To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{6 x 9}{5 x 9} \) + \( \frac{4 x 5}{9 x 5} \)

\( \frac{54}{45} \) + \( \frac{20}{45} \)

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

\( \frac{54 + 20}{45} \) = \( \frac{74}{45} \) = 1\(\frac{29}{45}\)

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:

\( \frac{4 x 3}{8 x 3} \) - \( \frac{2 x 2}{12 x 2} \)

\( \frac{12}{24} \) - \( \frac{4}{24} \)

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

\( \frac{12 - 4}{24} \) = \( \frac{8}{24} \) = \(\frac{1}{3}\)

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

You have 36 out of the total of 450 raffle tickets sold so you have a (\( \frac{36}{450} \)) x 100 = \( \frac{36 \times 100}{450} \) = \( \frac{3600}{450} \) = 8% chance to win the raffle.