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Here are 10 examples of where people use fractions in everyday life or in their careers. This is a small snapshot of where fractions are used in the real world, as they are essential in almost every career and in many different areas of everyday life.

Please note: The MathsCareers 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.

Pharmacy and Nursing

Fractions are very important for pharmacists and nurses, particularly because errors can have serious consequences.

For example, nurses need to be able to use the following stock equation in order to know how to dilute a solution.

    \[\text { Amount of Stock Required }=\frac{\text { Strength Required }}{\text { Stock Strength }} \times \text { volume required }\]

They could then be asked to solve a problem such as:

Question: How much stock is required to make 3 litres of 1 in 80 solution from a stock strength of 1 in 40?

Answer: The basic equation gives

    \[\text { Amount of stock required }=\frac{\frac{1}{80}}{\frac{1}{40}} \times 3=\frac{1}{2} \times 3=1.5 \text { litres }\]

These examples are taken from the Mathcentre information on Dilution of solutions for nurses.

Engineering

There would be no buildings, cars, aeroplanes or manufacturing without engineering, it is the foundation of the modern world. If you want to study Engineering at university, most courses will require A-level mathematics and many will recommend the study of A-level Further Mathematics, showing just how important maths is to this subject. One example of the use of fractions is in air-fuel ratios. Inside a car’s engine you need both air and fuel to burn together, but how do you decide on the right proportions? The air-fuel ratio can be calculated like this:

    \[\text { Air-}\text {Fuel Ratio }=\frac{\text { Mass of Air }}{\text { Mass of Fuel }}\]

For a petrol engine the theoretically perfect air-fuel ratio is around 14.7, but then this can be adjusted to affect driving performance and fuel-economy. Engineers will design their engines to make the most of the air-fuel ratio.

Set Design and Architecture

If you are making a scale model such as in architecture or set design, then you will definitely need fractions. If your model is at a scale of 1:200 then this means that you need to take the real lengths and multiply them by \frac{1}{200} to get the model length. Another interesting use of fractions is in movie making and the technique of forced perspective. In the film The Hobbit, actor Martin Freeman who plays Hobbit Bilbo Baggins appears much smaller than Gandalf. This is achieved by the use of forced perspective.

Forced perspective equation \theta=\frac{L}{d}

\{\theta is the angle the object makes to the camera; L is the height of the object; d is the distance from the camera}

This means that if you make the distance larger, then the viewing angle will be small meaning that the object appears small to the viewer. Apparently in the Hobbit, the filming crew were armed with tape measures to make sure that Bilbo Baggins always looked the same height.

Baking and Recipes

Cooking is full of fractions. What if you have a recipe for four people which contains \frac{1}{2} teaspoon of vanilla extract and you want to make your cake for six people? You will need to perform the calculation \frac{1}{2} \times \frac{6}{4}=\frac{6}{8}=\frac{3}{4} teaspoon. On the Great British Bake Off Paul Hollywood once asked the contestants to “take \frac{2}{5} of your dough and divide it into six biscuit balls”. How much should each biscuit ball weigh? For further uses of maths in baking read this article on the maths used in the Great British Bake Off.

Grades and Exams

You have just received your latest test results – but what percentage did you get? You will need to be able to work this out when you are a student and also if you become a teacher or lecturer. For example, if you score 22 out of 27 in a test, then you need to calculate \frac{22}{27} \times 100=81 \%.

Time

Understanding fractions will make it much easier to calculate with real life time problems. Most people now use digital watches, but still talk about time in terms of fractions – a quarter of an hour, half an hour and so on. What if a beautician has 45 minutes to see each client and a half hour lunch break. How many clients can they fit in during an 8 hour day? Take off the half an hour, leaving 7 \frac{1}{2} hours. 45 minutes is \frac{3}{4} of an hour, meaning we can calculate 7 \frac{1}{2} \div \frac{3}{4}=10 time slots.

Scientists

All scientists will need to have an excellent understanding of mathematics, including in areas such as Biology. While it is true that some Biology and Chemistry degrees don’t ask for A-level mathematics, they may take an A-Level maths qualification into account. This is because these courses will contain substantial maths content and students who haven’t done A-level maths will need to put in extra work in order to thrive. At this level of maths, a GCSE level understanding of fractions will underpin most concepts, particularly when it comes to Calculus and rates of change. A specific example from biology is the SIR equations which show how an infectious disease spreads through a population – this isn’t GCSE level maths – but you need a GCSE understanding of fractions to even let you begin to grasp what is going on.

Susceptible (S) \quad \rightarrow \quad Infectious (I) \quad \rightarrow \quad Removed (R)

The SIR equations are a group of differential equations which model how many people will catch a disease over time. To understand what they mean, you will need to have studied some A-level calculus.

\frac{d S}{d t}=-\beta S I

\frac{d I}{d t}=\beta S I-\lambda I

\frac{d R}{d t}=\lambda I

Find out more

Shopping

Fractions and percentages come up all the time when shopping – and retailers are always trying to bamboozle customers by using unusual fractions which are difficult to visualise. If a shop offers 6 soups for £3 you can easily work out in your head \frac{3}{6} = 0.5 (50p) per soup. If a shop offers 7 tins of soup for £5 then this is the fraction \frac{5}{7} which nobody is familiar with. (A calculator reveals that this will mean 71.4p per soup.)

What about an offer which is advertised at \frac{1}{3} off – for example a kettle which is £45 down to £30. Next to it is a kettle which is £50 down to £35 – which is the better saving?

Kettle 1 – \frac{1}{3} off

£45 down to £30 representing a 33.3% saving

Kettle 2

£50 down to £35

\left(1-\frac{35}{50}\right) \times 100=30 \%

Kettle 1 is a better deal, depending on the quality of the kettles.

Surveys

Surveys and polls are really important. In an election if a party thinks they have a comfortable lead then they won’t put much effort into campaigning, which could have disastrous consequences if the polls turn out to be wrong. Imagine you have 10,000 people in a town who fall into the following age categories:

Number of people
Age 18-38 4,000
Age 39-58 3,000
Age 59-78 2,000
Age 79+ 1,000

What if you only have the money to survey 1,000 people. How many people should you survey from each age category? You are going to survey 1,000/10,000 = \frac{1}{10} of the people. This means you should interview:

Number of people to interview
Age 18-38 4,000 x \frac{1}{10} = 400
Age 39-58 3,000 x \frac{1}{10} = 300
Age 59-78 2,000 x \frac{1}{10} = 200
Age 79+ 1,000 x \frac{1}{10} = 100

This is called stratified sampling and is one of the many techniques used in market research.

Building and DIY

Professional builders use GCSE maths all the time – including fractions. Lots of people also carry out DIY at home – most homeowners will perform simple tasks such as putting up shelves at some point. For example if you buy a length of wood and want to make three shelves arranged vertically then you will need to divide your wood length into thirds. You will also need to measure the vertical height between the top and bottom shelf and divide that in half in order to locate the middle shelf. To locate the shelves in the middle of your wall, you will need to subtract the length of one shelf from the width of the wall and then divide what is left in half.

Fractions, Decimals, Percentages and Ratios

Don’t forget that fractions, decimals, percentages and ratios are all connected – for example a percentage means parts out of 100, so that 65% is the same as \frac{65}{100}. This means that a good understanding of fractions will enable you to understand situations which include decimals, percentages and ratios.

Featured image via Freecodecamp.org
Medication image by Diana Polekhina on Unsplash
Cookies image by May Lawrence on Unsplash
Shop mannequins by Artem Beliaikin on Unsplash