Verify the property x × (y × z) = (x × y) × z

Question:

Verify the property x × (y × z) = (x × y) × z of rational numbers by using

Solution:

(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

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