The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

You have 16 out of the total of 400 raffle tickets sold so you have a (\( \frac{16}{400} \)) x 100 = \( \frac{16 \times 100}{400} \) = \( \frac{1600}{400} \) = 4% chance to win the raffle.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{35}{100} \) = \( \frac{35 x 15}{100} \) = \( \frac{525}{100} \) = 5 shots

The center makes 30% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{5}{\frac{30}{100}} \) = 5 x \( \frac{100}{30} \) = \( \frac{5 x 100}{30} \) = \( \frac{500}{30} \) = 17 shots

to make the same number of shots as the guard and thus score the same number of points.

By buying two shirts, Frank will save $24 x \( \frac{15}{100} \) = \( \frac{$24 x 15}{100} \) = \( \frac{$360}{100} \) = $3.60 on the second shirt.