Numbers & Arithmetic

A school trip lasts 135 minutes. The schedule needs that time written as hours and leftover minutes:

2 hours 15 minutes

How can Python split one number into those two useful parts?

We will build that payoff in three lessons. Each idea climbs the same ladder: minimal, one twist, then realistic. Read every Notice line before moving up.

You will learn

Calculate with whole numbers and decimals using Python's arithmetic symbols.
Use parentheses, division, quotients, and remainders to control a calculation.
Convert between text and numbers when you read input or build output.
Compare values and read the True or False result.

Lesson 1: Calculate with Whole Numbers

Arithmetic operators

Python can calculate with whole numbers called integers. The symbols +, -, and * mean add, subtract, and multiply.

Minimal: add two integers.

print(8 + 4)

Output

Notice

Numbers need no quotation marks. Python calculates 8 + 4 before printing 12.

One twist: saved numbers can take part in calculations.

tickets = 6
price_each = 4
print(tickets * price_each)

Output

Notice

tickets * price_each uses the values saved in both variables.

One twist: multiplication happens before addition.

print(2 + 3 * 4)

Output

Notice

Python multiplies 3 * 4 first, then adds 2, giving 14.

One twist: parentheses choose a different order.

print((2 + 3) * 4)

Output

Notice

Parentheses make 2 + 3 happen first, giving 20 after multiplication.

Realistic: combine operations to find how many seats remain.

rows = 5
seats_per_row = 8
students = 34
open_seats = rows * seats_per_row - students
print(f"Open seats: {open_seats}")

Output

Open seats: 6

Notice

Multiplication happens before subtraction, so 40 seats are counted before 34 students are removed. Parentheses can make a chosen order clear.

Powers

Minimal: ** raises a number to a power.

print(2 ** 5)

Output

Notice

2 ** 5 means 2 multiplied by itself five times, giving 32.

Quotients and remainders

The operator // gives the whole-number quotient. The operator % gives the remainder. We will use both only with non-negative numbers.

Minimal: divide 17 items into groups of 5.

print(17 // 5)
print(17 % 5)

Output

3
2

Notice

17 makes 3 complete groups of 5 with 2 left over.

One twist: an f-string can calculate inside its braces.

print(f"{3 + 4}")

Output

Notice

Python calculates 3 + 4 inside the braces and prints 7.

One twist: label both quotient and remainder results.

stickers = 29
team_size = 6
print(f"Each team gets: {stickers // team_size}")
print(f"Stickers left: {stickers % team_size}")

Output

Each team gets: 4
Stickers left: 5

Notice

The same two given values answer two related questions.

Realistic: return to the trip schedule.

total_minutes = 135
hours = total_minutes // 60
minutes_left = total_minutes % 60
print(f"{hours} hours {minutes_left} minutes")

Output

2 hours 15 minutes

Notice

// finds the 2 complete hours, and % finds the 15 minutes left over.

Repeated text

Minimal: multiply a string by an integer to repeat it.

print("=" * 12)

Output

============

Notice

Multiplying "=" by 12 prints twelve equal signs in one line.

One twist: use the repeated line above and below a title.

divider = "=" * 12
print(divider)
print("MATH CLUB")
print(divider)

Output

============
MATH CLUB
============

Notice

Saving the divider lets the same twelve-character line frame both sides of the title.

Lesson 2: Work with Number Types

Division and floats

A number with a decimal point is a float. The / operator performs regular division.

Minimal: divide 10 by 2.

print(10 / 2)

Output

5.0

Notice

/ gives a float, // gives an int. The output above is exactly 5.0.

One twist: a division can produce a half.

print(7 / 2)

Output

3.5

Notice

Python shows the computed float exactly as 3.5.

Realistic: calculate the average of three given scores.

score_one = 3
score_two = 4
score_three = 5
average = (score_one + score_two + score_three) / 3
print(f"Average: {average}")

Output

Average: 4.0

Notice

The parentheses add the three scores first. The exact printed average is 4.0.

One twist: show a price with two digits after the decimal point.

price = 3.5
print(f"{price:.2f}")

Output

3.50

Notice

:.2f displays 3.5 as 3.50; it changes the printed format, not the saved number.

Convert between text and numbers

int() turns suitable text into an integer. float() turns suitable text into a float. str() turns a value into text.

Minimal: convert quoted digits before calculating.

age_text = "12"
age = int(age_text)
print(age + 1)

Output

Notice

The sample value is "12" with quotes, so it begins as text. After int(age_text), Python can calculate 13.

One twist: joining text and adding numbers use the same symbol but do different jobs.

print("3" + "4")
print(3 + 4)

Output

34
7

Notice

"3" + "4" joins text to make 34, while 3 + 4 calculates 7.

