Percentage — conversions and percentage of quantity

The word percent comes from the Latin phrase per centum. We need to find what this phrase means.

In Latin, per means 'for every' and centum means 'hundred'. Together, per centum means 'for every hundred'.

The correct answer is 'For every hundred'. This is why a percentage is always a fraction out of 100, and why the symbol % contains two zeros (representing the two zeros in 100).

We need to know the literal meaning of the word 'percent', which comes from Latin.

'For every ten' is incorrect. That would describe the prefix deci- (as in decimal). Percent specifically refers to hundreds.

'Part of a whole' is a general description of a fraction, not the literal meaning of the Latin word per centum.

'Out of fifty' is not the meaning of per centum. Fifty is not related to the Latin root of percent.

'For every hundred' is correct. Per means 'for every' and centum means 'hundred' in Latin.

The denominator is 20. Since $20\times 5=100$, we can use Method 1 — making an equivalent fraction with denominator 100.

$\frac{3}{20}=\frac{3\times 5}{20\times 5}=\frac{15}{100}$

$\frac{15}{100}=15\%$ The answer is 15%.

We need to convert $\frac{3}{20}$ to a percentage by finding an equivalent fraction out of 100.

3% would mean $\frac{3}{100}$. But our fraction has denominator 20, not 100, so 3% is incorrect.

20% would equal $\frac{20}{100}=\frac{1}{5}$. Our fraction $\frac{3}{20}$ is not equal to $\frac{1}{5}$, so 20% is wrong.

60% would mean $\frac{60}{100}=\frac{3}{5}$. Our fraction $\frac{3}{20}$ is much smaller than $\frac{3}{5}$, so 60% is wrong.

15% is correct: $\frac{3}{20}=\frac{15}{100}=15\%$, since $3\times 5=15$ and $20\times 5=100$.