Percentage Questions on Non-Calculator Numeracy Tests
When you’re reduced to working on paper on a numeracy test, you need to know some techniques for quickly dealing with percentage questions. Luckily, you have several ways of dealing with percentages.
Converting percentages into other forms
Converting a percentage into a decimal is as easy as converting pennies into pounds – in fact, it’s the same sum!
If you have a two-digit percentage (such as 25%), all you need to do is put a zero and a dot in front of the first number. For this example, 25% is the same as 0.25.
If you have a one-digit percentage, you have to put a zero, a dot and another zero in front of your number – so 9% is the same as 0.09.
Finding a percentage
Percentage questions in non-calculator tests tend to work with comparatively easy percentages, and here are the steps you take to work out a number as a percentage of another, for example, 45 as a percentage of 180:
Label the smaller number as the ‘part’ and the larger number the ‘whole thing.’
Divide the ‘whole thing’ number by 10. This gives you 10%.
If you’re looking for 45 as a percentage of 180, you can work out that 18 is 10%.
Double your answer from step 1.
This gives you 20% of the number. In this example, you have 36.
Repeatedly add your 10% number until you go past your part number.
Be sure to write down which percentage you’ve figured out at each stage. If you reach your number exactly, the percentage you got to is your answer!
If the ‘part’ number is halfway between two of your answers, split the difference.
For example, you know that 20% is 36 and 30% is 54. 45 is halfway between 36 and 54, so the percentage is halfway between 20 and 30: 25%. This is your answer.
This method works in almost all non-calculator percentage questions.
If you need to find a percentage of a number, here’s what you do – for example, to find 35% of 240:
Divide the number by 10 to find 10%.
In this case, 10% is 24.
Multiply this number by how many tens are in the percentage you’re looking for – in this case, that’s 3, so you work out 30% to be 24 x 3 = 72.
If your percentage number was a multiple of ten, this is your answer!
If your percentage number isn’t a multiple of ten, you need to find 1%.
You do this by dividing your answer from Step 1 by 10 again. In this case, 1% is 2.4.
Multiply this number by the number of units in your answer – here, that’s 5, and you get 5% = 5 x 2.4 = 12.
Add your answers from Steps 2 and 4 to get your answer.
Here, it’s 72 + 12 = 84.
Percentage increase and decrease
Percentage increase and decrease aren’t any more difficult than simply finding percentages, except that there’s an extra step involved. Here are some situations where you might need to work out a percentage increase or decrease:
A price has gone up or down by a given percentage.
You want to give a certain percentage of a meal price as a tip.
You’re given a price without tax and need to add the tax rate.
You’re given an investment or a loan and an interest rate.
You’re told that a value has gone up or down by a given percentage since the previous year.
This type of question is fairly common in numeracy tests, and as long as you keep your head it’s quite straightforward. In this recipe, you can work out what happens if the price of a £180 bike goes up or down by 15%. Here are the steps you take if you want to find the value after an increase or decrease:
Work out the given percentage of the full price. Fifteen per cent of £180 is £27.
If it’s an ‘increase’ question, add this on to the original value; this is your answer. If the price of the bike went up 15%, it would now cost £207.
If it’s a ‘decrease’ question, take this away from the original value. If the price of the bike had dropped by 15%, it would now be £153. Bargain!
Be very careful to read the question and give the value it asks for – if it only wants the interest, or the tax, or the increase, or the saving (rather than the amount after the increase or decrease) you have to give the answer from Step 1!