The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 40 and 44 have in common.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{9 x 5}{6 x 5} \) + \( \frac{5 x 3}{10 x 3} \)

\( \frac{45}{30} \) + \( \frac{15}{30} \)

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

\( \frac{45 + 15}{30} \) = \( \frac{60}{30} \) = 2

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

\( \frac{1}{9} \) x \( \frac{1}{7} \) = \( \frac{1 x 1}{9 x 7} \) = \( \frac{1}{63} \) = \(\frac{1}{63}\)

There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 19 people needing transportation leaving 19 - 16 = 3 who will have to find other transportation.

The number of students taking German or Spanish is 11 + 6 = 17. Of that group of 17, 2 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 17 - 2 = 15 who are taking at least one language. 29 - 15 = 14 students who are not taking either language.