Betty scored 81% on the test meaning she earned 81% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.81 = 195 points. Each question is worth 3 points so she got \( \frac{195}{3} \) = 65 questions right.

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:

32,000 fans x \( \frac{3}{4} \) = \( \frac{96000}{4} \) = 24,000 fans.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0002117 in scientific notation is 2.117 x 10^-4

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 have in common.

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{5} \) ÷ \( \frac{2}{6} \) = \( \frac{4}{5} \) x \( \frac{6}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{5} \) x \( \frac{6}{2} \) = \( \frac{4 x 6}{5 x 2} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)