Henry Ernest Dudeney/Modern Puzzles/9 - Fractional Value/Solution

Modern Puzzles by Henry Ernest Dudeney: $9$

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 $3 \oldpence$

$\blacksquare$

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $9$. -- Fractional Value