A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

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

\( \frac{7 x 5}{9 x 5} \) + \( \frac{5 x 3}{15 x 3} \)

\( \frac{35}{45} \) + \( \frac{15}{45} \)

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

\( \frac{35 + 15}{45} \) = \( \frac{50}{45} \) = 1\(\frac{1}{9}\)

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

\( \frac{2}{9} \) ÷ \( \frac{4}{6} \) = \( \frac{2}{9} \) x \( \frac{6}{4} \)

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

\( \frac{2}{9} \) x \( \frac{6}{4} \) = \( \frac{2 x 6}{9 x 4} \) = \( \frac{12}{36} \) = \(\frac{1}{3}\)

The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 have in common.

The number of students taking German or Spanish is 14 + 11 = 25. Of that group of 25, 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 25 - 3 = 22 who are taking at least one language. 35 - 22 = 13 students who are not taking either language.