Some of Tom’s favourite maths life hacks as featured in the University of Oxford Staff Bulletin.

**Percentages: x% of y = y% of x**

This might look a little complicated with the general symbols, but what it really says is that you can work out a percentage in whatever order is easiest. For example, 4% of 75 is the same as 75% of 4, which we know to be 3.

The reason it works is due to the multiplications involved when doing a percentage calculation. Taking the example above, for 4% of 75 we are really working out 4/100 * 75. Because the order in which we multiply or divide numbers doesn’t matter (commutativity is the technical term), we can instead rearrange this to be 75/100 * 4 which is exactly how we would calculate 75% of 4. Therefore, we get the same answer!

I made a short social media video explaining this trick which you can watch here.

**Temperature conversions: changing from Fahrenheit to Celsius**

Fortunately, there aren’t many countries around the world still using the Fahrenheit system, but for the few that still do (here’s looking at you America), it can be a real pain trying to work out whether or not you need your coat when heading out for the day. But, not to worry, there’s a simple trick you can use to get a pretty accurate estimate when converting from Fahrenheit to Celsius: subtract 30 and divide by two. Here are a few examples:

100^{o }F = (100 – 30)/2 = 70/2 = 35^{o }C [*actual value 38 ^{o} C*]

60^{ o }F = (60 – 30)/2 = 30/2 = 15^{ o} C [*actual value 16 ^{o} C*]

30^{ o }F = (30 – 30)/2 = 0/2 = 0^{ o} C [*actual value -1 ^{o} C*]

So, whilst not perfect, it certainly gives you a very good idea of whether or not to bring your coat… (For anyone looking for the exact formula, subtract 32 and multiply by 5/9).

I made a short social media video explaining how to convert the other way around – from Celsius to Fahrenheit – which you can watch here.

*Tipping*: *calculating 5%, 10%, 15%, 17.5% and 20% tips*

When eating out in the UK, chances are you’re either not expected to tip, or if you do, it’s a nice and simple 10%. To calculate a 10% tip just take the total and move the decimal point one place to the left. For example, on a bill of £65.10, moving the decimal point one place to the left gives a 10% tip of £6.51.

Now in the US, things aren’t quite so simple – I’ve seen everything from 12.5%, 15%, 17%, 17.5%, 18%, 20%… But, there are a few tricks you can use to help make the calculations easier. A good starting point is often to use the same 10% trick as described above, i.e. move the decimal point one place to the left. The reason it’s helpful to start out knowing 10% is that this can then be halved (and if needed halved again) to give you 5% (and 2.5% respectively). Let’s take a $88.40 bill as an example:

10% = $8.84 by moving the decimal point one place to the left

5% = $4.42 by halving the 10% value

2.5% = $2.21 by halving the 5% value

Once we have these key values, we can now calculate a 12.5%, 15% or 17.5% tip by adding together the required amounts. You still need to do some addition of course, but it’s certainly a lot easier than trying to do 17.5% of $88.40 right from the off!

A 20% tip works very similarly, with the 10% value just now needing to be doubled. So here, that will give a 20% tip of two times $8.84 which gives $17.68.

Finally, for the trickier 17% or 18% tips we go back to the 10% value and use the same trick of moving the decimal point to the left to calculate 1% of the total. Doing this twice from our original value of $88.40 gives $0.88 which is equal to 1%. Now just as before, we can add the required number of 1% values to the 15% tip until we get to the desired 17% or 18% tip.

You could of course do all of this on your phone calculator, but what better way to practice your mental arithmetic and also impress your friends at the same time!