A percentage is a way of calculating how much there is of something in relation to the whole. 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 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 PercentagesTo 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:
How to Solve Percentage ProblemsHow to Solve Percentage Problems
To translate decimals into percentages is even easier. Simply multiply the decimal figure by 100 to calculate the percentage:
How to Solve Percentage ProblemsHow to Solve Percentage Problems
Finally, to convert percentages into decimals is also very straightforward. You need to divide the percentage by 100 to calculate the decimal:
How to Solve Percentage ProblemsHow to Solve Percentage Problems
How to Work Out the Percentage of a Known Value
This is a particularly useful technique, as it allows you to work out how much of a whole value a particular percentage would be. This is the formula you would need to use:
How to Solve Percentage ProblemsHow to Solve Percentage Problems
This is something that people use all the time. For example, if you went out for dinner, spent £56 and wanted to leave a 10% tip, this is how you would work it out:
(£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.
