You have 4 out of the total of 100 raffle tickets sold so you have a (\( \frac{4}{100} \)) x 100 = \( \frac{4 \times 100}{100} \) = \( \frac{400}{100} \) = 4% chance to win the raffle.

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{48} \) = \( \frac{\frac{28}{4}}{\frac{48}{4}} \) = \( \frac{7}{12} \)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

By buying two shirts, Charlie will save $21 x \( \frac{30}{100} \) = \( \frac{$21 x 30}{100} \) = \( \frac{$630}{100} \) = $6.30 on the second shirt.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{37}{12} \) = 3\(\frac{1}{12}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.