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Estimation is a very useful skill when solving number problems. You will find below some examples of the different ways you might estimate the answer to a problem before you calculate.

Find the upper limit

Let’s start with a very simple approximation that will act as a warning sign that our calculation is very wrong.

To make things simple, let’s imagine the tablets are 60 micrograms. How much medication would we get if we had 10 tablets. This is easy to work out as we only have to multiply by 10.

60 x 10 = 600 micrograms.

So, 10 tablets is way too many – if we get an answer more than 10 when we calculate something is clearly wrong. In fact, you might notice that 600 micrograms is more than double the prescription of 250 micrograms. So, we can say that if our calculation gives more than 5 tablets (half of 10 tablets), then something has gone wrong.

If you are reasonably confident with your maths, you can first round the numbers and then simply continue adding until you get close to the answer. For example, you might round 62.5 down to 60. You can keep adding 60 until you get close to 250 micrograms.

60 + 60 + 60 + 60 = 240

So, four tablets is close to the answer.

Dosage

Another way to spot mistakes when you calculate is to look at the dosage recommendation on the bottle (or in the British National Formulary). In this case, the bottle states that the medicine is to be administered three times a day and that no more than 18 tablets should be given daily.

We know that no single dose is likely to be more than 6 tablets, because: 18 tablets divided by 3 times a day = 6 tablets, three times a day.

So, we should not expect an answer that is more than 6 tablets.

Simplify the numbers

When estimating, the first step is usually to simplify the numbers. The amount you simplify depends on the type of estimation you are doing and your confidence with numbers.

In this case, you might start by doing a very rough simplification and imagine the tablets were 50 micrograms.

If you were a little more confident you might simplify 62.5 micrograms to be 60 microgram tablets. 60 is still an easier ‘whole number’ to work with.

Using these simplified numbers will be helpful in having a rough feel for what numbers you should expect to get from your calculations.

Remember – when estimating your goal is to get a ‘feel’ for what the size of the numbers should be, not an exact answer. You will still need to complete the calculation using the correct formula, if necessary.