Multiplication of Rational Numbers

Multiplication of Rational Number:

1) Multiplication of rational number with whole number:

Let us multiply the rational number `(- 3)/5 "by 2, i.e., we find" (- 3)/5 xx 2`. 

On the number line, it will mean two jumps of `3/5` to the left.

We reach at `(- 6)/5`. Let us find it as we did in fractions.

`(- 3)/5 xx 2 = (- 3 xx 2)/5 = (- 6)/5`.

We arrive at the same rational number.

So, we find that while multiplying a rational number by a positive integer, we
multiply the numerator by that integer, keeping the denominator unchanged.

Let us now multiply a rational number by a negative integer,

`(- 2)/9 xx (- 5) = (-2  xx  (- 5))/9 = 10/9`

2) Multiplication of two rational number:

We multiply two rational numbers in the following way:

Step 1: Multiply the numerators of the two rational numbers.

Step 2: Multiply the denominators of the two rational numbers.

Step 3: Write the product as the product of `"numerators"/"product of denominators"`.

`(-3)/5 xx 2/7 = (-3 xx 2)/(5 xx 7) = (-6)/35`.

`(-5)/8 xx (-9)/7 = (- 5 xx (-9))/(8 xx 7) = 45/56`.