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In many places I have seen formula to calculate $x$ % of amount $A$ given as $\frac{x}{100}\times A$.

But I feel writing this way doesn't explains what we are actually computing.

What I have understood by $x$ % of $A$ is first we have to divide $A$ into hundred equal parts i.e. we look for one hundredth part of $A$, and then scale it by $x$.

So may be writing $\frac{A}{100} \times x$ well explains $x$ % of $A$.

Although both are similar, I prefer to write second one. Is my logic correct or the first one also has some reasoning?

ogirkar
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    The expressions are equivalent. Use whichever one you like. This seems like a matter of opinion to me. – saulspatz Sep 08 '21 at 16:24
  • As "%" is an abbreviation for "${}\cdot\frac{1}{100}$", it's just a different representation of a fraction. Consider $\frac58$ of $24$, that is $\frac58\cdot24$. You divide $24$ in $8$ parts and then multiply by $5$: $$\frac58\cdot24=\frac{24}{8}\cdot5.$$ – Michael Hoppe Sep 08 '21 at 17:50

1 Answers1

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We would like to know what amount equals $x\%$ of quantity $A.$

  • $(\frac{x}{100}\times A)$ determines the answer by first converting the percentage into a fraction.
  • $(\frac{A}{100} \times x)$ first determines what $1\%$ of the quantity is, then scales that according to the given percentage.

Both expressions give the same correct answer.

ryang
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