Basic Fraction Skills Needed for Passing Numeracy Tests
When brushing up on your basic maths skills before taking a numeracy test, you're going to have to deal with fractions. A fraction is a pair of numbers, one on top of the other. Think of it as representing a number of slices of cake or pizza.
The bottom (or denominator) tells you how big each slice is; the top (or numerator) tells you how many of the slices there are.
So, 3/4 represents the pizza in the figure: the pizza was split into four slices (so the number on the bottom is four), and three of the slices are still there (so the number on the top is three).
You could have split up the pizza into eight slices and be left with six, or into twelve and have nine slices left (so three-quarters is the same thing as 6/8 or 9/12). It’s also the same as 75/100, or 30/40, or 270/360.
Equivalent fractions and cancelling down
Two fractions are equivalent if you can get from one to the other by multiplying or dividing the top and bottom by the same number.
So, 3/4 is equivalent to 6/8 because you can get from one to the other by multiplying both the top and bottom by two. In the same way, 50/100 is the same as 1/2 because you can get from one to the other by dividing both the top and bottom by fifty. This process – dividing top and bottom by the same number – is known as cancelling down or simplifying a fraction.
Add and take away fractions
The most common fraction sums, both in real life and in numeracy tests, involve adding and taking away fractions.
The big trick to doing adding and take-away sums is to make sure the number on the bottom of both fractions is the same. This is just like making sure your units are the same when you’re adding up measurements – you wouldn’t add miles to kilometres; you’d make sure to put both distances into the same units first.
Here’s the recipe for adding or taking away fractions:
Find an equivalent fraction for the first fraction by multiplying the top and bottom by the bottom of the second fraction. If you multiply the top and bottom of 2/3 by 4, you get 8/12.
Find an equivalent fraction for the second fraction by multiplying top and bottom by the original bottom of the first fraction. The bottoms of the two new fractions should now be the same. If you multiply the top and bottom of 1/4 by 3, you get 3/12.
Add the tops of the new fractions, and write the answer over the new bottom you found in step 2. Adding 8/12 to 3/12 gives you 11/12.
Cancel down if you can – if you see a number you can divide the top and bottom by, divide by it! There’s nothing you can evenly divide both 11 and 12 by (except 1, which doesn’t help), so your answer is 11/12.
Repeat Step 4 until you can’t see any more numbers to cancel. Once you’ve done this, the fraction is in its simplest form.
Fractions of a number
Working out a fraction of a number is a simple, two-step process. Once you’ve done a few sums like this, the process becomes almost automatic. Here are the steps:
Divide the number by the bottom of the fraction. If you have to find 7/10 of 300, you divide 300 by 10 to get 30.
Multiply the answer by the top of the fraction. Multiply 30 by 7 to get 210.
Multiply and divide fractions
In some numeracy tests, you may be asked to multiply two fractions together or to divide one fraction by another. This falls into the ‘straightforward but pointless’ category, but if it’s in your test, you need to know how to do it.
Here’s how you multiply two fractions:
Multiply the top of the first fraction by the top of the second. Write this number down.
Multiply the bottom of the first fraction by the bottom of the second fraction. Write this number down underneath your answer to step 1. Draw a line between the two answers you just wrote down. This is your answer.
Cancel it down if you see an obvious number you can divide the top and the bottom by.
To divide fractions, it’s only one step more complicated:
Flip the second fraction upside down. If the second fraction was 3/4, it would become 4/3.
Multiply the first fraction by the flipped second fraction using the fraction multiplication recipe.
Convert between decimals and fractions
Fractions and decimals are two sides of the same coin – they both give you a way of talking about numbers that aren’t whole. Converting from a decimal to a fraction is quite easy. Here’s what you do to convert 0.54 into a fraction:
Rewrite the original number without a dot in it. If it starts with zeros, you can ignore them. In this case, it’d be 54.
Count how many digits are after the dot in the original number. Write down 1 followed by this many zeros underneath the number you wrote down in Step 1. You’d now have 54/100.
Cancel down this fraction as far as you can. The top and bottom of the fraction in Step 2 are both even, so you can halve them both to get 27/50, which is as far as it goes.