Question

Find the fourth proportion for $3\frac{1}{3},1\frac{2}{3},2\frac{1}{2}$

Answer 1

Firstly we will simplify all the numbers

$\Rightarrow 3\frac{1}{3}=\frac{(3\times 3)+1}{3}=\frac{10}{3}$

$\Rightarrow 1\frac{2}{3}=\frac{(1\times 3)+2}{3}=\frac{5}{3}$

$\Rightarrow 2\frac{1}{2}=\frac{(2\times 2)+1}{2}=\frac{5}{2}$

So the three numbers are

$\frac{10}{3},\frac{5}{3},\frac{5}{2}$

Let the third proportion be $x$

$\Rightarrow \frac{10}{3}:\frac{5}{3}::\frac{5}{2}:x$

$\Rightarrow \frac{\frac{10}{3}}{\frac{5}{3}}=\frac{\frac{5}{2}}{x}$

Simplify we get

$\Rightarrow \frac{10}{3}\times \frac{3}{5}=\frac{5}{2\times x}$(3 gets cancelled)

$\Rightarrow \frac{10}{5}=\frac{5}{2\times x}$

$\Rightarrow 2=\frac{5}{2\times x}$

Cross multiply we get

$\Rightarrow 4\times x=5$

$\Rightarrow x=\frac{5}{4}$

$\Rightarrow x=1\frac{1}{4}$