wanted!

"10" * 2 means "repeat the text '10' twice" → "1010"

We need to convert the text to a number:

• int(x) converts x to an integer (whole number like 5, -3, 100)
• float(x) converts x to a float (decimal number like 3.14, -0.5, 100.0)

# The right way:
text_number = input("Enter a number: ")  # User types: 10
actual_number = int(text_number)         # Convert text to integer
doubled = actual_number * 2
print(doubled)
# Output: 20  ← Correct!

Shorthand (doing it on one line):

number = int(input("Enter a number: "))
doubled = number * 2
print(doubled)

Examples

When to use int() vs float():

# Use int() for whole numbers
age = int(input("Enter your age: "))
num_students = int(input("How many students? "))
 
# Use float() for decimal numbers
price = float(input("Enter price: "))
temperature = float(input("Temperature in Celsius: "))
weight = float(input("Your weight in kg: "))

A practical calculator:

# Simple calculator
print("Python Calculator")
print("-" * 20)
 
num1 = float(input("Enter first number: "))
num2 = float(input("Enter second number: "))
 
print(f"\nResults:")
print(f"{num1} + {num2} = {num1 + num2}")
print(f"{num1} - {num2} = {num1 - num2}")
print(f"{num1} × {num2} = {num1 * num2}")
print(f"{num1} ÷ {num2} = {num1 / num2:.2f}")

The :.2f means "show 2 decimal places". So 3.333... shows as 3.33.

# Tip calculator
print("=== Tip Calculator ===")
bill = float(input("Enter the bill amount ($): "))
tip_percent = float(input("Tip percentage (e.g., 15 for 15%): "))
 
tip_amount = bill * (tip_percent / 100)
total = bill + tip_amount
 
print(f"\nBill:   ${bill:.2f}")
print(f"Tip:    ${tip_amount:.2f}")
print(f"Total:  ${total:.2f}")

Common Question: "What happens if the user types text when we expect a number?" Python will crash with a ValueError. We'll learn how to handle this gracefully in Course 7 (Exception Handling). For now, trust users to enter numbers.

Practice

Build a temperature converter: Ask the user for a temperature in Celsius and display it in Fahrenheit. Formula: F = (C × 9/5) + 32

celsius = float(input("Enter temperature in Celsius: "))
# Your calculation here
# Print the result nicely formatted

Part 3: Practical Math Programs (30 minutes)

Explanation

Let's put math to practical use. Real-world problems are much more motivating than abstract exercises.

Common math patterns in programs:

# Percentages
discount_rate = 0.20  # 20%
original_price = 100
discount_amount = original_price * discount_rate
final_price = original_price - discount_amount
 
# Averages
total = 85 + 90 + 78 + 92 + 88
num_grades = 5
average = total / num_grades
 
# Unit conversions
km = 42.195  # marathon distance
miles = km * 0.621371
 
# Areas and geometry
length = 5
width = 3
area = length * width
perimeter = 2 * (length + width)

Rounding numbers:

import math  # We'll learn about imports in Course 4
 
pi = 3.14159265358979
 
print(round(pi))         # 3       (round to nearest integer)
print(round(pi, 2))      # 3.14    (round to 2 decimal places)
print(round(pi, 4))      # 3.1416  (round to 4 decimal places)
 
# Or use f-string formatting:
print(f"{pi:.2f}")       # 3.14
print(f"{pi:.4f}")       # 3.1416

Examples

A complete unit converter:

print("=== Unit Converter ===")
print("Convert kilometers to miles and meters")
print()
 
km = float(input("Enter distance in kilometers: "))
 
miles = km * 0.621371
meters = km * 1000
cm = km * 100000
 
print()
print(f"{km} km = {miles:.2f} miles")
print(f"{km} km = {meters:.0f} meters")
print(f"{km} km = {cm:.0f} centimeters")

