Question

7. Consider three rational numbers :

a= 1/2
b= 2/3
c= 3/5

Find:-
i)commutative law of multiplication

ii) associative law of multiplication

can you pls help me in solving this..​

Answer 1

Closure property of multiplication of rational numbers:

The product of two rational numbers is always a rational number.

If a/b and c/d are any two rational numbers then (a/b × c/d) is also a rational number.

For example:

(i) Consider the rational numbers 1/2 and 5/7. Then,

(1/2 × 5/7) = (1 × 5)/(2 × 7) = 5/14, is a rational number .

(ii) Consider the rational numbers -3/7 and 5/14. Then

(-3/7 × 5/14) = {(-3) × 5}/(7 × 14) = -15/98, is a rational number .

(iii) Consider the rational numbers -4/5 and -7/3. Then

(-4/5 × -7/3) = {(-4) × (-7)}/(5 × 3) = 28/15, is a rational number.

Commutative property of multiplication of rational numbers:

Two rational numbers can be multiplied in any order.

Thus, for any rational numbers a/b and c/d, we have:

(a/b × c/d) = (c/d × a/b)

For example:

(i) Let us consider the rational numbers 3/4 and 5/7 Then,

(3/4 × 5/7) = (3 × 5)/(4 × 7) = 15/28 and (5/7 × 3/4) = (5 × 3)/(7 × 4)

= 15/28

Therefore, (3/4 × 5/7) = (5/7 × 3/4)

(ii) Let us consider the rational numbers -2/5 and 6/7.Then,

{(-2)/5 × 6/7} = {(-2) × 6}/(5 × 7) = -12/35 and (6/7 × -2/5 )

= {6 × (-2)}/(7 × 5) = -12/35

Therefore, (-2/5 × 6/7 ) = (6/7 × (-2)/5)

(iii) Let us consider the rational numbers -2/3 and -5/7 Then,

(-2)/3 × (-5)/7 = {(-2) × (-5) }/(3 × 7) = 10/21 and (-5/7) × (-2/3)

= {(-5) × (-2)}/(7 × 3) = 10/21

Therefore, (-2/3) × (-5/7) = (-5/7) × (-2)/3