How To Calculate Percentages.

Percentages help us report in a simpler manner, numbers that are too big to read, especially if we compare diiferent things. They tell us about a contribution of a part to the whole.

Whenever you see a percentage, you must see it as a fraction or a decimal. It is the multiplication by \(100\) that converts fractions and decimals to percentage.

A number like \(0.3\) becomes \(30%\) when converted to percentage. Similarly, \(\frac{1}{5}\) becomes \(20%\) when multiplies by \(100\). Rememmber we said that percentage is simply, a multiplication of a decimal or a fraction by a 100.

The mathematical definition is therefore:

$${Percentage= \frac{part}{whole} \times {100\%}}$$

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.

1. In a pie of eight pieces, Nicole ate eight pieces. What is the percentage of pie that Nicole are?

   There is a total of pieces and Nicole ate only two, therefore the calculation is as follows:

   \begin{gather} Percentage = \frac{2}{8} \times 100\%\\ =25\% \end{gather}

2. 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?

   So you hsave used 80%. 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.

   $${whole = \frac{part}{percentage}\times {100\%}}$$

   Now let us get the answer.

   \begin{gather} whole = \frac{3GB}{20\%} \times 100\%\\ = 15GB \end{gather}

   Note: You can ignore units when substituting.

3. Mandla says he fills his fuel tank when he has used 75% of the fuel. If his fuel tank is \(53l\), what is the fuel level that tells him to fill the tank?

   The level that he uses is when the fuel is 25% of the volume. In this question we are looking for the part. We need to rearrange the equation so we calculate the part.

   $${part = \frac{percentage \times {whole}}{100\%}}$$

   Now we say,

   \begin{gather} part = \frac{25\% \times {53l}}{100\%}\\ =13.25l \end{gather}

4. 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?

   \begin{gather} Percentage = \frac{48}{64} \times 100\%\\ =75\% \end{gather}

5. 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.

   $${whole = 8200+6730+7270+5800=28000}$$

   \begin{multline*} whole = 8200+6730+7270\\ +5800=28000 \end{multline*}

   \begin{gather} Percentage = \frac{6730}{28000} \times 100\%\\ =24\% \end{gather}