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.

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.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{12 + 6 + 13 + 5}{4} \) = \( \frac{36}{4} \) = 9

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 7}{5 x 7} \) - \( \frac{8 x 5}{7 x 5} \)

\( \frac{49}{35} \) - \( \frac{40}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{49 - 40}{35} \) = \( \frac{9}{35} \) = \(\frac{9}{35}\)

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.