### Theory:

Multiplication of rational numbers is similar to the multiplication of integers.
• All we have to do is multiply the numerator and the denominators by the given numbers.
• Thus we can say that the product of rational numbers is the ratio of multiplication of numerators and denominators.
Example:
The following result is obtained by multiplying the numerators and the denominators.

$\begin{array}{l}\frac{2}{4}×\frac{3}{7}=\frac{2×3}{4×7}\\ =\frac{6}{28}\end{array}$
If the product has an even number of negative multipliers, then the multiplication is positive, because the product of two negative numbers is a positive number.

If the product has an odd number of negative multipliers, then the product is negative.
Example:
• $6×\left(-4\right)×\left(-2\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}48$ (multiplies by two negative numbers - even number).
• $\left(-6\right)×\left(-4\right)×\left(-1\right)×2\phantom{\rule{0.147em}{0ex}}=-48$ (multiplies by three negative numbers - odd number).

• $\left(-1\right)×\left(-1\right)×\left(-\frac{1}{3}\right)×\left(-\frac{1}{3}\right)\phantom{\rule{0.147em}{0ex}}=\frac{1}{9}$

• $\left(-1\right)×\left(-0.2\right)×\left(-1\right)×\left(-0.2\right)×\left(-1\right)\phantom{\rule{0.147em}{0ex}}=-0.04$
This law also applies to division or division and multiplication together.

For instance, $\left(-2\right):1×\left(-6\right)×5:\left(-2\right)\phantom{\rule{0.147em}{0ex}}=-30$

The operations shall be carried out successively, resulting in a minus sign ($$-$$) because there are three negative numbers.