The greatest common factor (GCF) is the greatest factor that divides two integers.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{8 x 5}{8 x 5} \) - \( \frac{5 x 4}{10 x 4} \)

\( \frac{40}{40} \) - \( \frac{20}{40} \)

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

\( \frac{40 - 20}{40} \) = \( \frac{20}{40} \) = \(\frac{1}{2}\)

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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 35% 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 = \( \frac{8}{\frac{35}{100}} \) = 8 x \( \frac{100}{35} \) = \( \frac{8 x 100}{35} \) = \( \frac{800}{35} \) = 23 shots

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