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Multiplication of Rational Numbers

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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`.

Example

Multiply the following rational numbers.
`9/13 xx 4/7`

`9/13 xx 4/7 = (9 xx 4)/(13 xx 7) = 36/91`.

Example

Multiply the following rational numbers.

`3/5 xx (- 4)/5`

`3/5 xx (- 4)/5 = (3 xx (- 4))/(5 xx 5) = (- 12)/25`.

Example

Multiply the following rational numbers.

`9/13 xx 26/3`

`9/13 xx 26/3 = (3 xx 2)/1 = 6/1.`

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