To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{60} \) = \( \frac{\frac{28}{4}}{\frac{60}{4}} \) = \( \frac{7}{15} \)

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

43,000 fans x \( \frac{5}{6} \) = \( \frac{215000}{6} \) = 35,833 fans.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{61}{10} \) = 6\(\frac{1}{10}\)

So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.

To fill a 16 gallon tank exactly halfway you'll need 8 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{8 \text{ gallons}}{2 \text{ gallons}} \) = 4