Question

How many unique values can be created by forming the fraction $\frac{x}{y}$ where $x$ is either 4, 8, or 12 and $y$ is either 4, 8, or 12?

Answer 1

7 unique values can be created.

`1,2,3,(1)/(2),(1)/(3),(2)/(3),(3)/(2)`

Explanation:

We need to find unique values that can be created by forming the fraction

`(x)/(y)`

where,
`x` is either 4, 8, or 12 and
`y` is either 4, 8, or 12.

Now, possible ordered pairs are (4,4), (4,8), (4,12), (8,4), (8,8), (8,12), (12,4), (12,8), (12,12).

For these ordered pairs the value of
`(x)/(y)` are:

`(4)/(4),(4)/(8),(4)/(12),(8)/(4),(8)/(8),(8)/(12),(12)/(4),(12)/(8),(12)/(12)`

`1,(1)/(2),(1)/(3),2,1,(2)/(3),3,(3)/(2),1`

Here, 1 is repeated three times. So, unique values are

`1,2,3,(1)/(2),(1)/(3),(2)/(3),(3)/(2)`

Therefore, 7 unique values can be created.