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

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 $100$.

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