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My problem with math is how I talk about it, the words of math. I know math is a language but I don’t translate it very well.

For example, if you have $40$ units and I have $60$ units, from my perspective, you have a third fewer than I do. From your perspective I have half as many again. It’s all relative. Do I have a third more or a half more? Do you have a third less or a half less? Either way it’s still $20$ units in question. Where am I mistranslating the problem?

Apurv
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IsaiahBenJamin
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  • If $a$ has 40% fewer dollars than $b$, how much does $a$ have if $b$ has 100 dollars? –  Jul 15 '15 at 02:05

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Percentages change depending on the base. Your second sentence it exactly correct and you should have stopped there. You have half more. I have a third less. The problem comes because you think these are contradictory. They are not. From a mathematical perspective, (if we scale it) I have $1$ and you have $1+x/100$, so you have $x\%$ more than me. Claiming I have $x\%$ less than you is claiming $(1+x/100)(1-x/100)=1$, which is false. $(1+x/100)(1-x/100)=1-x^2/10,000$. If $x$ is small, you can ignore the last term and your intuition works.

Ross Millikan
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