To subtract 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 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

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

\( \frac{2 x 7}{3 x 7} \) - \( \frac{3 x 3}{7 x 3} \)

\( \frac{14}{21} \) - \( \frac{9}{21} \)

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

\( \frac{14 - 9}{21} \) = \( \frac{5}{21} \) = \(\frac{5}{21}\)

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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{10\sqrt{21}}{2\sqrt{7}} \)
\( \frac{10}{2} \) \( \sqrt{\frac{21}{7}} \)
5 \( \sqrt{3} \)

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:

41,000 fans x \( \frac{2}{3} \) = \( \frac{82000}{3} \) = 27,333 fans.

1