 Percentages Questions | Worksheets and Revision | MME

## Percentages

Percentage means “number of parts per one hundred” and is denoted by the $\bf{\%}$ sign. For example, $50\%$ of a number means $50$ parts of it out of a total of $100$, and since $50$ is one half of $100$, $50\%$ means half of the total amount.

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Level 4-5

## Skill 1: Percentage of an Amount

To calculate the percentage of an amount, we convert the percentage to a decimal or fraction and then multiply this by the amount.

Example: Calculate $\textcolor{blue}{16 \%}$ of $\textcolor{blue}{60}$.

With a calculator:

We need to multiply $\textcolor{blue}{16\%}$ as a decimal by $60$

$0.16 \times 60 = \dfrac{16}{100} \times 60 = 9.6$

Without a calculator it is better to split $\textcolor{blue}{16\%}$ into amounts that are easier to work out such as $\textcolor{blue}{10\%}$, $\textcolor{blue}{5\%}$, and $\textcolor{blue}{1\%}$

$\textcolor{blue}{10\%} \text{ of } 60 = 6, \quad \textcolor{blue}{5\%} \text{ of } 60 = 3, \quad \textcolor{blue}{1\%} \text{ of } 60 = 0.6$

\begin{aligned} \textcolor{blue}{16\%} & = 10\% + 5\% + 1\% \\ &= 6 +3+ 0.6 = 9.6 \end{aligned}

Level 1-3
Level 4-5

## Skill 2: Percentage Increase

For a percentage increase, the decimal or fraction that you multiply the amount by will be greater than $\bf{1}$

Example: Jane deposits $\textcolor{blue}{£1,360}$ into her bank account which has an interest rate of $\textcolor{blue}{2.2\%}$ per year. Assuming that she does not deposit or withdraw any money, how much money will she have in a year’s time?

The new total value of Jane’s account will be equal the original total plus $\textcolor{blue}{2.2\%}$ of the original total. To find this total we multiply $\textcolor{blue}{£1,360}$ by $\textcolor{blue}{1 + 0.022} = \textcolor{blue}{1.022}$.

Therefore, the total value is,

$\textcolor{blue}{1,360} \times \textcolor{blue}{1.022} = \pounds 1,389.92$

Level 1-3

## Skill 3: Percentage Decrease

For a percentage decrease, the decimal or fraction that you multiply the amount by will be less than $\bf{1}$

Example:

If Jane decides to withdraw $\textcolor{blue}{25\%}$ of the total $\textcolor{blue}{£1,389.92}$, we find the decimal equivalent as $1 - 0.25 = \textcolor{blue}{0.75}$

Therefore after the withdrawal, the value of the account is,

$\textcolor{blue}{1,389.9} \times \textcolor{blue}{0.75} = \pounds 1,042.44$

Level 1-3
Level 4-5

## Skill 4: Percentage Change

Percentage change is used to find the change in a value as a percentage.

$\text{\textcolor{Black}{Percentage `Change'}} = \dfrac{\text{\textcolor{Red}{Change}}}{\text{\textcolor{blue}{Original}}} \times \textcolor{black}{100}$

Example: Calculate the percentage change when a car goes down in value from $\textcolor{blue}{£8,500}$ to $\textcolor{black}{£7,000}$

Using the equation above we can calculate the percentage change by first calculating the difference, which is,

$\textcolor{black}{£8,500} - \textcolor{black}{£7,000} = \textcolor{Red}{£1,500}$

We then need to divide this difference by the original amount and multiply by $\textcolor{black}{100}$ to get the percentage change:

$\text{\textcolor{black}{Percentage Change}} = \dfrac{\textcolor{Red}{£1,500}}{\textcolor{blue}{£8,500}} \times \textcolor{black}{100} = \textcolor{black}{17.65\%}$

Level 4-5

### Example Questions

In order to solve this question, we will need to break down the $33\%$ into easier, and more manageable, chunks. $33\%$ can be broken down as follows:

$3 \times 10\% + 3 \times 1\%$

$10\%$ is a very easy amount to calculate since all we need to do is divide by $10$:

$10\%\text{ of }180 = 180\div 10 = 18$

Therefore, $30\%$ of $180$ is $3\times 18 = 54$.

Next, we will find $3\%$ by first finding $1\%$ and multiplying the answer by $3$. To find $1\%$ of $180$, we need to divide the total by $100$:

$1\%\text{ of }180 = 180\div 10 = 1.8$

Therefore, $3\%$ of $180$ is $3\times 1.8 = 5.4$.

Finally, we need to add together the $30\%$ amount and the $3\%$ amount, so $33\%$ is:

$54+5.4=59.4$

To convert anything into a percentage, it is a lot easier to write the amount as a fraction first. If Matteo scored “$99$ out of $150$”, then we should write this as:

$\dfrac{99}{150}$

To convert a fraction into a percentage, you need to divide the top by the bottom (it helps if you remember that the line in a fraction means ‘divide’) and then multiply by $100$

So, Matteo’s score as a percentage can be calculated as follows:

$(99 \div 150) \times 100 = 66\%$

In this question the difference between the two salaries is

$\pounds25,338 - \pounds24,600 = \pounds738$

The original amount (the amount before it was increased) was $£24,600$, so the percentage increase can be calculated as follows:

$\dfrac{\pounds738}{\pounds24,600} \times 100 = 3\%$

To most people, this would appear a very easy question with an answer of $20\%$, but this answer is, sadly, incorrect!

The easiest thing to do to solve this question is to invent a price for the motorbike. You can invent any price you want, but it would be advisable to make the price a nice, easy number and, since this question concerns percentages, giving the motorbike a price of $£100$ makes life extremely easy.

If the motorbike costs $£100$, when if it is reduced by $10\%$, then its new value is $£90$.

If the motorbike now costs $£90$ and is further reduced by $10\%$, then we need to deduct $10\%$ from this $£90$ value (and not the previous $£100$ value).

$10\%$ of $£90 = £9$

So the new value of the motorbike is $£81$.

So the motorbike has decreased in value from $£100$ to $£81$. Since we set the motorbike’s original price as $£100$, the percentage decrease here should be relatively obvious. If not, remember that to calculate a percentage decrease (or increase), you need to divide the difference between the two values by the original value and multiply by $100$.

The original value of the motorbike was $£100$, and its new value is $£81$, so the percentage decrease can be calculated as follows:

$\dfrac{\pounds100 - \pounds81}{\pounds 100} \times 100 = 19\%$

Therefore, the motorbike has decreased in value by $19\%$ and not $20\%$.

### Worksheets and Exam Questions

#### (NEW) Percentages Exam Style Questions - MME

Level 4-5 New Official MME

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