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

To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3

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

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:

38,000 fans x \( \frac{5}{6} \) = \( \frac{190000}{6} \) = 31,667 fans.

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

\( \frac{1}{5} \) x \( \frac{2}{9} \) = \( \frac{1 x 2}{5 x 9} \) = \( \frac{2}{45} \) = \(\frac{2}{45}\)