## How Is GCSE Maths Used in Everyday Life?

Here are 10 examples of where people use Negative Numbers in everyday life or in their jobs. From keeping on top of your bank balance to following a career in computer games design, negative numbers are everywhere.

Please note: The maths careers website is a resource which is aimed at the whole of the United Kingdom, and any mention of GCSEs and A-levels can also be applied to equivalent qualifications in Scotland.

## Bank Accounts and Personal Finance

If you see a negative number appear on your bank statement, then it means that you have spent more money than you have in your account. If you see a figure of -£100, but you know that your salary is £2000 per month, then how much will you have left once you are paid? That’s right – you will have -£100 + £2000 = £1900.

If on the other hand you see a negative figure for income tax on your pay slip, it means that you are being given back tax, because you have paid too much tax in the past. (Tax is a deduction, so a negative deduction will result in a positive gain for your wallet.) This will happen more often for workers who earn different amounts each month, as they may have paid too much tax in a previous month.

If you want to become an accountant, actuary, or work in finance you will need to have a good grasp of negative numbers, as they are fundamental to the world of money.

## Temperature

Back in 2007 a Scratch Card called ‘Cool Cash’ caused confusion and had to be withdrawn from sale when lots of players didn’t understand if they had won. The aim of the scratch card was to reveal a temperature which was lower than the one printed on the card. It turned out that many players thought temperatures such as -6 degrees were lower than -10 degrees. (If you were outside in the snow you would have no doubt that  is colder.)

This is a trivial example, but it shows how important it is to understand negative numbers when it comes to temperature. Lots of people deal with temperature in their jobs, from workers operating big freezers in warehouses, to scientists who are monitoring temperatures as part of their experiments. It might also help you think twice about that next holiday to Lapland!

## Height Above Sea Level

If you want to measure the height of a mountain, town or even airport then you need to find its ‘Height above sea level’ or ‘Elevation’, with sea level being measured as height 0. There are lots of places around the world which are below sea level. This means that they have a negative elevation.

In the UK, the Fens have an elevation of -2.75m, as they are mostly reclaimed wetlands which are now protected by pumps and drainage banks. Badwater Basin, in Death Valley, California has an elevation of -86m and is the lowest point in North America. Understanding the elevation of a region will be crucial to calculating the impact of climate change.

## Lift Numbering Systems

Another place you might spot negative numbers is in a lift, where they normally represent the basement floors. It can be helpful to think of the number line a bit like a high rise building – if you are working out -5+3, you can imagine you are 5 floors below ground level and that you are moving up 3 floors, so now you are at floor -2.

## Standard Form

Standard Form is used to make very large or very small numbers much easier to deal with. If we want to talk about a very small number, then we’ll need a negative power.  For example, the length of a virus is approximately (equal to 0.0000002m). Being able to work confidently with negative numbers while using Standard Form is particularly important for scientists and engineers.

## Board Games

Tabletop gaming is making a big comeback, with board game shops and cafes popping up all over the UK. Some of these board games use negative scoring, where you can lose points as well as gain points. It is helpful to be able to add and subtract with negative numbers so that you can keep an accurate score. An example of a boardgame where you can end up with a negative final score is Patchwork. Another couple of games which involve negative scoring are Azul: Stained Glass of Sintra and Ticket to Ride.

## Golf

Unlike in most sports, the aim in golf is to get the lowest score by completing the course in as few strokes as possible. In a recent PGA Championship, Shane Lowry won with a final score of -17, taking away a cool £1.3 million in prize money.

Each hole in golf has a ‘par’ which is the expected number of strokes for that particular hole.

There are special names for how well you do. For example, if the hole has a par of 4 and you complete it in 2 strokes, you have achieved an ‘Eagle’ and a score of minus 2. (Because you did it in two less than what was expected.)

 Name Score Condor -4 Albatross -3 Eagle -2 Birdie -1 Par 0 Bogey 1 Double Bogey 2 Triple Bogey 3

## Computer Games

Negative numbers crop up all the time when designing computer games. One of the ways they are used is with vectors.

Imagine you have a character you want to move around a scene. If you want to move them 3 units to the right and 2 units down, then you will need to move your character using the vector

Now suppose you have two characters in your game:

A which has a position vector of and

B with a position vector of .

Which vector would move player A to join player B? That’s right, the answer is

Vectors can also be used to find out how far apart two characters are. This is important to stop characters bumping into each other and to find out if a pursued character has been caught. In the example above, for players A and B we can find out how far apart they are by calculating the magnitude of the vector which is .

There are many other things to learn about vectors if you want to become a games designer and all of them will require you to use negative numbers.

## Negative Windspeeds in Athletics

Everyone knows that running into the wind can be tough and that a strong wind can dramatically affect performance. In athletics, wind is either classed as a tailwind (a positive value) or a headwind (a negative value), and there are strict rules governing wind velocities.

Mathematical modellers have developed a table which shows the potential impact in seconds on the 100m sprint of different wind velocities.

The impact on performance has led to IAAF rules which state:

‘The average wind velocity … shall not exceed plus 2 metres per second.’

https://www.worldathletics.org/records/recordsrules

All world records are listed against their windspeed, and unsurprisingly very few of them list a negative value. Every athlete will however be keeping a close eye on those negative windspeeds, both in competition and training.

## History

This final example is not strictly about negative numbers, because the minus sign isn’t written down, however it works in the same way. The use of BCE after a date is very much like putting a minus sign before a number. For example, if the Pharaoh Tutankhamun was born in 1341 BCE and died in 1323 BCE then how old was he when he died? We can replace the BCE at the end of the year with a minus before the year and calculate the answer: (-1323) – (-1341) = 18. If you are feeling confused in History, it could be worth turning to your negative numbers.

Article by Hazel Lewis

#### Image Credits

Boat Image by congerdesign from Pixabay

Plant Photo by micheile henderson on Unsplash

Thermometer Image by Clker-Free-Vector-Images from Pixabay

Cliff Image by Frank Winkler from Pixabay

Elevator Numbers Tony Webster from Minneapolis, Minnesota, United States, Elevator Negative Floor Numbers in Ireland (16785350923), CC BY 2.0

Standard Form Image by Gerd Altmann from Pixabay

Patchwork Image Pongrácz Zsolt, Quilt in a game of Patchwork, CC BY-SA 3.0

Golf Image via Pixabay (free for use)

Computer Game Image by Stephan from Pixabay