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

\( \frac{2}{6} \) ÷ \( \frac{3}{9} \) = \( \frac{2}{6} \) x \( \frac{9}{3} \)

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

\( \frac{2}{6} \) x \( \frac{9}{3} \) = \( \frac{2 x 9}{6 x 3} \) = \( \frac{18}{18} \) = 1

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

\( \frac{42\sqrt{10}}{6\sqrt{5}} \)
\( \frac{42}{6} \) \( \sqrt{\frac{10}{5}} \)
7 \( \sqrt{2} \)

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

To simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)

The number of students taking German or Spanish is 6 + 10 = 16. Of that group of 16, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 3 = 13 who are taking at least one language. 19 - 13 = 6 students who are not taking either language.