# 1.02.02 Adding and subtracting positive and negative numbers.

Imagine you have two bank accounts, one with a balance of £100 in it and a second account with a balance of -£20. If you combined these into a single account the balances from each would be added together and you would have a total balance of £80. (This is the same balance you would have had if you had just withdrawn £20 from your first account.) This illustrates rule 1:
Adding a negative number, is the same as subtracting a positive number of the same magnitude.

Examples

• 4 + (-3) is the same as 4 - 3 = 1 .
• 20 + (-15) is the same as 20 - 15 = 5 .
• 12 + (-5) is the same as 12 - 5 = 7 .

## Subtracting negative numbers.

If your account has a balance of -£50 and your bank manager kindly agrees to "write off" your debt. i.e. to remove the balance of -£50, this would leave you with a balance of £0. (If you had deposited £50 into your account, this would have achieved the same result). This illustrates rule 2:
Subtracting a negative number, is the same as adding a positive number of the same magnitude.

• 6 - (-2) is the same as 6 + 2 = 8 .
• 14 - (-9) is the same as 14 + 9 = 23 .
• 20 - (-13) is the same as 20 + 13 = 33 .

In the above examples, once you have applied either of the rules to rearrange the sum, you are left with a simple familiar calculation. However this is not always the case and you may be faced with several possible unfamiliar procedures.
you may be required to:

• subtract a large positive number from a smaller positive number .
• subtract a positive number from a negative number .
• add a positive number to a negative number .

The next page shows how to deal with these situations.