Question

Determine the value of the following expression.

$\frac{4}{9}\cdot \frac{3}{2}$

Short answer

The value of the given expression is $\frac{\mathbf{2}}{\mathbf{3}}$.

Step-by-step solution

Step 1. Given information.

Given expression is:

$\frac{4}{9}\cdot \frac{3}{2}$

Step 2. Write the concept.

The rule for multiplying fractions is:

$\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$

Step 3. Solve the expression.

The given expression can be solved as in below:

$\begin{array}{l}\frac{4}{9}\cdot \frac{3}{2}=\frac{4\cdot 3}{9\cdot 2}\\ =\frac{12}{18}\end{array}$

Then,

$\begin{array}{l}\frac{4}{9}\cdot \frac{3}{2}=\frac{12}{18}\\ =\frac{2}{3}\end{array}$