To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{56} \) = \( \frac{\frac{36}{4}}{\frac{56}{4}} \) = \( \frac{9}{14} \)

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{55}{100} \) = \( \frac{55 x 15}{100} \) = \( \frac{825}{100} \) = 8 shots

The center makes 45% 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 = \( \frac{8}{\frac{45}{100}} \) = 8 x \( \frac{100}{45} \) = \( \frac{8 x 100}{45} \) = \( \frac{800}{45} \) = 18 shots

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

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 8 people needing transportation leaving 8 - 6 = 2 who will have to find other transportation.

1

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

\( \frac{1}{6} \) ÷ \( \frac{2}{7} \) = \( \frac{1}{6} \) x \( \frac{7}{2} \)

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

\( \frac{1}{6} \) x \( \frac{7}{2} \) = \( \frac{1 x 7}{6 x 2} \) = \( \frac{7}{12} \) = \(\frac{7}{12}\)