So fractions, you may think they can be a bit scary at times but once you get your head round them, they’re very useful and really not that bad.
Fractions can be used to show numbers that are not whole, in a similar way to decimals and percentages.
You are also able to convert between fractions, decimals and percentages and like whole numbers fractions can be positive or negative.
First things first we’re going to look at ordering fractions. The easiest way to order a range of fractions is to convert each fraction so they all have the same denominator, take a look at this example for instance:
Order these numbers in terms of size, smallest to largest: 2/3, 3/5, 5/8, 3/4, 3/5, 5/8, 2/3, 3/4.
In this case, put them all over 120.
Next we’re going to focus on calculations using fractions, including addition, multiplication and subtraction.
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 = 21/4.
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
Now let’s take a look at multiplying fractions.
When you’re multiplying two fractions together, you simply multiply the top parts of the fraction together and the bottom parts of the fraction together.
For example if you were multiplying 1/2 × 1/3 this would equal 1/6.
This is because you multiply the top parts together (1 x 1) and then multiply the bottom parts together (2 x 3).
When adding or subtracting fractions together you must find a common denominator.
For example if you were asked to calculate: 1/2 + 1/4.
You need to firstly find a common denominator, in this case four (don’t forget to change the top of the fraction in the same way as you changed the bottom.
This will give us the answer of 3/4.
When you’re looking to divide a fraction simply turn the second fraction upside down and multiply the fractions rather than divide.
So 4/5 ÷ 2/5 gives us 2. (remembering to cancel where possible!)
Finally let’s take a look at adding and subtracting mixed numbers. (in other words numbers that are both whole and a fraction).
The easiest way to explain this is by looking at an example, so here it is:
2 and 3/4 is a mixed number. 2 is a whole number, and 3/4 is a fraction.
You can change this into a top-heavy fraction by writing 2 x 4 + 3/4 = 11/4.
To change a top-heavy fraction into a mixed number, you first divide the top of the fraction (numerator) by the bottom (denominator).
For example 13/4 = 3 1/4, because 4 divides into 13 three times, with one left over.