Respuesta :
Answer:
7 unique values can be created.
[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]
Step-by-step explanation:
We need to find unique values that can be created by forming the fraction
[tex]\dfrac{x}{y}[/tex]
where, [tex]x[/tex] is either 4, 8, or 12 and [tex]y[/tex] 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 [tex]\dfrac{x}{y}[/tex] are:
[tex]\dfrac{4}{4},\dfrac{4}{8},\dfrac{4}{12},\dfrac{8}{4},\dfrac{8}{8},\dfrac{8}{12},\dfrac{12}{4},\dfrac{12}{8},\dfrac{12}{12}[/tex]
[tex]1,\dfrac{1}{2},\dfrac{1}{3},2,1,\dfrac{2}{3},3,\dfrac{3}{2},1[/tex]
Here, 1 is repeated three times. So, unique values are
[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]
Therefore, 7 unique values can be created.
