Multiplication of Rational numbers — lesson. Mathematics State Board, Class 8.

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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} \times \frac{3}{7} = \frac{2 \times 3}{4 \times 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:

$6 \times (- 4) \times (- 2) = 48$ (multiplies by two negative numbers - even number).

$(- 6) \times (- 4) \times (- 1) \times 2 = - 48$ (multiplies by three negative numbers - odd number).
$(- 1) \times (- 1) \times (- \frac{1}{3}) \times (- \frac{1}{3}) = \frac{1}{9}$
$(- 1) \times (- 0. 2) \times (- 1) \times (- 0. 2) \times (- 1) = - 0. 04$

This law also applies to division or division and multiplication together.

For instance,

(- 2) : 1 \times (- 6) \times 5 : (- 2) = - 30

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

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3. Multiplication of Rational numbers

Theory: