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9. If ‘p’ and ‘q’ are two different numbers taken from the numbers 1 – 100. What is the largest value
pq pq
−
+
that can have? What is the largest value that can have?
pq pq
+
−
Multiplication of Rational Numbers

We follow the same procedure for the multiplication of rational numbers as we followed for fractions.

Multiplication of a Rational Number by an Integer

While multiplying a rational number by an integer, we multiply the numerator by the integer,
keeping the denominator same and simplify the product thus obtained.

p p Integer ProductofNumerators
In general, × integer = × =
q q 1 ProductofDenominators

 −  2
Let us now multiply a rational number   by an integer (–5).
 7  Remember

2
 −  2 − ( ) ×− ( ) 5 10 3 Every integer can be expressed
as a rational number by
  7   ×− ( ) =5 7 = 7 = 1 7 placing 1 in denominator.

5 5 ( − 21 3 )
5 (
Let us take another example, ×− ( 21) = × =× − 3) =− 15
7 1 7 1
Example 10: Multiply the following:
2  3   3   −  4
(a) ×− ( 3) (b) 15 ×   (c)   ×− ( 14) (d)   × 5
3  − 5  − 7   25 
Solution: We have,
×
(a) 2 ×− ( 3) = 2 ×− ( 3) = − 6 =− 2 (b) 15 ×   3  = 15 3 = 45 =− 9

3 3 3 2  − 5 − ( 5) − 5
4
(c)   3  ×− ( 14) = 3 ×− ( 14) = 6 (d)   −  4  ×= − ( ) ×4 5 1 = − ( ) × 1 = −4
5

7 

−
1 − ( 7)  25  5 25 5 5
Multiplication of a Rational Number by Another Rational Number
We can 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.

ProductofNumerators
Step 3: Product of two rational numbers =
ProductofDenominators
5
−  5
For example,    9  × 2 = − ( ) × 2 = −10

3
93
27
×
67 Rational Numbers