small doubt about Percentage formula

Question

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?

Answer 1

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.