Lesson 5
Division: / // %
After this lesson: You'll divide numbers in three ways: exactly, without remainder, and get just the remainder.
Video
The video for this lesson is coming soon.
Explanation
I have 17 candies and 5 friends. How many does each get? And how many are left for me? Python has three kinds of division for this!
Three kinds of division
| Sign | What it calculates | 17 ... 5 |
|---|---|---|
/ | exact division (with a decimal point) | 17 / 5 = 3.4 |
// | how many each gets (no remainder) | 17 // 5 = 3 |
% | how many are left (the remainder) | 17 % 5 = 2 |
In a moment we'll share 17 candies among 5 friends and you'll see all three: each will get 3 - that's 17 // 5. 2 will be left - that's 17 % 5. And if we could cut candies into pieces, each would get 3.4 - that's 17 / 5.
Bajtek shares his candies 🎬
Click Next to go step by step. Watch the candies fly to the plates - this story shows all three divisions: //, % and /.
17 candies, 5 friends
Bajtek has 17 candies in a bowl and 5 friends came to visit. He wants to give everyone the same amount. How?
Now you share the candies
Click the arrow: in every round each friend gets one candy. When there are fewer candies than friends left - we stop.
To share: 17
The candies in code
The same as in the animation: // says how many each gets, and % how many are left. The third line shows how many it would be if we cut the candies.
1print("Each gets:", 17 // 5)2print("Left for me:", 17 % 5)3print("If we cut them:", 17 / 5)
▍Three divisions in a program
The same numbers, three different results.
1print(17 / 5)2print(17 // 5)3print(17 % 5)
▍Pizza for 6 people 🍕
We share 20 slices of pizza among 6 people.
To share: 20
The pizza in code 🍕
The same numbers as in the animation: each gets 3 slices, and 2 are left. With / Python prints lots of digits after the point, because the pieces don't divide evenly - that's normal. The last digit can look a bit odd: that's how computers store fractions.
1print("Each gets:", 20 // 6)2print("Left over:", 20 % 6)3print("If we cut them:", 20 / 6)
▍Chocolate for 5 people 🍫
We share 24 pieces of chocolate among 5 people.
To share: 24
A chocolate bar 🍫
24 pieces for 5 people: how many each, how many are left and how many if we could cut pieces.
1print("Each gets:", 24 // 5)2print("Left over:", 24 % 5)3print("With cutting:", 24 / 5)
▍Division with a decimal point
The result of / always has a decimal point - even when it divides evenly: 20 / 4 is 5.0, not 5. Such a number with a point is a different kind of number for Python (we call it a float). If a task wants a result without a point, use //.
The point is always there
1print(20 / 4)2print(20 // 4)3print(7 / 2)4print(1 / 4)
▍When nothing is left
12 candies for 4 friends - they divide evenly, the remainder is 0.
To share: 12
12 candies in code
It divides evenly, but / still gives a point: 3.0.
1print("Each gets:", 12 // 4)2print("Left over:", 12 % 4)3print("If we cut them:", 12 / 4)
▍Not enough candies
3 candies and 5 friends - you can't even give one each. Everyone gets 0, and all 3 are left.
To share: 3
3 // 5 = 0 (what each one gets)
3 % 5 = 3 (what's left over - the remainder)
3 candies in code
Too few to give everyone even one: each gets 0, and all 3 are left.
1print("Each gets:", 3 // 5)2print("Left over:", 3 % 5)3print("If we cut them:", 3 / 5)
▍Splitting the bill 💸
Money can be divided exactly - then we use /.
Click the arrow - we'll split the bill equally.
1print(10 / 4)2print(30 / 4)3print(9 / 3)
▍What is the remainder % good for?
The remainder is very useful:
- Even or odd? A number is even when
number % 2gives 0 (it divides by 2 with no remainder). - A clock: 135 minutes is
135 // 60= 2 hours and135 % 60= 15 minutes. - The last digit:
2026 % 10is 6, and2026 // 10is 202 - the number without its last digit.
Even or odd?
Remainder 0 - even, remainder 1 - odd.
Click the arrow - we'll put every number into pairs.
1print(24, "->", 24 % 2)2print(37, "->", 37 % 2)3print(100, "->", 100 % 2)4print(1, "->", 1 % 2)
▍Bajtek's birthday at school 🎂
Click Next to go step by step. Watch the sweets fly from the bag to the friends' plates - and how many stay in the bag.
