What is the meaning of an inverse of a percentage?

Question

Suppose there are 50 marbles (denoted $M$) in a bag. 20 of these marbles are red (denoted $R$).

$$ R / M = 20 / 50 = 0.4 $$

I interpret this as: for every 1 unit of $M$, there are $0.4$ units of $R$.

The inverse is:

$$ M / R = 50 / 20 = 1.25 $$

Which is interpreted as "for every 1 unit of $R$, there are 1.25 units of $M$".

All is good until you translate these back to 'marble-speak'. The percentage suggests that "out of 50 marbles 20 are red". By analogy, inverse percentage suggests that "out of 20 red marbles 50 are marbles." The latter statement seems non-sensical to me and I wonder if there is a better way to phrase the 'marble-speak'.

Answer 1

Answering my own question -

Suppose 10 marbles are blue (denoted $B$). Thus, $10/50=0.2$ and $50/10=5$.

Comparing percentages $B$ vs $R$ yields 'prevalence', that is, $R=0.4$ is more prevalent than %B=0.2%

Inverse percentage yields 'uniqueness'. That is, $B=5$ is more unique than $R=1.25$

Answer 2

Note that ${\frac{50}{20}=2.5\neq 1.25}$.

It's just the phrasing that's thrown you off. It's not "out of ${20}$ red marbles, ${50}$ are marbles". What the ratio ${\frac{50}{20}=2.5}$ is actually telling you is that for every red marble, there are ${2.5}$ total marbles. So if I have ${2}$ red marbles, I must have ${2.5 + 2.5 = 5}$ total marbles. Then if I have ${3}$ red marbles, I must have ${2.5 + 2.5 + 2.5 = 7.5}$ total marbles...... and if I have ${20}$ red marbles, I must have

$${\underbrace{2.5 + 2.5 + 2.5 + ... + 2.5}_{20 \text{ times}}=2.5\times 20 = 50\text{ total marbles}}$$

Just as you'd expect :D