Percentages are used very widely in both mathematics and everyday situations, and they are really useful for understanding relative amounts and making them meaningful. Here are some common ways that percentages are used in day-to-day life:
Calculating how well a student has performed on a test Working out how much VAT you need to pay on a purchase Calculating how much to leave as a tip in a restaurant
Percentages are usually represented by the % symbol, and there are a few basic rules you need to understand to be able to manipulate percentages: If you need to find the total of £200 + 10% + 15%, the initial thought might be to calculate £200 + 25%. Instead, you need to calculate them separately and in order. First, add 100 to each percentage and then convert it to make a decimal larger than 1: 10% becomes 110% which is converted to 1.10 15% becomes 115% which is converted to 1.15 The original value is then multiplied by these numbers. To ensure that the number is manipulated correctly, the multiplication needs to be completed in the order that it is presented in the question: 200 x 1.10 = 220 This is the first step: £200 + 10% 220 X 1.15 = 253 This is the second step: (£200 + 10%) + 15% Therefore, the answer to £200 + 10% + 15% is 253.### How to Multiply Percentages To multiply percentages, you can convert them into decimals, multiply the decimals, convert back into a percentage. For example, if you are asked to multiply 15% and 40% together, the calculation would look like: 15% = 0.15 40% = 0.40 0.15 x 0.40 = 0.06 0.06 x 100 = 6% If you prefer to work in fractions, the calculation can also be done that way. For example, if you need to multiply 10% by 30%, you would convert them into fractions out of 100 then simplify: 10% = 10/100 = 1/10 30% = 30/100 = 3/10 Then multiply each fraction together. There is already a common denominator: 1/10 x 3/10 = 3/100 Then convert the fraction back into a percentage: 3/100 = 3%
How to Subtract Percentages
To subtract one percentage from another, just ignore the percentage signs and treat them like whole numbers. For example, to subtract 20% from 50%, perform the sum 50 – 20 to get 30. The answer is 30%. If you are subtracting a percentage from a whole number, you first need to convert it to a decimal. If you are asked to subtract 25% from 45 (for example, when calculating a discount), then you need to start by converting 25% to a decimal, which is 0.25. To calculate the amount that should be subtracted, multiply the original number by the decimal: 45 x 0.25 = 11.25 Then subtract this amount from the base figure: 45 – 11.25 = 33.75 You can also take the decimal you converted the percentage into, subtract it from 1, then multiply the original number by it: 25% = 0.25 1 – 0.25 = 0.75 0.75 x 45 = 33.75
Converting Decimals and Fractions to Percentage Values
When taking a numerical reasoning test, you may be required to move fluidly between questions using percentages, fractions and decimals. It is very straightforward to convert numbers between these different representations, and these are key techniques to learn. To translate fractions into percentages, you should divide the bottom number in the fraction by the top number. This will give a decimal figure. Then multiply that decimal figure by 100, to create the percentage. Here’s an example: (£56/100) x 10 = £5.60 There are ten practice questions below. Should you need further practice afterwards, we recommend the practice packages available from JobTestPrep. These tests include percentages questions, with full explanations for all answers.
Question 1: Calculating the Percentage of a Known Value
Calculating the percentage of a known value is quite straightforward. In a numerical reasoning test, these questions tend to require you to identify/manipulate the relevant information in order to use the formula. Graphs or tables will often be used to present the information, such as the one below. Table 1: Passenger Numbers Using Rail Services at Different Times of Day What percentage of the apples are green? The formula you need to use to calculate this is: Using percentages like this is also useful for comparing changes to different numbers, where it can be difficult to see at a glance what the impact has been.
Question 3: Percentage Increases
Car Insurance Costs There are two ways of calculating a percentage discount. Firstly, you can calculate the discount and then subtract this from the starting price. To do this you would use the following steps: To do this you would need to use the following steps: Who paid the least for their new trainers? For example, if Shimmy bought a house for £150,000 in 2010, its value may increase over the years and in 5 years’ time, it is worth 20% more than he paid for it. The new value could be calculated by:
Converting the percentage to a decimal: 120% = 1.2 Multiplying the starting value by 1.2: £150,000 x 1.2 = £180,000
Therefore, in 2015 his house was worth £180,000. You can also reverse this process and work out what the starting value may have been. For example, Shimmy’s friend Elissa also bought a house in 2010. She recently had it valued and found it was now worth £230,000. This is 80% greater than what she originally paid for it. To work out the original value of the house, you need to use the following process: How much was her initial investment?
Make sure that if you are converting decimals to percentages (or vice versa) that you get the decimal point in the right place. Often the multiple-choice answers to numerical reasoning tests will include incorrect answers with exactly this error, so if you have made this mistake there may well be an answer waiting to catch you out. When comparing percentages make sure that you have a common baseline (otherwise the percentages will be unrelated to one another). One area that often catches people out is year-on-year percentage increases. For example, Freya has £10 and each year this increases by 5%. How much will she have after 3 years? Some people can be tempted to add together the 5% for the 3 years i.e. 15% and multiply the £10 by 15% giving £11.5. This is incorrect. The correct way of approaching questions like this is to remember that EACH year the initial £10 increased by 5%. So at the end of year 1, Freya would have £10 x 1.05 = £10.5. At the end of year 2, she would have £10.5 x 1.05 = 11.025, and so on. It is important to add in each of these steps to arrive at the correct answer. Another common error is around percentage increases. For example, the price of a loaf of bread increases by 10%. After the increase the price was £1.10, how much did the bread cost before the increase. A really common error is for people to try and solve this type of question by calculating: £1.10 x 0.9 = £0.99. This is incorrect. Remember, that £1.10 = 110%, therefore you must use this calculation: (£1.10/110) x 100 = £1.00 Avoid using the % button on your calculator unless you are really confident in what you are doing. It might seem like a sensible short cut but it can lead to you making basic errors.
If you would like to practise more percentage-based questions, we recommend the practice packages available from JobTestPrep. These tests include numerous percentage questions, with full explanations for all answers.
