Final answer:
The division of nonzero rationals is not associative.
Step-by-step explanation:
The division of nonzero rationals is not associative. In general, the division of nonzero rational numbers does not follow the associative property. This means that for any three nonzero rational numbers a, b, and c, (a ÷ b) ÷ c is not necessarily equal to a ÷ (b ÷ c).
For example, let's consider a = 2, b = 3, and c = 4. We have (2 ÷ 3) ÷ 4 = (2/3) ÷ 4 = (2/3) × (1/4) = 1/6. On the other hand, a ÷ (b ÷ c) = 2 ÷ (3 ÷ 4) = 2 ÷ (3/4) = 2 × (4/3) = 8/3. Since 1/6 is not equal to 8/3, we can conclude that division of nonzero rationals is not associative.