Question:
Which of the following expressions shows that rational numbers are associative under multiplication.
(a) $[(2 / 3) \times((-6 / 7) \times(3 / 5))]=[((2 / 3) \times(-6 / 7)) \times(3 / 5)]$
(b) $[(2 / 3) \times((-6 / 7) \times(3 / 5))]=[(2 / 3) \times((3 / 5) \times(-6 / 7))]$
(c) $[(2 / 3) \times((-6 / 7) \times(3 / 5))]=[((3 / 5) \times(2 / 3)) \times(-6 / 7)]$
(d) $[((2 / 3) \times(-6 / 7)) \times(3 / 5)]=[((-6 / 7) \times(2 / 3)) \times(3 / 5)]$
Solution:
(a) $[(2 / 3) \times((-6 / 7) \times(3 / 5))]=[((2 / 3) \times(-6 / 7)) \times(3 / 5)]$
Because, the arrangement of above rational numbers is in the form of Associative law of Multiplication $[a \times(b \times c)]=[(a \times b) \times c]$