### Теория:

Multiplication of Rational Numbers
Multiplication of rational numbers is similar to the multiplication of integers. All we have to do is multiply the numerator of the numbers and multiply the denominators. Thus we can say that the product of rational numbers is the ratio of multiplication of numerators and multiplication of denominators.
Example:
The following result is obtained by multiplying the numerators and multiplying 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:
• $6\cdot \left(-4\right)\cdot \left(-2\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}48$ (multiplies by two negative numbers - even number)
• $\left(-6\right)\cdot \left(-4\right)\cdot \left(-1\right)\cdot 2\phantom{\rule{0.147em}{0ex}}=-48$ (is multiplied by three negative numbers and an odd number)

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

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

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

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