2.1 Calculating with negative numbers

You may be required to perform arithmetic operations (addition, subtraction, multiplication and division) involving negative numbers. There are good reasons why negative numbers should be handled in the way that they are, but these reasons can be quite difficult to understand. This activity simply gives a series of rules to apply, with examples of each.

Adding a negative number is the same as subtracting the corresponding positive number.

So, for example:

Subtracting a negative number is the same as adding the corresponding positive number.

So, for example:

Note the way in which brackets have been used in the examples to make it clear how the numbers and signs are associated. If you are struggling to see why subtracting 3 from -5 should give -8, whereas adding 3 to -5 gives -2, you may find it helpful to revisit the financial analogy. If your account is £5 overdrawn and you spend a further £3, you will end up with an overdraft of £8. However, if your account is £5 overdrawn and you repay £3, your overdraft will be reduced to £2.

If you multiply or divide two numbers which have the same sign, the answer is positive.

So, , as you already know, but also

, as you already know, but also

If you multiply or divide two numbers which have different signs, the answer is negative.

So and

Question 2.3

Do the following calculations, without using your calculator.

- a.

- b.

- c.

- d.

Make sure that you know how to input negative numbers into your own calculator. With some calculators you will be able to enter expressions like those in Question 2.3 more or less as they are written, with or without brackets. With other calculators you may need to use a key labelled as +/- or in order to change a positive number into a negative one.