Functional Skills: Percentages
Functional Skills: Percentages Revision
Percentages
Percent means “out of 100” and is denoted by the \% sign. e.g. 40\% means 40 percent which is 40 out of 100.
Percentages can be written as fractions or decimals: 40\% = \dfrac{40}{100} = 0.4
There are 6 skills you need to learn for percentages.
For LEVEL 1, you will only deal with percentages in multiples of 5\%, such as 5\%, 10\%, 50\% etc. For LEVEL 2 you will need to use these skills for more complicated percentages, such as 3\%, 4.5\% etc.
Make sure you are happy with the following topics before continuing.
Skill 1: Percentage of an Amount
There are some important percentages that you should know how to work with when you do not have a calculator:
Divide by 2 to find 50\%
Divide by 10 to find 10\%
Divide by 20 (or 10 then 2) to find 5\%
Example: Calculate \textcolor{blue}{15 \%} of \textcolor{blue}{70}.
With a calculator:
Multiply \textcolor{blue}{15\%} as a decimal or fraction by 70
0.15 \times 70 = \dfrac{15}{100} \times 70 = \textcolor{black}{10.5}
Without a calculator:
Split \textcolor{blue}{15\%} into amounts, such as \textcolor{blue}{10\%} and \textcolor{blue}{5\%}:
\textcolor{blue}{15\% = 10\% + 5\%}
\textcolor{blue}{10\%} \text{ of } 70 = 70 \times 0.1 = 70 \div 10 = 7
\textcolor{blue}{5\%} \text{ of } 70 = 70 \times 0.05 = 70 \div 20 = 3.5
So,
\begin{aligned} \textcolor{blue}{15\%} & = 10\% + 5\% \\ &= 7 + 3.5 = \textcolor{black}{10.5} \end{aligned}
Note: For large percentages you could subtract from 100\% instead, e.g. for 80\% you could find 20\% and then subtract this from the original number.
Follow Our Socials
Our Facebook page can put you in touch with other students of your course for revision and community support. Alternatively, you can find us on Instagram or TikTok where we're always sharing revision tips for all our courses.
Skill 2: Number as a Percentage of Another
Example: A cinema screen has 150 seats. 81 of the seats have been taken.
What percentage of seats have been taken?
Here, we need to calculate 81 as a percentage of 150.
Divide the first number by the second number:
81 \div 150 = \textcolor{purple}{0.54}
Convert this into a percentage by multiplying by 100:
0.54 \times 100 = \textcolor{purple}{54\%}
Skill 3: Percentage Increase
For a percentage increase, the decimal that you multiply the amount by will be greater than \bf{1}.
Example: Sue owns a vintage car. Last year it was worth \textcolor{blue}{£6,500}.
This year, the value of the car has increased by \textcolor{red}{5\%}.
What will be the value of the car this year?
Step 1: Add the percentage increase to 100\% and convert to a decimal to find the multiplier:
\textcolor{red}{5\% + 100\% = 105\% = 105 \div 100 = 1.05}
Step 2: Multiply the original amount by the multiplier to find the new increased value:
\textcolor{blue}{£6,500} \times \textcolor{red}{1.05} = \textcolor{black}{£6,825}
So,
the value of the car this year is \textcolor{black}{£6,825}
Note: If you find it easier, you can find 5\% of £6,500:
\dfrac{5}{100} \times £6,500 = 5 \div 100 \times £6,500 = £325
and then add this on:
£6,500 + £325 = \textcolor{black}{£6,825}
Skill 4: Percentage Decrease
For a percentage decrease, the decimal that you multiply the amount by will be less than \bf{1}.
Example: Last year, a company made a profit of \textcolor{blue}{£30,000}. This year, the profits are down by \textcolor{red}{10\%}.
How much profit does the company make this year?
Step 1: Subtract the percentage decrease from 100\% and convert to a decimal to find the multiplier:
\textcolor{red}{100\% - 10\% = 90\% = 0.90}
Step 2: Multiply the original amount by the multiplier to find the new decreased value:
\textcolor{blue}{£30,000} \times \textcolor{red}{0.90} = \textcolor{black}{£27,000}
So,
this year, the company makes a profit of \textcolor{black}{£27,000}.
Note: Like for percentage increase, you may find it easier to find the percentage of the number and then add this on.
Skill 5: Percentage Change
You may be given the original amount and the value after a percentage increase or decrease, and will need to find what the percentage change was.
\text{\textcolor{limegreen}{Percentage Change}} = \dfrac{\text{\textcolor{Red}{Change}}}{\text{\textcolor{blue}{Original}}} \times \textcolor{black}{100}
If the answer is positive then the change was an increase. If the answer is negative then it was a decrease.
Example: Calculate the percentage change of the value of a boat when it goes down from \textcolor{blue}{£8,000} to \textcolor{black}{£6,000}.
