Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (2 + 4) ÷ 4 x 4 - 2²
P: 2 + (6) ÷ 4 x 4 - 2²
E: 2 + 6 ÷ 4 x 4 - 4
MD: 2 + \( \frac{6}{4} \) x 4 - 4
MD: 2 + \( \frac{24}{4} \) - 4
AS: \( \frac{8}{4} \) + \( \frac{24}{4} \) - 4
AS: \( \frac{32}{4} \) - 4
AS: \( \frac{32 - 16}{4} \)
\( \frac{16}{4} \)
4

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.

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:

\( \sqrt{\frac{4}{9}} \)
\( \frac{\sqrt{4}}{\sqrt{9}} \)
\( \frac{\sqrt{2^2}}{\sqrt{3^2}} \)
\(\frac{2}{3}\)

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.

Putting these two equations together and solving for width (w):

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

46,000 fans x \( \frac{2}{3} \) = \( \frac{92000}{3} \) = 30,667 fans.