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

\( \frac{4}{6} \) ÷ \( \frac{3}{8} \) = \( \frac{4}{6} \) x \( \frac{8}{3} \)

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

\( \frac{4}{6} \) x \( \frac{8}{3} \) = \( \frac{4 x 8}{6 x 3} \) = \( \frac{32}{18} \) = 1\(\frac{7}{9}\)

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 equation for this sequence is:

a_n = a_n-1 + 6

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 6
a₆ = 25 + 6
a₆ = 31

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 45mph \times 3h \)
135 miles

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{9 x 3}{2 x 3} \) - \( \frac{6 x 1}{6 x 1} \)

\( \frac{27}{6} \) - \( \frac{6}{6} \)

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

\( \frac{27 - 6}{6} \) = \( \frac{21}{6} \) = 3\(\frac{1}{2}\)