The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

40,000 fans x \( \frac{5}{6} \) = \( \frac{200000}{6} \) = 33,333 fans.

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

\( \frac{2}{8} \) ÷ \( \frac{4}{7} \) = \( \frac{2}{8} \) x \( \frac{7}{4} \)

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

\( \frac{2}{8} \) x \( \frac{7}{4} \) = \( \frac{2 x 7}{8 x 4} \) = \( \frac{14}{32} \) = \(\frac{7}{16}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{30mi}{30mph} \)
1 hour

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