Question

Fill in the blanks:

$\frac{1}{\square }=\frac{12}{30}=\frac{36}{\square }$

Answer 1

Given,

$\frac{1}{\square }=\frac{12}{30}=\frac{36}{\square }$

on taking first and second

$\frac{1}{\square }=\frac{12}{30}$

To get the numerator $1$ from $\frac{12}{30}$, we have to divide both numerator and denominator by $12$.

Then we get, $\frac{12÷12}{30÷12}=\frac{1}{\left({\displaystyle \frac{5}{2}}\right)}$ ($30÷12$, divide by the common factor $6$, we get $\frac{5}{2}$ )

Therefore, $\square =\frac{5}{2}$

on taking second and third

$\frac{12}{30}=\frac{36}{\square }$

To get the numerator $36$ from $\frac{12}{30}$, we have to multiply both numerator and denominator by $3$.

Then we get, $\frac{12\times 3}{30\times 3}=\frac{36}{90}$

Therefore, $\square =90$

Hence, $\frac{1}{\left({\displaystyle \frac{5}{2}}\right)}=\frac{12}{30}=\frac{36}{90}$