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I was wondering if there is any quick way of calculating some common percentages such as $15\%$, $25\%$, $50\%$, $75\%$, $90\%$ etc.

The best think I could come up with is just simplifying the fraction they represent. So for $75%$, which is $\frac{3}{4}$, you just multiply by $3$ and divide by $4$. Is this the method some advanced mathematicians also use for quick, mental calculations? Or is there a better way? Thank you in advance.

Camelot823
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    Some mental arithmetic calculations are psychologically easier than others: a few years ago people discussed $75%$ of $4$ being $3$ as an easy calculation, while $4%$ of $75$ took longer despite multiplication being commutative. – Henry Aug 03 '23 at 23:27
  • @Henry I don't think that the fact that one of these is easier than the other has much to do with psychology. It's just easier to work with $3/4$ than with $4/100$. – Ethan Bolker Aug 03 '23 at 23:39
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    @EthanBolker but it is just multiplication with $75\times4 = 4\times 75$. The psychology comes from seeing $75%$ and thinking $\frac34$ – Henry Aug 03 '23 at 23:43

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10% is easy, just divide by 10, in other words shift the decimal point. Half of the result gives you 5%, add them and that's 15%.

50%, just divide by 2.

25%, divide by 4 either in one step, or by 2 then by 2 again.

75%, divide by 2 to get 50%, divide by 2 again to get 25%, add those two results.

90%, easy to find 10%, then subtract from the original.

David
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You can just multiply using decimals. For example, if you want to find the $25\%$ of 70, you can just multiply $$70 \cdot 0,25 = 17,5$$ In general, to find the $a \%$ of $x$ just do $$x \cdot 0,a$$

IkerUCM
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  • I think decimal multiplication is much useful for arbitrary percentages such as $29%$. For simple ones such as $20%$ they seem needless. – Camelot823 Aug 03 '23 at 23:57