You have 14 out of the total of 350 raffle tickets sold so you have a (\( \frac{14}{350} \)) x 100 = \( \frac{14 \times 100}{350} \) = \( \frac{1400}{350} \) = 4% chance to win the raffle.

To add 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{7 x 5}{8 x 5} \) + \( \frac{5 x 4}{10 x 4} \)

\( \frac{35}{40} \) + \( \frac{20}{40} \)

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

\( \frac{35 + 20}{40} \) = \( \frac{55}{40} \) = 1\(\frac{3}{8}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

40,000 fans x \( \frac{3}{4} \) = \( \frac{120000}{4} \) = 30,000 fans.