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Sorry, I feel like an idiot for not knowing this, but assume my old number is -10. How would I calculate a 50% growth of that -10? Multiplying -10 by 1.50 results in -15 which is going in the wrong direction.

But multiplying 1.50 with the absolute value of -10 is not correct either. I think I am missing something fundamental here..

sudden_clarity_clarence
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    I think we need to know more about what you mean by growth. Could you add more detail? – Rylan Schaeffer Jan 04 '21 at 21:16
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    For instance, if this were a loan, and the principal you owed was $10 with a 50% interest rate, $15 would indeed be the new amount owed after 1 interest period. – Rylan Schaeffer Jan 04 '21 at 21:17
  • So by growth, it was in the context of growth in sales (dollars). The negative number represents more refunds than there are sales. Although the report does not specifically make this distinction, that's what the underlying meaning is. – sudden_clarity_clarence Jan 04 '21 at 21:36
  • This is a problem with the english language and with mathematics. $-3 < 0 < 1$. That means $-3$ is less than $1$ but does that mean $-3$ is smaller than $1$? We know what "less" and "greater" mean mathematically (it means left or right) but what does "small" and "large" mean. It makes sense to talk of magnitude and the size of the absolute value. $-3$ has a bigger magnitude than $1$! If $M$ "grows" $150%$ than means it goes from $M$ to $1.5M$. It's magnitude grows. But if $M$ was negative it has now become "more negative". In other words it's ... become less... – fleablood Jan 04 '21 at 21:53
  • I think the issue is the word "growth". There's no question that $150%$ of $-10$ is $-15$ but is going from $-10$ to $-15$ a "growth". I'd say not, but who said a value going from $100%$ to $150%$ was a "growth" in the first place? If the value was negative then $150%$ of something negative doesn't have t be a "growth". – fleablood Jan 04 '21 at 22:01

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If you start with minus ten and increase it by 50%, you will end up with -15. Imagine you have £10,000 in the bank. Increase it by 50% and you'll get £15,000. But if you owe the bank £10,000 and increase that by 50% the logic works just the same the other way around.

If you start with -10 and want to increase it to get a less negative number, you need to be looking at addition rather than multiplication. I am guessing there's some context here. What is the -10 you are trying to increase/reduce?

Andrew Day
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  • Thanks Andrew, I think I understand your point. The negative -10 in my context is sales in dollars. And so any negative amount means there were more refunds than there were sales. So I get that a 50% growth on this number would be growth of refunds, not sales. – sudden_clarity_clarence Jan 04 '21 at 21:34
  • It might be useful to think it terms of magnitude. $-500000 < 1$ but $-50000$ is certainly "larger" in maginitude than $1$. A change of $150%$ means something goes from $M\to 1.5M$. Is that a "growth"? It is if $M$ was positive but if $M$ is negative its magnitude has grown. And increasing a numbers NEGATIVE quality makes it larger in the negative direction. ... or its ABSENCE is bigger, and when an ABSENSE is bigger the overall net change is .... a loss. – fleablood Jan 04 '21 at 21:57