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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{8 x 2}{6 x 2} \) + \( \frac{2 x 1}{12 x 1} \)

\( \frac{16}{12} \) + \( \frac{2}{12} \)

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

\( \frac{16 + 2}{12} \) = \( \frac{18}{12} \) = 1\(\frac{1}{2}\)

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{4}{100} \) x 9 = \( \frac{4 \times 9}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour

So, in an average hour, the machine will produce 9 - 0.36 = 8.64 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.64 = 146.9 error free parts were produced yesterday.

There are 2 5-passenger taxis available so that's 2 x 5 = 10 total seats. There are 13 people needing transportation leaving 13 - 10 = 3 who will have to find other transportation.

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

\( \frac{2}{9} \) x \( \frac{1}{7} \) = \( \frac{2 x 1}{9 x 7} \) = \( \frac{2}{63} \) = \(\frac{2}{63}\)

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 have in common.