To determine how many points Uncle Drew averaged per minute during his [tex]$5 \frac{5}{6}$[/tex] minutes in the game, we need to follow these steps:
1. Convert the mixed number to an improper fraction:
[tex]\( 5 \frac{5}{6} \)[/tex] can be converted to an improper fraction by multiplying the whole number part (5) by the denominator (6), and then adding the numerator (5). This gives us:
[tex]\[
5 \frac{5}{6} = \frac{5 \cdot 6 + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6}
\][/tex]
2. Calculate the points per minute:
To find the average points per minute, we divide the total points scored by the total time in minutes:
[tex]\[
\text{Average points per minute} = \frac{\text{Total points scored}}{\text{Total time in minutes}}
\][/tex]
Given that Uncle Drew scored 28 points in [tex]\( \frac{35}{6} \)[/tex] minutes, we can set up the calculation as:
[tex]\[
\text{Average points per minute} = \frac{28}{\frac{35}{6}}
\][/tex]
To divide by a fraction, we multiply by its reciprocal:
[tex]\[
\text{Average points per minute} = 28 \times \frac{6}{35}
\][/tex]
3. Simplify the multiplication:
Before multiplying, we can simplify [tex]\( 28 \)[/tex] and [tex]\( 35 \)[/tex] by their greatest common divisor, which is 7:
[tex]\[
\frac{28}{7} = 4 \quad \text{and} \quad \frac{35}{7} = 5
\][/tex]
So,
[tex]\[
\frac{6}{35} = \frac{6}{5 \cdot 7}
\][/tex]
Now,
[tex]\[
28 \times \frac{6}{35} = 4 \times \frac{6}{5}
\][/tex]
Then,
[tex]\[
4 \times \frac{6}{5} = \frac{4 \cdot 6}{5} = \frac{24}{5} = 4.8
\][/tex]
Therefore, Uncle Drew averaged [tex]\( \boxed{4.8} \)[/tex] points per minute during the [tex]\( 5 \frac{5}{6} \)[/tex] minutes he played.