A mixed text-and-number join stops with a TypeError. Read the final traceback line in this broken example.

Read the error

print("Age: " + 12)

The final line says TypeError: can only concatenate str (not "int") to str. Convert the number to text, or let an f-string place it in the sentence.

age = 12
print("Age: " + str(age))
print(f"Age: {age}")

Output

Age: 12
Age: 12

Notice

Both repaired lines print Age: 12; each line keeps text and number types compatible.

Try a broken conversion: read the final traceback line to find out why these letters cannot become an integer.

Read the error

int("abc")

Notice

int("abc") raises a ValueError because the text does not contain digits for an integer.

Try real input: run the next cell yourself. It waits for an age, then converts it to an integer.

Try it yourself

age = int(input("Age: "))
print(f"Next year: {age + 1}")

Notice

input() supplies text, and int() converts it before the addition.

Realistic: use a fixed value to make the same calculation repeatable in the next cell.

age_text = "12"
age = int(age_text)
print(f"Next year: {age + 1}")

Output

Next year: 13

Notice

The fixed value keeps the lesson repeatable; the real-input cell above lets you try your own age.

Lesson 3: Ask Number Questions

Comparisons and booleans

A comparison asks a yes-or-no question. Its result is a boolean value: True or False.

Minimal: compare two numbers.

print(4 < 9)
print(9 > 4)

Output

True
True

Notice

< asks whether the left value is less, while > asks whether it is greater. Both comparisons print the boolean True.

One twist: include the boundary with less-than-or-equal and greater-than-or-equal.

score = 8
print(score <= 8)
print(score >= 8)

Output

True
True

Notice

<= and >= include equality, so both comparisons print True when the two values match.

Minimal: == asks whether two values are equal.

print(8 == 8)

Output

True

Notice

8 == 8 is True; use two equal signs to compare, rather than one equal sign to save a value.

One twist: != asks whether two values differ.

print(8 != 9)

Output

True

Notice

8 != 9 is True because the numbers are different.

Realistic: test equality and inequality directly.

score = 8
print(score == 8)
print(score != 10)

Output

True
True

Notice

== asks whether two values are equal, while != asks whether they are different. Each comparison prints a boolean. A single = saves a value instead.

Split digits

Quotient and remainder can separate the digits of a non-negative integer.

Minimal: split a two-digit number from 10 through 99.

number = 47
tens = number // 10
ones = number % 10
print(tens)
print(ones)

Output

4
7

Notice

Complete tens come from // 10; the leftover ones come from % 10.

One twist: rebuild the original value.

number = 63
tens = number // 10
ones = number % 10
rebuilt = tens * 10 + ones
print(rebuilt)

Output

Notice

Place value reverses the split: 6 tens plus 3 ones makes 63.

Realistic: print a labeled digit report for a two-digit number from 10 through 99.

number = 82
tens = number // 10
ones = number % 10
print(f"Number: {number}")
print(f"Tens: {tens}")
print(f"Ones: {ones}")

Output

Number: 82
Tens: 8
Ones: 2

Notice

The stated 10-through-99 range guarantees exactly one tens digit and one ones digit.

Try real input: type a two-digit number from 10 through 99 to see its place values.

Try it yourself

number = int(input("Two-digit number: "))
tens = number // 10
ones = number % 10
print(f"Tens: {tens}")
print(f"Ones: {ones}")

Notice

int() turns the typed text into a number before // and % split its digits.

Notice — peek ahead (not needed for the exercises):

Adding every integer from 1 through 100 by hand would be tedious. Read this example; you do not need to write or change it.

For each number n from 1 to 100, add it to total.

total = 0
for n in range(1, 101):
    total = total + n
print(total)

Output

Notice

The displayed result is 5050. The repeated pattern is a preview only; the exercises use the number tools taught above.

Final build

Use the given trip length to print the schedule line from the opening. Then change total_minutes to another non-negative value and observe how both parts update.

# Change this value to test another trip length.
total_minutes = 135

hours = total_minutes // 60
minutes_left = total_minutes % 60
print(f"{hours} hours {minutes_left} minutes")

Output

2 hours 15 minutes

Notice

One given number now controls a useful hours-and-minutes report. Quotient and remainder create the two parts.

Recap

Integers are whole numbers; floats can have a decimal part.
+, -, *, /, and ** calculate; parentheses change the order.
// gives a whole-number quotient and % gives a remainder.
int(), float(), and str() convert a suitable value to the type you need.
A comparison such as minutes > 60 produces True or False.

You can now turn a trip length into hours and leftover minutes.