To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{80} \) = \( \frac{\frac{20}{20}}{\frac{80}{20}} \) = \( \frac{1}{4} \)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{36}} \)
\( \frac{\sqrt{81}}{\sqrt{36}} \)
\( \frac{\sqrt{9^2}}{\sqrt{6^2}} \)
\( \frac{9}{6} \)
1\(\frac{1}{2}\)

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

You have 12 out of the total of 250 raffle tickets sold so you have a (\( \frac{12}{250} \)) x 100 = \( \frac{12 \times 100}{250} \) = \( \frac{1200}{250} \) = 5% chance to win the raffle.