To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{56} \) = \( \frac{\frac{32}{8}}{\frac{56}{8}} \) = \( \frac{4}{7} \)

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.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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 simplify a radical, factor out the perfect squares:

\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)