Henry Ernest Dudeney/Puzzles and Curious Problems/105 - Equal Fractions/Solution

by : $105$

 * Equal Fractions

Solution
The examples given by are:


 * $\dfrac 2 4 = \dfrac 3 6 = \dfrac {79} {158}$


 * $\dfrac 3 6 = \dfrac 7 {14} = \dfrac {29} {58}$


 * $\dfrac 3 6 = \dfrac 9 {18} = \dfrac {27} {54}$


 * $\dfrac 2 6 = \dfrac 3 9 = \dfrac {58} {174}$

The fifth case which he offers up is:
 * $\dfrac {\cdotp 2} 1 = \dfrac {\cdotp 6} 3 = \dfrac {97} {485}$

where it is noted that the first two fractions are not actually proper fractions.

It is worth calling into question 's definition of a vulgar fraction, as he is unclear.