Question

Find the fourth proportion for $1\frac{5}{7},2\frac{3}{14},3\frac{3}{5}$.

Answer 1

Firstly we will simplify all the numbers

$\Rightarrow 1\frac{5}{7}=\frac{(1\times 7)+5}{7}=\frac{12}{7}$

$\Rightarrow 2\frac{3}{14}=\frac{(2\times 14)+3}{14}=\frac{31}{14}$

$\Rightarrow 3\frac{3}{5}=\frac{(3\times 5)+3}{5}=\frac{18}{5}$

So the three numbers are

$\frac{12}{7},\frac{31}{14},\frac{18}{5}$

Let the third proportion be $x$

$\Rightarrow \frac{12}{7}:\frac{31}{14}::\frac{18}{5}:x$

$\Rightarrow \frac{\frac{12}{7}}{\frac{31}{14}}=\frac{\frac{18}{5}}{x}$

Simplify we get

$\Rightarrow \frac{12}{7}\times \frac{14}{31}=\frac{18}{5\times x}$

$\Rightarrow \frac{12\times 2}{31}=\frac{18}{5\times x}$

$\Rightarrow \frac{24}{31}=\frac{18}{5\times x}$

Cross multiply we get

$\Rightarrow 120\times x=18\times 31$

$\Rightarrow x=\frac{558}{120}$

$\Rightarrow x=\frac{93}{20}$

$\Rightarrow x=4\frac{13}{20}$