If p = - 8 27 , q = 3 4 and r = - 12 15 , then verify that p × ( q × r ) = ( p × q ) × r .

Given, p = - 8 27 , q = 3 4 and r = - 12 15 To verify: p × ( q × r ) = ( p × q ) × r Using associative property of multiplication of rational number p q × r s × t u = p q × r s × t u L.H.S. = p × ( q × r ) = - 8 27 × 3 4 × - 12 15 = - 8 27 × - 3 5 = ( - 8 ) × ( - 3 ) 27 × 5 = 24 27 × 5 = 8 45 R.H.S. = ( p × q ) × r = - 8 27 × 3 4 × - 12 15 = - 2 9 × - 12 15 = 8 45 Thus, L . H . S . = R . H . S . Hence, the given rational numbers satisfy the associative property of multiplication of rational number.

If p = - 8 27 , q = 3 4 and r = - 12 15 , then verify that p × ( q - r ) = p × q - p × r .

p = - 8 27 , q = 3 4 and r = - 12 15 L.H.S = p × ( q - r ) = - 8 27 × 3 4 - - 12 15 = - 8 27 × 45 + 48 60 = - 8 27 × 93 60 = - 62 135 R.H.S = p × q - p × r = - 8 27 × 3 4 - 8 27 × - 12 15 = - 2 9 - 32 135 = - 30 - 32 135 = - 62 135 ∴ L . H . S . = R . H . S . Hence, the given rational numbers satisfy the distributive property of multiplication over subtraction.