Bajtek's birthday
It's Bajtek's birthday! He brought a bag with 23 sweets to school and wants to share them with 5 friends. Everyone should get the same amount. Bajtek wants to know: how many sweets will be left in his bag?
How many sweets should Mum give? 🛍️
Bajtek wants as many sweets as possible left in his bag after sharing with 5 friends. He checks different numbers of sweets in Python: after the arrow is what stays in his bag.
Click the arrow - Bajtek will check different numbers of sweets. Every group of 5 sweets is one round for 5 friends, and what doesn't fill a group stays in the bag.
1print(20, "->", 20 % 5)2print(21, "->", 21 % 5)3print(22, "->", 22 % 5)4print(23, "->", 23 % 5)5print(24, "->", 24 % 5)6print(25, "->", 25 % 5)
▍The most are left with 24 sweets - 4 for me! 🎉 And with 25 nothing is left, because 25 divides by 5 with no remainder. The remainder of dividing by 5 is always less than 5: 0, 1, 2, 3 or 4. Mum, give me 24! 🛍️
What does print(10 // 3) print?
Which number is odd?
print(8 % 2)print(9 % 2)print(10 % 2)
What does print(2026 // 10) print?
Don't divide by zero!
print(5 / 0) stops the program with a ZeroDivisionError - you can't divide by zero, just like in maths. The same goes for // and %.
Dividing by zero
The program prints the first line and stops on the second.
1print(10 / 2)2print(10 / 0)3print(10 / 5)
▍Apples in baskets
We put 23 apples equally into 4 baskets. 🍎
To share: 23
The apples in code
1print("In each basket:", 23 // 4)2print("Left over:", 23 % 4)3print("If we cut them:", 23 / 4)
▍How many in each basket, how many left?
Shoes in pairs 👟
We pair up 9 shoes - that is, divide by 2. One will be left without a pair!
To share: 9
The shoes in code 👟
Click the arrow - we have 9 shoes to sort into pairs.
1print("Pairs:", 9 // 2)2print("Without a pair:", 9 % 2)3print("Exactly:", 9 / 2)
▍Digits of a number: % 10 and // 10
This is a very common contest task! Let's start with the simplest part: how do we get the last digit of a number?
Just take the remainder of dividing by 10: 472 % 10 is 2.
Why? 472 is 47 full tens and 2 more. Those 2 don't make another ten - they are left over as the remainder. And that's exactly the last digit!
The last digit of 472
% 10 is the remainder of dividing by 10.
The last digit in code
For any number % 10 gives its last digit - even for a 0 at the end and for a one-digit number.
Click the arrow - we'll take the last digit out of every number.
1print("Last digit of 472:", 472 % 10)2print("Last digit of 2026:", 2026 % 10)3print("Last digit of 150:", 150 % 10)4print("Last digit of 7:", 7 % 10)
▍And how do we cut the last digit off? That's // 10: 472 // 10 is 47 - the number without its last digit (47 full tens).
Cutting the last digit off
Click the arrow - we'll cut the last digit off every number.
1print("472 without its last digit:", 472 // 10)2print("2026 without its last digit:", 2026 // 10)3print("7 without its last digit:", 7 // 10)
▍A clock: minutes to hours
A film lasts 135 minutes. How many hours and minutes is that? An hour has 60 minutes, so:
- full hours:
135 // 60= 2, - minutes left over:
135 % 60= 15.
The film lasts 2 hours and 15 minutes. 🎬
A film in hours and minutes
We have 135 minutes. Click the arrow - let's see how many full hours fit in.
1print(135 // 60, "h")2print(135 % 60, "min")
▍What is 7 % 2?
Which operation gives the last digit of 359?
Seconds to minutes ⏱️
200 seconds: a minute has 60 seconds.
We have 200 seconds. Click the arrow - let's see how many full minutes fit in.
1print(200 // 60, "min")2print(200 % 60, "s")
▍How many weeks to Christmas? 🎄
There are 78 days left to Christmas Eve. A week has 7 days.
We have 78 days. Click the arrow - let's see how many full weeks fit in.
1print("Weeks:", 78 // 7)2print("Plus days:", 78 % 7)
▍Remember
/divides exactly and always gives a number with a point.//says how many each gets (no remainder).%says how many are left (the remainder).% 2checks even/odd,% 10gives the last digit.- You can't divide by zero.
Now you share the candies! In the tasks pick the right kind of division.
Tasks from the video
We solve them together in the video - pause it and try first on your own.
Practice tasks
Try to solve them without the video. Stuck? Every task has hints and an editorial.
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