Maths Tricks to Blow Your Mind

A Journey Through Viral Maths

Kyle D. Evans, Kyle D Evans

• Publisher: Allen & Unwin
• Year: 2021
• Print ISBN: 9781838958763
• eBook ISBN: 9781838953676
• Topic: Mathematics
• Subtopic: Games in Mathematics
• Index: Mathematics

What is 4% of 75? Can you calculate 60 + 60 x 0 + 1? Which is bigger, an 18-inch pizza or two 12-inch pizzas? Join award-winning maths presenter Kyle D Evans on an entertaining tour of viral maths problems that have gone wild on social media in recent years. From the infamous 'Hannah's sweets' exam question to percentages 'life-hacks', viral maths problems seem to capture the public's imagination without fail. In Maths Tricks to Blow Your Mind, Kyle presents over 50 viral maths problems with background information, explanations and solutions to similar problems, all in a humorous, accessible and inclusive manner. Want to dazzle and delight your friends and family? This book shows you how!

1

THIS ONE COOL MATHS TRICK WILL BLOW YOUR MIND

Maths tricks and ‘life hacks’

#1

Calculate 4% of 75.

Some of the most satisfying maths ‘tricks’ can be those that were under our noses for years and years but that we never noticed. Recently I was starting a lesson with an A-level maths class when one of my 17-yearold students entered, marched to the front of the room, picked up a whiteboard pen and proudly wrote in huge letters on the board:

4% of 75 is 75% of 4

The student then charismatically replaced the whiteboard pen lid (just about resisting the urge to drop the pen to the floor in the time-honoured ‘mic drop’ style) before turning to face the room to revel in the adulation of his peers. Well, half of his peers. Half of the class were as mind-blown as he was – and, perhaps, you were? – whereas the other half remained thoroughly nonplussed. They’d realized the truth of this little mathematical nugget years ago.

This, of course, is the trick mentioned in the introduction, and every few months something like this bubbles up on Facebook or Twitter, with varying levels of virality. Here is the example from 2019 that my student had seen, garnering tens of thousands of likes and retweets on Twitter:

Here are some suitably stunned replies:

This just broke my brain.

I used to teach maths for reporters and wish I’d had this explanation in my back pocket. I had other tricks for mathsphobes but this is far more elegant.

You have won Twitter today, Mr Stephens!

And here are some people who have no room for joy in their life:

Seriously? All you’re saying is 3 × 2 = 6. As does 2 × 3. Do you really think people don’t understand such a simple concept enough to know this? Good grief.

Why is this news? This is called ‘propiedad conmutativa’ (Commutative property) in spanish and it’s taught in elementary school. Millennials discover… .

More about that ‘propiedad conmutativa’ later. Let’s break it down a little bit and first check that the trick definitely does work, before getting into why it works.

75% of 4

A fundamental of working with percentages is knowing their equivalent fractions and ratios: 75% is simply three-quarters, so we can very quickly see that three-quarters of 4 is 3.

4% of 75

This is a little harder to calculate (without knowing the trick!), since 4% is not a ‘nice easy’ fraction. A method schoolchildren might be shown is to use 10% and 1% as starting points, using the fact that 10% of a number is ten times smaller than the original number, and 1% is ten times smaller again. In this case:

100% of 75 = 75

10% of 75 = 7.5

1% of 75 = 0.75

To find 4% of 75 from here, we can put together four lots of 1%, i.e. 4 lots of 0.75 is 3.

So if faced with the need to calculate 4% of 75, it’s much easier to swap and calculate 75% of 4 instead. Don’t fancy calculating 42% of 10? No problem – do 10% of 42 instead, much easier! It even works for percentages above 100. Try finding 25% of 400 – easy, right? A quarter of 400 is obviously 100. Our method says this should be the same as 400% of 25, and of course it is: 400% of 25 simply means four lots of 25: also 100. Calculations like this take us a little closer to the ‘why’, more of which shortly.

Try it yourself

(a) 73% of 10

(b) 12% of 25

(c) 16% of 75

(d) 44% of 5

(e) 13% of 25

I find this little mathematical trick very satisfying, not least because I still remember working it out for myself in maths class and peering around the class to see if anyone else had cottoned on. They hadn’t! It seemed that only I knew this incredible secret – I’m not even sure if the teacher knew!

By the way, I don’t claim to be some great genius in working the trick out for myself. Many a greater mathematician than I have gone much of their adult life without knowing this trick: in writing this book I surveyed my army of followers on social media to find out how many knew about this trick. Although they’re probably slightly more maths-savvy than the average social media user, the results still showed nearly half who did not know that 4% of 75 was equal to 75% of 4:

Learnt it in school: 16.4%

Learnt it from social media: 25.2%

Learnt it from somewhere else: 15%

Did not know: 43.5%^*

So if you had your mind blown by this, you’re in good company. It was interesting that in the comments many teachers stated that they didn’t know this until they began teaching, much as many people express dismay that they were never taught this in school. Now you know why: your teachers didn’t know either! But that’s fine; every day’s a school day (especially if you work in a school). Let’s zoom in a little closer to the de...

Table of contents

• Cover
• Title
• Copyright
• Contents
• Introduction
• 1 This One Cool Maths Trick will Blow Your Mind:
• 2 It was Different in my Day:
• 3 Back to School:
• 4 Out of Order:
• 5 Bad Maths:
• 6 Get into Shape:
• Conclusion:
• Solutions
• Acknowledgements