# 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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