In your studies in Mathematics, you will come across many fractions. In this lesson, we will look at some of the common fractions you are likely to encounter in Mathematics, and learn their equivalence in percentages and decimals.

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A benchmark fraction is a common fraction that is usually used as a reference point. Examples include \(\frac{1}{2}, \frac{1}{4}, \frac{1}{3}\) and \(\frac{3}{4}\). These fractions can be represented as decimals or percentages.

They are mostly found on tickets, reciepts, invoices etc.

Some of the common conversions are included in the table below:

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1. Converting Fractions to Decimals:

Divide the numerator (top number) by the denominator (bottom number).

Example: \(\frac{3}{4} = 3 \div 4 = 0.75\)

Note:

You can use the long division to convert fractions to decimals.

2. Converting Decimals to Percentages:

Multiply the decimal by 100 and add the percentage symbol (%).

Example: \(0.75 \times 100 = 75\%\)

3. Converting Percentages to Fractions:

Write the percentage as a fraction with a denominator of 100, then simplify.

Example: \(75\% = \frac{75}{100} = \frac{3}{4}\)

To learn more about converting between fractions, decimals and percentages, click here.

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Example 1

Complete the following conversions:

Show Solution

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Solve the following:

1. If you eat \(\frac{1}{4}\) of a pizza, what percentage of the pizza have you eaten?

2. A survey shows that \(20\%\) of students prefer reading as a hobby. Express this percentage as a fraction and a decimal.

3. Write the decimal and percentage equivalents for the following fractions:

\((i) \frac{1}{5}\)

\((ii) \frac{3}{5}\)

\((iii) \frac{1}{6}\)

4. Convert the following percentages to fractions and decimals:

\((i) \ \ 25\%\)

\((ii) \ \ 66.67\%\)

\((iii) \ \ 80\%\)

5. Convert the following decimals to fractions and percentages:

\((i) \ \ 0.2\)

\((ii) \ \ 0.75\)

\((iii) \ \ 0.3333\dots\)

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Test yourself on what you have learnt so far. Click on the link below when you are ready.

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