How do you multiply $\dfrac{5}{9} \times \dfrac{3}{4}$ ?

Hint: Whenever two fractions are given always multiply the numerator of one with the numerator of the other and then the denominator of one with the denominator of the other. Now write their products in expansion form in the numerator and denominator to cancel out common terms and to get a more simplified fraction or a constant.

Complete step-by-step answer:
The given fractions which are to be multiplied are, $\dfrac{5}{9} \times \dfrac{3}{4}$
Now multiply the numerators of both the given fractions.
$\Rightarrow \dfrac{{15}}{{9 \times 4}}$
Now multiply the denominators of the given fractions.
$\Rightarrow \dfrac{{15}}{{36}}$
Now write the numerator in expanded product form as below,
$\Rightarrow \dfrac{{3 \times 5}}{{36}}$
Do the same to the denominator so that we can cancel out the common terms to get a more simplified solution which might be a fraction or a constant.
$\Rightarrow \dfrac{{3 \times 5}}{{2 \times 2 \times 3 \times 3}}$
Now cancel out the common terms from the numerator and the denominator.
$\Rightarrow \dfrac{5}{{2 \times 2 \times 3}}$
Now, this is the solution to the given expression. Evaluate it to get a fraction.
$\Rightarrow \dfrac{5}{{2 \times 2 \times 3}} = \dfrac{5}{{12}}$

$\therefore \dfrac{5}{9} \times \dfrac{3}{4} = \dfrac{5}{{12}}$ on simplification.

Additional information: If an improper fraction is given, we must first convert it to a mixed fraction. For that, we must first divide the denominator with the numerator. Then we write the answer in the whole number part i.e., in front of the fraction. Now, we write the remainder in the numerator part and the denominator remains as it is. A mixed fraction is a whole number and a fraction part combined. The units will always remain the same.

Note:
Always write the multiplied product in expanded form to easily cancel out the terms in the numerator and the denominator. Then evaluate to get the final answer which might be a fraction or a constant.