To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{5 x 3}{8 x 3} \) - \( \frac{7 x 2}{12 x 2} \)

\( \frac{15}{24} \) - \( \frac{14}{24} \)

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

\( \frac{15 - 14}{24} \) = \( \frac{1}{24} \) = \(\frac{1}{24}\)

There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 9 people needing transportation leaving 9 - 4 = 5 who will have to find other transportation.

To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 1 gallons so:

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

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{74}{6} \) = 12\(\frac{1}{3}\)

So, it will take 12 full vans and one partially full van to transport the entire team making a total of 13 vans.

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

46,000 fans x \( \frac{4}{5} \) = \( \frac{184000}{5} \) = 36,800 fans.