A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
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To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{5} \) x \( \frac{4}{9} \) = \( \frac{1 x 4}{5 x 9} \) = \( \frac{4}{45} \) = \(\frac{4}{45}\)

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

You have 28 out of the total of 400 raffle tickets sold so you have a (\( \frac{28}{400} \)) x 100 = \( \frac{28 \times 100}{400} \) = \( \frac{2800}{400} \) = 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.