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You have 31 out of the total of 450 raffle tickets sold so you have a (\( \frac{31}{450} \)) x 100 = \( \frac{31 \times 100}{450} \) = \( \frac{3100}{450} \) = 7% chance to win the raffle.

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

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 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:

\( \frac{8 x 4}{6 x 4} \) - \( \frac{5 x 3}{8 x 3} \)

\( \frac{32}{24} \) - \( \frac{15}{24} \)

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

\( \frac{32 - 15}{24} \) = \( \frac{17}{24} \) = \(\frac{17}{24}\)