# 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.

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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\%}

**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 PFS### Percentages L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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