Firstly, calculate the difference, which is:
\textcolor{black}{£6,000} - \textcolor{black}{£8,000} = \textcolor{Red}{-£2,000}
Then, use the formula above:
\text{\textcolor{limegreen}{Percentage Change}} = \dfrac{\textcolor{Red}{-2000}}{\textcolor{blue}{8000}} \times \textcolor{black}{100} = \textcolor{black}{-25\%}
So, the value of the boat has decreased by \textcolor{black}{25\%}.
Skill 6: Reverse Percentages
Sometimes we are given the result of a percentage change and have to work backwards to find the original value.
Example: Sheila buys a jacket in a sale. It is reduced by \textcolor{red}{30\%} down to a price of \textcolor{blue}{£56}. Work out the original price of the jacket.
Step 1: Calculate the cost of the jacket as a percentage of its original value. We know it has \textcolor{red}{30\%} off so:
100\% - \textcolor{red}{30\%} = 70\%
Step 2: Divide the cost by 70\% to find 1\% of the original value:
\begin{aligned} (\div \, 70) \, \, \, \, \, 70\% &= \textcolor{blue}{£56} \,\,\,\,\, (\div \, 70) \\ 1\% &= £0.80 \end{aligned}
Step 3: Multiply by 100 to get 100\% and the original value:
\begin{aligned} (\times \, 100) \, \, \, \, \, 1\% &= £0.80 \,\,\,\,\, (\times \, 100) \\ 100\% &= \textcolor{purple}{£80} \end{aligned}
Functional Skills: Percentages Example Questions
Question 1: A quiz is marked out of 120 points. Team A score 75\%. What points do Team A get?
Do not use a calculator.
[2 marks]
Since 75\% is a big number, you could instead find 100\% - 75\% = 25\% and then subtract this from 120:
25\% = 10\% + 10\% + 5\%
10\% \text{ of } 120 = 120 \div 10 = 12
5\% \text{ of } 120 = 12 \div 2 = 6
So,
\begin{aligned} 25\% & = 10\% + 10\% + 5\% \\ &= 12 + 12 + 6 = 30 \end{aligned}
Hence,
75\% \text{ of } 120 = 120 - 30 = 90
Question 2: Calculate 23\% of 190, without using a calculator.
[2 marks]
Split 23\% into amounts, such as 10\%, and 1\%:
23\% = 10\% + 10\% + 1\% + 1\% + 1\%
10\% \text{ of } 190 = 190 \div 10 = 19
1\% \text{ of } 190 = 190 \div 100 = 1.9
So,
\begin{aligned} 23\% & = 10\% + 10\% + 1\% + 1\% + 1\% \\ &= 19 + 19 + 1.9 + 1.9 + 1.9 = 43.7 \end{aligned}
Question 3: Matt scored 87 out 150 on an exam. What is his score as a percentage?
[2 marks]
Divide the first number by the second number:
87 \div 150 = 0.58
Convert into a percentage by multiplying by 100:
0.58 \times 100 = 58\%
Question 4: Last year, Dipak scored 60 on a test. This year, Dipak scores 5\% higher on the test.
What score did Dipak get on the test this year?
[2 marks]
Add the percentage increase to 100\% and convert to a decimal to find the multiplier:
5\% + 100\% = 105\% = 105 \div 100 = 1.05
Multiply the original amount by the multiplier to find the new increased value:
60 \times 1.05 = 63
Question 5: Carol’s salary has increased from £22,600 to £23,278.
By what percentage has her salary increased?
[2 marks]
The difference between the two salaries is
\pounds23,278 - \pounds22,600 = \pounds678
The percentage change can be calculated as follows:
\dfrac{678}{22600} \times 100 = 3\%
Therefore, Carol’s salary has increased by 3\%
Question 6: A recovery bar contains 16.2 g of protein. 18\% of the bar is protein.
Calculate the total mass of the bar.
[2 marks]
To find the total mass of the bar, divide the mass of protein by 0.18:
16.2 g \div \, 0.18 = 90 g
Functional Skills: Percentages Worksheet and Example Questions
Percentages L1
FS Level 1NewOfficial PFSPercentages L2
FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]
Revision Products
Functional Skills Maths Level 2 Pocket Revision Guide
Revise and practice for your functional skills maths level 2 exam. All topics covered in this compact revision guide.
Functional Skills Maths Level 2 Mini Tests
Practice for your functional skills Maths level 2, questions from every topic included.
Functional Skills Maths Level 2 Revision Cards
Revise for functional skills maths level 2 easily and whenever and wherever you need. Covering all the topics, with revision, questions and answers for every topic.
Functional Skills Maths Level 2 Practice Papers
This 5 set of Functional Skills Maths Level 2 practice papers are a great way to revise for your Functional Skills Maths Level 2 exam. These practice papers have been specially tailored to match the format, structure, and question types used by each of the main exam boards for functional skills Maths. Each of the 5 papers also comes with a comprehensive mark scheme, so you can see how well you did, and identify areas to improve on.
Functional Skills Maths Level 2 Practice Papers & Revision Cards
This great value bundle enables you to get 5 functional skills maths level 2 practice papers along with the increasingly popular flashcard set that covers the level 2 content in quick fire format.