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Positive and negative numbers

From everyday life you should already understand positive and negative numbers, however, you may not understand the way in which we can manipulate these numbers.

In the previous section we looked at adding and subtracting numbers using a number line, but what if we now decided to subtract a negative number? You may be able to work out that when doing this you move up the number line. In other words, subtracting a negative number is the same as adding that same number. Or we could say that ‘two minuses make a plus’.

e.g. 6-(-3)=6+3=9

When we multiply two negative numbers, we again get a positive.

e.g. (-2) \times (-3)=2 \times 3=6

There is clearly a rule which we can follow here: that whenever we have two negatives we can replace them with a plus. This is the pattern for all numbers when multiplying:

Positive and negative calculations

We can use the same rule when we divide positive and negative numbers:

Dividing positive and negative numbers

These are the fundamental calculations between numbers and you should make sure that you know these very well.

For your exam you will need to purchase a scientific calculator and it is recommended that you read through the instructions when you purchase the calculator so that you know how to perform these basic operations.

Using 0 and 1

Another basic skill which you will need to learn is what happens when we use 0 and 1 in our manipulation of numbers. Clearly, when adding or subtracting 1 we simply move one number up or down, but adding or subtracting 0 does nothing. When multiplying by 1, this also does nothing to a number and just leaves it the same; however, this is not the case when multiplying by 0. If we multiply any number by zero then we get an answer of 0.

This is summarised in the following table:

One and zero calculations

As you see from the table above, division by zero is ‘undefined’, however, do not worry – you do not need to know what this means or use this idea for your test!

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