The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 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.

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{5} \) ÷ \( \frac{2}{6} \) = \( \frac{1}{5} \) x \( \frac{6}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{5} \) x \( \frac{6}{2} \) = \( \frac{1 x 6}{5 x 2} \) = \( \frac{6}{10} \) = \(\frac{3}{5}\)

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 6 out of the total of 100 raffle tickets sold so you have a (\( \frac{6}{100} \)) x 100 = \( \frac{6 \times 100}{100} \) = \( \frac{600}{100} \) = 6% chance to win the raffle.