To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{3 x 5} \) + \( \frac{6 x 3}{5 x 3} \)

\( \frac{15}{15} \) + \( \frac{18}{15} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{15 + 18}{15} \) = \( \frac{33}{15} \) = 2\(\frac{1}{5}\)

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:

41,000 fans x \( \frac{3}{4} \) = \( \frac{123000}{4} \) = 30,750 fans.

The greatest common factor (GCF) is the greatest factor that divides two integers.

The amount of flour you need is (3\(\frac{3}{4}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{30}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{29}{8} \) cups
3\(\frac{5}{8}\) cups

44% of the water consumption is industrial use and 32% is personal use so (44% - 32%) = 12% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 40,000 gallons = 4,800 gallons.