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

\( \frac{3}{6} \) x \( \frac{4}{9} \) = \( \frac{3 x 4}{6 x 9} \) = \( \frac{12}{54} \) = \(\frac{2}{9}\)

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

39,000 fans x \( \frac{4}{5} \) = \( \frac{156000}{5} \) = 31,200 fans.

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

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{65}{13} \) = 5

Jennifer scored 81% on the test meaning she earned 81% of the possible points on the test. There were 280 possible points on the test so she earned 280 x 0.81 = 228 points. Each question is worth 4 points so she got \( \frac{228}{4} \) = 57 questions right.