Question

The property of rational numbers used in the statement (-3/2) x 5/4 + (-3/2) x (-7/6) = (-3/2) x{5/4 + (-7/6)} is​

Answer 1

Answer:

(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.  

Step-by-step explanation:

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