Question

Find two rational numbers greater than 1/3 whose

product is less than 1/3 Explain your reasoning to a classmate.

Answer 1

`(3)/(7),\ (2)/(3)`

Explanation:

Consider numbers

`x=(3)/(7) \\ \\y=(2)/(3)`

First, check that these numbers are greater than
`(1)/(3):`

For x:

`(3)/(7)=(9)/(21)\\ \\(1)/(3)=(7)/(21)\\ \\(9)/(21)>(7)/(21)\Rightarrow x=(3)/(7)>(1)/(3)`

For y:

`(2)/(3)>(1)/(3)`

Now, find the product xy:

`xy=(3)/(7)\cdot (2)/(3)=(2)/(7)=(6)/(21)<(7)/(21)=(1)/(3)`