Question

Find: $4÷\left(\frac{8}{3}\right)$

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$}\right.}}=\frac{b}{a}$.

• To perform division between two fractions, the division sign is converted into a multiplication sign by making the later fraction reciprocal.
• For example, $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

The given expression is $4÷\left(\frac{8}{3}\right)$.

Step 2: Simplify the expression

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

$$\begin{gathered} \Rightarrow 4÷\left(\frac{8}{3}\right)=1\times \frac{3}{2} \\ \Rightarrow 4÷\left(\frac{8}{3}\right)=\frac{1\times 3}{2} \\ \Rightarrow 4÷\left(\frac{8}{3}\right)=\frac{3}{2} \end{gathered}$$

Hence, the value of $\mathbf{4}\mathbf{÷}\mathbf{\left(}\frac{\mathbf{8}}{\mathbf{3}}\mathbf{\right)}$ is $\frac{\mathbf{3}}{\mathbf{2}}$.