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 fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{9 x 4}{6 x 4} \) - \( \frac{2 x 3}{8 x 3} \)

\( \frac{36}{24} \) - \( \frac{6}{24} \)

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

\( \frac{36 - 6}{24} \) = \( \frac{30}{24} \) = 1\(\frac{1}{4}\)

You have 21 out of the total of 350 raffle tickets sold so you have a (\( \frac{21}{350} \)) x 100 = \( \frac{21 \times 100}{350} \) = \( \frac{2100}{350} \) = 6% chance to win the raffle.

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

\( \frac{3}{6} \) x \( \frac{4}{7} \) = \( \frac{3 x 4}{6 x 7} \) = \( \frac{12}{42} \) = \(\frac{2}{7}\)