In the proportion: $\frac{x}{100} = \frac{a}{total}$ which is the percent: $x$ or $\frac{x}{100}$?

For example, when asked to find $50\%$ of $2$, I would answer $a=\frac{50}{100}\cdot2=1$.

Here $\frac{50}{100}$ is the percent because $50\% =\frac{50}{100}=\frac{1}{2}$.

When asked what percent $3$ is of $4$, I would answer $x=\frac{3}{4}\cdot100=75\%$

Now $x$ alone is a percent, not $\frac{x}{100}$ What am I doing wrong?

Answer: Percent is the numerator of a fraction whose denominator is $100$.

  • $\begingroup$ $x$ is the percent. Write it as $x$% $\endgroup$ – Claude Leibovici May 30 '14 at 9:53
  • 2
    $\begingroup$ In other words, $\frac{x}{100} = x\%$. This is the definition of percentage (per hundred). $\endgroup$ – Eff May 30 '14 at 10:04
  • $\begingroup$ $x$ is the percent; $x/100$ is the fraction. When you need to operate, use the fraction. Keep the percent for words. Cheers. $\endgroup$ – Claude Leibovici May 30 '14 at 10:05

When you are asked for the percentage, it is $x\%$. When you are asked for the fraction, it is $\frac{x}{100}$.


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