Question

Find: $\left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)$

Answer 1

Step 1: Define reciprocals and the division of fractions and state the given data

Reciprocals and the division of fractions:

1. The reciprocal of a fraction can be determined by interchanging the values of its numerator and denominator with each other.
2. For example, the reciprocal of a fraction $\frac{a}{b}$ is defined as $\frac{1}{{\displaystyle \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right.}}=\frac{b}{a}$.
3. In order to perform division between two fractions, the division sign is converted into a multiplication sign by making the later fraction reciprocal.
4. For example, $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

The given expression is $\left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)$.

Step 2: Simplify the expression

$\left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)=\frac{4}{9}\times \frac{3}{2}$ $\left[\because \mathrm{the}\mathrm{reciprocal}\mathrm{of}\frac{8}{7}=\frac{7}{8}\right]$

$$\begin{gathered} \Rightarrow \left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)=\frac{2}{9}\times \frac{3}{1} \\ \Rightarrow \left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)=\frac{2}{3}\times \frac{1}{1} \\ \Rightarrow \left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)=\frac{2}{3}\times 1 \\ \Rightarrow \left(\frac{4}{9}\right)÷\left(\frac{2}{3}\right)=\frac{2}{3} \end{gathered}$$

Hence, the value of $\left(\frac{4}{9}\right)\mathbf{÷}\left(\frac{2}{3}\right)$ is $\frac{\mathbf{2}}{\mathbf{3}}$.