A grade calculator:

print("=== Grade Calculator ===")
print()
 
name = input("Student name: ")
g1 = float(input("Grade 1 (out of 100): "))
g2 = float(input("Grade 2 (out of 100): "))
g3 = float(input("Grade 3 (out of 100): "))
g4 = float(input("Grade 4 (out of 100): "))
g5 = float(input("Grade 5 (out of 100): "))
 
average = (g1 + g2 + g3 + g4 + g5) / 5
total = g1 + g2 + g3 + g4 + g5
 
print()
print(f"Student: {name}")
print(f"Grades: {g1}, {g2}, {g3}, {g4}, {g5}")
print(f"Total Points: {total}")
print(f"Average: {average:.1f}/100")

Practice

Area calculator: Write a program that:

1. Asks for the length and width of a room (in meters)
2. Calculates:
   • Area (length × width)
   • Perimeter (2 × (length + width))
   • Number of floor tiles needed if each tile is 0.5m × 0.5m
3. Displays all results neatly

Part 4: Hands-on Practice (30 minutes)

Exercise 1: Tip Split Calculator

Build a restaurant bill splitter:

Features:

• Ask for the total bill amount
• Ask for the tip percentage (15, 18, 20, 25?)
• Ask for how many people are splitting
• Calculate and display:
  • Tip amount
  • Total bill (bill + tip)
  • Each person's share

Expected output:

=== Bill Splitter ===

Enter total bill: $125.50
Tip percentage: 20
Number of people: 4

--- Results ---
Bill:            $125.50
Tip (20%):       $25.10
Total:           $150.60
Each person pays: $37.65

Exercise 2: Savings Goal Calculator

Build a savings calculator:

Features:

• Ask for the user's savings goal (e.g., $5000 for a laptop)
• Ask how much they can save per month
• Calculate how many months it will take
• Calculate how many years and remaining months

Expected output:

=== Savings Goal Calculator ===

Savings goal: $5000
Monthly savings: $350

You will reach your goal in:
- 15 months (1 year, 3 months)

Hint: For the year/month calculation, use // and %:

total_months = ??  # Calculate this
years = total_months // 12
remaining_months = total_months % 12

Bonus Challenge

Body Mass Index (BMI) Calculator: Formula: BMI = weight(kg) / height(m)²

Build a BMI calculator that:

• Asks for weight (kg) and height (cm)
• Converts height from cm to meters
• Calculates BMI
• Displays the BMI to 1 decimal place
• Displays a category:
  • Under 18.5: Underweight
  • 18.5-24.9: Normal weight
  • 25-29.9: Overweight
  • 30+: Obese (Use what you know - just print all categories, we'll learn how to choose one in Course 3!)

Key Takeaways

• Python arithmetic operators: +, -, *, /, // (floor div), % (modulo), ** (power)
• Operator precedence: ** first, then */%//, then +- (use parentheses to be explicit)
• input() always returns text - convert to numbers with int() or float()
• Use float() for decimals, int() for whole numbers
• Format decimal output with :.2f in f-strings for 2 decimal places
• // gives the whole-number result of division; % gives the remainder

Common Mistakes to Avoid

• Forgetting to convert input: num = input("...") gives text - must use int() or float()
• Using int() for decimals: int("3.14") crashes - use float("3.14") for decimals
• Dividing integers: 7 / 2 gives 3.5 (Python 3 does this correctly, unlike Python 2)
• Forgetting parentheses in formulas: Write (a + b) / 2 not a + b / 2 for average

Homework / Self-Study

1. Build: A currency converter. Ask the user for an amount in US dollars and convert it to:

   • Euros (× 0.92)
   • British Pounds (× 0.79)
   • Japanese Yen (× 149.50)
   • Indian Rupees (× 83.10) Display all conversions.

2. Explore: What happens when you do 1/0 in Python? What about 1//0? What about 0 ** 0? Try these in the Python shell and note the results.

3. Challenge: Write a program that calculates compound interest. Formula: A = P * (1 + r/n) ** (n*t) Where: P = principal, r = annual rate (as decimal), n = times compounded per year, t = years

Next Lesson Preview

In Lesson 6: Strings Basics, we'll:

• Explore strings (text) in much more depth
• Learn indexing - accessing individual characters
• Learn string concatenation and repetition
• Use the len() function
• Start building programs that process text

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