Henry Ernest Dudeney/Modern Puzzles/9 - Fractional Value

by : $9$

 * Fractional Value
 * What part of threepence is one-third of twopence?

Solution
Two-ninths of threepence.

Proof

 * $\dfrac 1 3 \times 2 = \dfrac 2 3$

So $\dfrac 1 3$ of $2 \oldpence$ is $\dfrac 2 3$ of a penny.

Then:
 * $\dfrac 2 3$ of a penny is $\dfrac 2 3$ of $\dfrac 1 3$ of $3 \oldpence$

That is:
 * $\dfrac 2 9$ of $3 \oldpence$