Which statement shows the associative property of multiplication?
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Answer:
Step-by-step explanation:
Let r and s be two rational numbers
Without loss of generality assume that r<s, because one number has to be necessarily less than the other otherwise two would be equal.
Then find mid value of r and s as
So we have atleast one rational number between r and s. Note that t is rational because it is sum of two rational numbers r/2 and s/2
Now using r and t we find one rational number say u between r and t.
Again with r and u we find another rational number between them
This process can be repeated infinitely
Thus we conclude there are infinitely many rational numbers in between any two distinct rational numbers.