Question

The expression of the division ${\displaystyle \frac{{\displaystyle \frac{1}{3}}}{{\displaystyle \frac{3}{4}}}}$ equals ______
A. ${\displaystyle \frac{4}{9}}$
B. ${\displaystyle \frac{4}{5}}$
C. ${\displaystyle \frac{1}{3}}$
D. ${\displaystyle \frac{1}{4}}$

Answer 1

Hint:
For the division of fractions, we take the reciprocal of the divisor and then multiply it with the dividend using the multiplication of fractions.

Complete step by step solution:
Here the divisor is ${\displaystyle \frac{3}{4}}$. Now, the reciprocal of ${\displaystyle \frac{3}{4}}$ is ${\displaystyle \frac{4}{3}}$ .
Now, multiplying the reciprocal of divisor with the ${\displaystyle \frac{1}{3}}$ using multiplication of fractions
$$\begin{gathered} {\displaystyle \frac{1}{3}}\times {\displaystyle \frac{4}{3}}\Rightarrow {\displaystyle \frac{1\times 4}{3\times 3}} \\ \Rightarrow {\displaystyle \frac{4}{9}} \end{gathered}$$

Therefore, the correct answer is A.

Note:
Always remember to take the reciprocal of the divisor before multiplying it with the dividend. Not following this, is a very common mistake.