Question

Rational numbers fail to satisfy inverse property under multiplication for zero.
Why

Answer 1

Answered, why rational numbers fail to satisfy inverse property under multiplication for zero.

• Inverse property:

Rational No. × Multiplicative Inverse = Multiplicative identity

• Multiplicative Inverse of a number is the reciprocal of number only.
• For zero, It's reciprocal will be

Reciprocal of zero = 1/0 which not a rational number, not even a real no. . Rather, 1/0 is not defined.

• Hence, rational numbers fail to satisfy inverse property under multiplication for zero because  1/0 is not defined.