Fractions are number representations that refer to a part, or a number of parts, of a whole. They are made up of a numerator and a denominator, separated by a line.
The numerator is the number above the line and indicates how many parts of the whole we are dealing with. The denominator sits below the line, and shows how many equal parts the whole has been divided into.
When we work out a fraction of a given number, we’re assigning a value to that fraction. Essentially, we are calculating how much of that number (the whole) the fraction equates to.
As a basic example, say you saw a sale item with ⅓ off the marked price. If the marked price was £30, you’d first need to calculate what ⅓ of £30 was before you could establish the sale price.
There are many other occasions where you may be required to work out a fraction of a number, for instance, when working with ingredients or material quantities, and of course, when answering questions in numerical ability tests.
A step-by-step guide to find fractions of numbers
When finding a fraction of a number we are, in simple terms, multiplying that number by the fraction. The easiest way to remember this is to replace the word ‘of’ with a multiplication sign, so the question ‘what is ½ of 20’ would be written as (½) x 20.
To multiply a number by a fraction, follow the steps below.
Multiply the whole number by the numerator
The first step is to take the whole number you’ve been given and multiply it by the numerator of the fraction. For example, if we’re asked to work out ¾ of 14, we first multiply 14 by 3, giving us a resulting figure of 42.
This step only applies when working with non-unit fractions, where the numerator is of a value greater than one. For unit fractions (e.g. ½, ⅓, ¼ etc.) this step is unnecessary, as the whole number remains the same when multiplied by one.
Note also that the same process is used when working with improper fractions, where the numerator is greater than the denominator.
Divide that result by the denominator
Next we take the result of our multiplication (in the example above, 14 x 3 = 42), and divide it by the denominator of the fraction.
Where the resulting figure is equally divisible by the denominator, this step is straightforward, as it will result in a whole number. However in our example, 42 is not equally divisible by 4.
We know that 4 goes into 42 ten times, leaving two remaining. In these cases, the remaining number is placed over the original denominator to give us the fractional part of a mixed fraction (i.e. a value made up of a whole number and a fraction).
So our answer to the question, what is ¾ of 14 is: 10 and 2/4
Simplify the answer if necessary
If the answer you’re left with is a mixed fraction as above, check to see if it can be simplified.
To simplify a fraction, both the numerator and denominator must be divisible by the same number. In our example, both 2 and 4 are divisible by 2, so we can simplify 2/4 to ½.
This gives us a final answer of 10 ½.
To recap, ¾ of 14 is:
14 x 3 = 42
42/4 = 10, 2 remaining, leaving 10 2/4
2/4 simplified is ½
Answer = 10 ½.
Below are some questions for you to try out yourself.
While the method for working out fractions of numbers is relatively simple in theory, it becomes more complex when working with larger figures. In these scenarios, there’s a few more steps you’ll need to take, which we’ve explained in example question 3 below.
Step 1: Example question 1
Kate has decided to buy a new television. The model she chose costs £450, but is due to go on sale at two-thirds of the price. If Kate waits for the sale, how much will she save?
To find the answer to this question, we first need to work out what the sale price would be, so we need to calculate ⅔ of 450.
Multiply the whole number by the numerator, and then divide the result by the denominator:
450 x 2 = 900
900/3 = 300
Now we know the sale price would be £300, we can subtract that from the original cost to work out the saving:
450 - 300 = 150
Kate would save £150.
Step 2: Example question 2
Sam works a 37-hour week in retail. He spends ¾ of his time on the shop floor, and the rest working in the warehouse. How many hours per week does Sam spend on the shop floor?
If we multiply the whole number by the numerator here, we get an answer of 111.
111 is not equally divisible by the denominator, so we know we’ll have a remainder.
4 goes into 111 27 times, leaving a remainder of 3. So we’re left with an answer of 27 ¾.
We can’t simplify ¾, so we can say that Sam spends 27 ¾ hours on the shop floor every week.
Step 3: Example question 3
Jack was rewarded with £550 by his parents for performing well in his previous exam. He decided to use 3/10 of this to purchase a new fitness device. How much does the fitness device cost?
As we’re working with larger numbers here, you may find it easier to simplify the equation first. To do this, look for common factors shared by the whole number and the denominator of the fraction, and cancel them out.
In this case, we can see that both 550 and 10 are divisible by 10, leaving 55 and 1 respectively. We can now simplify 3/10 of 550 to 3/1 of 55.
Now complete the equation by multiplying the whole number by the numerator, and dividing the result by the denominator:
55 x 3 = 165
165/1 = 165
The fitness device that Nate bought cost him £165.