Adding and subtracting: Positive and negative numbers made simple

I’ve found using the weather is the easiest way to explain positive and negative numbers.

When the weather has been hot like it has in the last few days the number is in the positives, for example 27 degrees.

If today the temperature was set to get hotter (by 5 degrees) it would be the equivalent of adding a positive:

If the weather was set to cool down by 5 degrees, it would be the equivalent of subtracting 5:

27-5 =22

This is fairly straight forward.

The problems seem to start when we delve into the negative numbers.
If the weather was -27 degrees instead of plus 27 the following rules would apply:

Today the weather is -27 degrees, but it is set to get 5 degrees warmer. The sum would be:

-27 + 5

This means because we are adding to a negative, the number is getting closer to zero.


By doing this it appears the number is getting smaller rather than bigger
-27+5 = -22


But if you understand that when the weather has been bitterly cold, by adding a few degrees it still isn’t enough to regard it as warm.


I hope that makes some sort of sense.


Another way of thinking about it is in terms of lending someone some money.


Imagine I lent someone £27. They then gave me £5 back.

They still owe my £22. Although the debt has reduced in size the amount owed is still in the negatives.


If I had lent someone (or borrowed) £27 but then borrowed an additional £5 the debt would be getting bigger, moving what I owed away from zero:

-£27-£5 = -£32

The one thing to remember though that if you have 2 negatives together they counteract each other and become a positive:


27 – -5 becomes 27+5 taking our answer to 32

I always think of a negative telling you to change direction.


Using a picture of a thermometer or a number line is something I always find helpful in working out positive and negative numbers as it makes the process of recognising the effect the actions have on the numbers.

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