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?

7 unique values can be created.

Step-by-step explanation:

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

where, is either 4, 8, or 12 and 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 are:

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

Therefore, 7 unique values can be created.

15 batches are the most you can make

step-by-step explanation: