Verify the property x × (y × z) = (x × y) × z of rational numbers by using
(a) x = 1, y = -1/2, z = 1/4
(b) x = 2/3, y = -3/7, z = 1/2
(c) x = -2/7, y = -5/6, z = 1/4
(d) x = 0, y = 1/2, z = 1/3
and what is the name of this property?

Solution:

(a) x = 1, y = -1/2, z = 1/4

x × (y × z) = 1 × (-1/2 × 1/4) = 1 × -1/8 = -1/8 = LHS

(x × y) × z =(1 × -1/2) × 1/4 = -1/2 × 1/4 = -1/8 = RHS

LHS = RHS

Hence verified the associative property

(b) x = 2/3, y = -3/7, z = 1/2

x × (y × z) = 2/3 × (-3/7 × 1/2) = 2/3 × -3/14 = -2/14 = -1/7 = LHS

(x × y) × z = (2/3 × -3/7) × 1/2 = -2/7 × 1/2 = -2/14 = -1/7 = RHS

LHS = RHS

Hence verified the associative property

(c) x = -2/7, y = -5/6, z = 1/4

x × (y × z) = -2/7 × (-5/6 × 1/4) = -2/7 × -5/24 =10/168= 5/84 = LHS

(x × y) × z = (-2/7 × -5/6) × 1/4 = 10/42 × 1/4 =10/168= 5/84 = RHS

LHS = RHS

Hence verified the associative property

(d) x = 0, y = 1/2, z = 1/3

x × (y × z) = 0 × (1/2 × 1/3) = 0 = LHS

(x × y) × z = (0 × 1/2) × 1/3 = 0= RHS

LHS = RHS

Hence verified the associative property

✦ Try This: Verify the property x × (y × z) = (x × y) × z of rational numbers by using

(a) x = 1, y = -1/2, z = 1/4

(b) x = 2/3, y = -3/7, z = 1/2

(c) x = -2/7, y = -5/6, z = 1/4

(d) x = 0, y = 1/2, z = 1/3 and what is the name of this property

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 109

Verify the property x × (y × z) = (x × y) × z of rational numbers by using (a) x = 1, y = -1/2, z = 1/4 (b) x = 2/3, y = -3/7, z = 1/2 (c) x = -2/7, y = -5/6, z = 1/4 (d) x = 0, y = 1/2, z = 1/3 and what is the name of this property

Summary:

Associative property for multiplication x × (y × z) = (x × y) × z of given rational numbers is verified (a) x = 1, y = -1/2, z = 1/4 (b) x = 2/3, y = -3/7, z = 1/2 (c) x = -2/7, y = -5/6, z = 1/4 (d) x = 0, y = 1/2, z = 1/3

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