In honestly when it comes to fractions and decimals getting all mixed together they can be a bit of a headache to deal with!

In this section we’re going to go over some of the most common examples of working with both fractions and decimals in exam questions.

To start with, we’re going to take a look at ordering. And as with most things in maths, it’s easiest to explain with the use of examples.

So, you may be asked to order the following numbers in size from smallest to largest: 5, ^{1}/_{5, }0.5, ^{1}/_{5, }0.5, 5.

The easiest way to do this is to convert all the fractions into decimals. Because looking at the same “type” of number makes it way more obvious!

As a decimal ^{1}/_{5 }= 0.2 which is smaller than 0.5. And from there you can order the numbers easily from 0.2 0.2 0.5 0.5 and 5. Easy!

Next we’re going to take a look at how powers impact decimals. A negative power means one over. Yeah that doesn’t mean much so let’s look at an example.

You may be asked to calculate something similar to the following:

Calculate: (^{2}/_{3})⁻² The answer is 2.25. As we know a negative power means one over. So, (^{2}/_{3})⁻² = 1/(^{2}/_{3})².

Which = (^{3}/_{2})² = 2^{1}/_{4}.

Pretty straightforward, just remember the rule!

So what about simplifying fractions?

No surprises, we’re going to use examples to illustrate how this is done.

Simplify the fraction as far as possible: ^{16}/_{500}

The answer is ^{4}/_{125. }Why? Because both are able to be divided by four.

What about some more complicated examples though.

Write the following as a simplified fraction: 0.232323232323….

The answer is ^{23}/_{99} but how did we get there?

Let the recurring decimal be d. Multiply d by 10, 100, 1000 etc so that one whole length of the repeating sequence moves to the left of the decimal point. In this case, multiply by 100. 100d = 23.2323…

Now take away the original decimal. 100d – d = 23.2323… – 0.2323… Ie. 99d = 23

So, d = ^{23}/_{99}

Lastly in this section is just a reminder on how you easily convert fractions to decimals. Just remember to divide the top of the fraction by the bottom to get the decimals.

And don’t worry here are the examples:

As a decimal, ^{3}/_{20} is 0.15 because 3 divided by 20 = 0.15.

Same principle with ^{1}/_{25 }divide the top by the bottom to give 0.04.