How does Modular Arithmetic work?

Question 6 from Tom Rocks Maths and I Love Mathematics - answering the questions sent in and voted for by YOU. This time we explore modular arithmetic through the familiar example of the 12-hour clock.

Q1: What is the probability I have the same PIN as someone else?
Q2: How long would it take to sink to the bottom of the ocean?
Q3: What is the gravitational field of a hollow Earth?
Q4: What is the best way to win at the board game Monopoly?
Q5: What are the most basic Mathematical Axioms?
Q6: How does Modular Arithmetic work?
Q7: What is the Gamma Function?
Q8: How many ping-pong balls would it take to lift the Titanic from the ocean floor?
Q9: What is the graph of x^x?
Q10: How can you show geometrically that Pi is between 3 and 4?

Produced by Dr Tom Crawford at the University of Oxford.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths

Get your Tom Rocks Maths merchandise here:

[adrianalapuerta]

I'm genuinely really impressed by how well you explained this. well done and thank you.

[marnierogers]

Just watched a 30min uni lecture explaining this twice ... still didn't get it. Watched the first 4 mins of this and understand completely. Cheers!

[doodelay]

I love how THOROUGHLY you explained the concept long before you gave the equation. I will definitely take this pedagogic lesson along with me now

[ChacingBugs]

Holy crap, always assumed modular arithmetic was super confusing, but you explained it so well it actually seems like fun.

[adhiyanthaprabhujeyashanka]

I have seen so many videos, but no one explained it as clear as you did, what I liked is the fact that you also included examples with negative numbers, and adding that a congruent to b (mod n) where b is negative is also true, but we don't usually put -ve values for b(the remainder when a is divided by n)

[ihrtashleylu]

i always knew that modular arithmetic had something to do with remainders, and im a visual learner so i loved the way you used the clock as an example. thanks this was so clear and showed me that i shouldn’t be scared of this concept cuz i always thought it was so hard ‼️

[ziaulhug]

I was really longing for this kind of explanation.
Everyone were like into the numbers but you told us what the number is about

I love it!!

[twentylulu]

Though this is a few years late, thanks a ton for this video! I was struggling with the idea of modular arithmetic, but the clock example really opened my eyes to how truly simple this is!

[exoticcoder]

You teach so well, it's my first time to understand clearly what it is comparing to other videos ! Thank you sir !

[ibehsuccess]

The best explanation for modular arithmetic, love your class

[Nanis-World]

WHERE HAVE YOU BEEN ALL MY COLLEGE LIFE!!!??? This was the easiest explanation out of like 7 videos I wasted time watching and you explained it so effortlessly and it ACTUALLY makes sense :) Thank you!

[patrickmayer]

Incredible explanation! It's awesome that we all use modular arithmetic when doing time math and we don't even realize it! Thanks for the video!

[vincentmessina]

Fantastic explanation, by far the best out there. Well appreciated Tom!

[lindenjohnson]

best elucidation of this concept I have seen thank you

[sanmore]

Ha. Trying to understand this for months....your clock example is just what I need. Thanks a lot. Keep up the good work

[madhureshminoshi]

This is the best explanation of modular on youtube. Great work. Thank you.

[imyame_se]

Thank you so much, I really appreciate the simple yet detailed explanation.

[vaishnaveesuriyanarayanan]

its so mind blowing the way concepts are explained using simple examples

[fisulohi]

The best explanation of modular arithmetic on the internet. Thank you!

[yelenalovrenovich]

Thank you so much for your simple, clear explanation! The penny has finally dropped!!