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How I show that minus a minus is a plus

September 14, 2011

Imagine you’re in a competition and the three judges give you these scores:


So you add them up and get a total of 10.


But the -3 score seems a bit harsh and it turns out that that judge is related to one of your competitors. Their score gets removed:


So you’re left with 8 and 5 which makes a new total of 13.


You used to have a score of 10. Then, the minus three score was taken away. Your new score was 13. In other words (or symbols):


It’s seems clear that taking away the negative score has the same effect as adding on the value.


Which leads to the generalisation that:


I find it’s well worth allowing the time that it takes for this to sink in. I often end up running through again with different values.


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  1. chris_1974 permalink

    I use a very similar approach to this – thinking about numbers in a cloud, but very much the same idea.What I’m still (15 yrs in the job) with is -ve x -ve = +ve. I can do it with a number pattern approach, but nothing really satisfactory for me.

  2. Anonymous permalink

    Yes – that’s an interesting question. Apart from number patterns I’m not sure I have another good reason for the multiplying negative numbers ‘rules’.

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