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:

\( \sqrt{\frac{49}{4}} \)
\( \frac{\sqrt{49}}{\sqrt{4}} \)
\( \frac{\sqrt{7^2}}{\sqrt{2^2}} \)
\( \frac{7}{2} \)
3\(\frac{1}{2}\)

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 have in common.

You have 4 out of the total of 50 raffle tickets sold so you have a (\( \frac{4}{50} \)) x 100 = \( \frac{4 \times 100}{50} \) = \( \frac{400}{50} \) = 8% chance to win the raffle.

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{64} \) = \( \frac{\frac{24}{8}}{\frac{64}{8}} \) = \( \frac{3}{8} \)