A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The equation for this sequence is:

a_n = a_n-1 + 6

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 + 6
a₆ = 25 + 6
a₆ = 31

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-6z⁵ + 2z⁵
(-6 + 2)z⁵
-4z⁵

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:

\( \sqrt{\frac{25}{64}} \)
\( \frac{\sqrt{25}}{\sqrt{64}} \)
\( \frac{\sqrt{5^2}}{\sqrt{8^2}} \)
\(\frac{5}{8}\)

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

40,000 fans x \( \frac{3}{4} \) = \( \frac{120000}{4} \) = 30,000 fans.