To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{5 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 2

The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{23}{8} \) - \( \frac{5}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups

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

\( \frac{4}{9} \) ÷ \( \frac{3}{7} \) = \( \frac{4}{9} \) x \( \frac{7}{3} \)

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

\( \frac{4}{9} \) x \( \frac{7}{3} \) = \( \frac{4 x 7}{9 x 3} \) = \( \frac{28}{27} \) = 1\(\frac{1}{27}\)

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

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

\( \frac{2}{9} \) x \( \frac{1}{9} \) = \( \frac{2 x 1}{9 x 9} \) = \( \frac{2}{81} \) = \(\frac{2}{81}\)