Percentages help us compare and contrast things. We can compare, for example, the number slices eaten from a loaf, the number of times a die rolled a 4 compared to the total rolls. We can also compare/contast the ball position of teams in a soccer match.
Whenever you see a percentage, you must see it as a fraction or a decimal multiplied by \(100\).
A number like \(0.3\) becomes \(30%\) when converted to percentage. Similarly, \(\normalsize \frac{1}{5}\) becomes \(20%\) when multiplies by \(100\). Rememmber we said that percentage is simply, a multiplication of a decimal or a fraction by a 100.
In simple terms, we can represent a percentage as:
$${\normalsize Percentage= \frac{part}{whole} \times {100\%}}$$Where part refers to the element we are comparing to the whole, which is all the parts added together. So, we are saying whole is the sum of parts.
Now let us try a few examples.
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In a pie of eight pieces, Nicole ate two pieces. What is the percentage of pie that Nicole ate?
Solution: is a total of pieces and Nicole ate only two, therefore the calculation is as follows:
$$ \normalsize \begin{align} Percentage &= \frac{2}{8} \times 100\%\\ &=25\% \end{align} $$ -
You are receiving an SMS that you have used 80% of your data. When you check your data balance, you realise you have 3GB left. How much data did you buy?
Solution: You have used 80% of the total total data. This means you now have 20% of the total data. So 3GB is 20% the data you bought.
For this question, we will have to rearrange the equation.
$${\normalsize whole = \frac{part}{percentage}\times {100\%}}$$Now let us get the answer.
$$ \normalsize \begin{align} whole = \frac{3GB}{20\%} \times 100\%\\ = 15GB \end{align} $$Note: You can ignore units when substituting.
This therefore means, you bought 15GB of data.
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Mandla says he fills his fuel tank when he has used 75% of the fuel. If his fuel tank's capcity is \(53l\), what is the fuel level that tells him to fill the tank?
Solution: level that he uses is when the fuel is 25% of the volume/capacity. In this question we are looking for the part. We need to rearrange the percentage equation so we calculate the part.
$${\normalsize part = \frac{percentage \times {whole}}{100\%}}$$Now we say,
$$ \normalsize \begin{align} part &= \frac{25\% \times {53l}}{100\%}\\ &=13.25l \end{align} $$Therefore, Mandla fills his fuel when he has \(\normalsize 13.25l\) left.
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To get a certificate, you need to pass at least 48 questions of a 64 multiple-choice exam questions. How many percents give you this certificate?
Solution:
$$ \normalsize \begin{align} Percentage &= \frac{48}{64} \times 100\%\\ &=75\% \end{align} $$To get the certificate, you must obtain 75%
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To contribute to a project, Khutso pays R8200, Lesego R6730, Lars R7270, and Azwi R5800. How many perecnts is Lesego's contribution to the project?
First we need to calculate the 'whole'. Then we can find the portion in percentage of Lesego's contribution.
Solution: We need to get the total contribution first. We will then compare Lesego's contribution the to the total.
$$ \normalsize \begin{align} \text{whole } &= 8200+6730+7270+5800\\ &=28000 \end{align} $$Lesego's contribution percentage:
$$ \normalsize \begin{align} Percentage &= \frac{6730}{28000} \times 100\%\\ &=24\% \end{align} $$