Functional Skills: Percentages

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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.

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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.

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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\%}

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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}

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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.

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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\%}.

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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}

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Functional Skills: Percentages Example Questions

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

 

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}

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\%

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

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\%

To find the total mass of the bar,  divide the mass of protein by 0.18:

 

16.2 g \div \, 0.18 = 90 g

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Percentages Worksheet and Example Questions

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Percentages L1

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Percentages L2

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