Verify the property x × (y × z) = (x × y) × z of rational numbers by using
(a) x = 1, y = -½ and z = ¼
In the question is given to verify the property x × (y × z) = (x × y) × z
The arrangement of the given rational number is as per the rule of associative property for multiplication.
Then, 1 × (-½ × ¼) = (1 × -½) × ¼
LHS = 1 × (-½ × ¼)
= 1 × (-1/8)
= -1/8
RHS = (1 × -½) × ¼
= (-½) × ¼
= -1/8
By comparing LHS and RHS
LHS = RHS
∴ -1/8 = -1/8
Hence x × (y × z) = (x × y) × z
(b) x = 2/3, y = -3/7 and z = ½
Solution:-
In the question is given to verify the property x × (y × z) = (x × y) × z
The arrangement of the given rational number is as per the rule of associative property for multiplication.
Then, (2/3) × (-3/7 × ½) = ((2/3) × (-3/7)) × ½
LHS = (2/3) × (-3/7 × ½)
= (2/3) × (-3/14)
= -6/42
RHS = ((2/3) × (-3/7)) × ½
= (-6/21) × ½
= -6/42
By comparing LHS and RHS
LHS = RHS
∴ -6/42 = -6/42
Hence x × (y × z) = (x × y) × z
(c) x = -2/7, y = -5/6 and z = ¼
Solution:-
In the question is given to verify the property x × (y × z) = (x × y) × z
The arrangement of the given rational number is as per the rule of associative property for multiplication.
Then, (-2/7) × (-5/6 × ¼) = ((-2/7) × (-5/6)) × ¼
LHS = (-2/7) × (-5/6 × ¼)
= (-2/7) × (-5/24)
= 10/168
RHS = ((-2/7) × (-5/6)) × ¼
= (10/42) × ¼
= 10/168
By comparing LHS and RHS
LHS = RHS
∴ 10/168 = 10/168
Hence x × (y × z) = (x × y) × z