Fractions, Decimals and Percentages

There is a rule that is easy to remember for converting between decimals and percentages.

Example: Convert $75$ to a decimal.

This time using the rule follow the arrow from percentage to decimal to find we need to divide by $100$.

$75$

For fractions that have $textcolor{blue}{100}$ as their denominator, the equivalent percentage is the value of the numerator.

Example: Find $dfrac{85}{100}$ as a percentage.

$textcolor{blue}{100}$ is the denominator so, the equivalent percentage is $textcolor{purple}{85$.

Your child may come across fractions that don’t have a denominator of $textcolor{blue}{100}$. In these cases they need to find an equivalent fraction that does have a denominator of $textcolor{blue}{100}$ and then the numerator of that fraction will be the percentage.

Example: Convert $dfrac{7}{20}$ into a percentage.

As the denominator does not equal $textcolor{blue}{100}$, find an equivalent fraction to $dfrac{7}{20}$ that has the denominator of $textcolor{blue}{100}$.

$100 = 20 textcolor{red}{times 5}$

So, multiply the numerator by $textcolor{red}{5}$ as well to form the equivalent fraction.

$7 textcolor{red}{times 5} = 35$

So,

$dfrac{7}{20} = dfrac{textcolor{purple}{35}}{textcolor{blue}{100}}$

Now, it’s easy to see that $dfrac{7}{20}$ as a percentage is $textcolor{purple}{35$.

To convert the opposite way from percentage to fraction, put the percentage as the numerator and the denominator as $textcolor{blue}{100}$. Then, simplify the fraction if necessary.

Example: Convert $45$ to a fraction and simplify it.

Put the percentage as the numerator and $textcolor{blue}{100}$ as the denominator.

$dfrac{45}{100}$

This can be simplified as both $45$ and $100$ are divisible by $textcolor{red}{5}$.

$dfrac{45 textcolor{red}{div 5}}{100 textcolor{red}{div 5}} = dfrac{9}{20}$

Similar to when your child converts fractions to percentages, converting from fractions to decimals involves finding an equivalent fraction with a denominator of $textcolor{blue}{100}$.

Example: Convert $dfrac{3}{25}$ into a decimal.

First, find an equivalent fraction with a denominator of $textcolor{blue}{100}$.

$dfrac{3 textcolor{red}{times 4}}{25 textcolor{red}{times 4}} = dfrac{12}{100}$

Then, to find the fraction as a decimal it’s important for your child to remember that the line in a fraction just means ‘divide’.

So, the calculation to find the decimal becomes:

$12 div 100 = 0.12$

Converting from a decimal to a fraction is the same process in reverse.

Example: Convert $0.92$ into a fraction.

Start by multiplying the decimal by $textcolor{darkturquoise}{100}$, your child may remember that this is how to convert a decimal to a percentage.

$0.92 times 100 = 92$

Then, put this number as the numerator of a fraction with the denominator as $textcolor{blue}{100}$.

$dfrac{92}{100}$

This fraction can be left as it is or simplified, your child should be aware from the question how they should express their answer.