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

\( \frac{2}{6} \) x \( \frac{2}{9} \) = \( \frac{2 x 2}{6 x 9} \) = \( \frac{4}{54} \) = \(\frac{2}{27}\)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $600
i = 0.05 x $600

No payments were made so the total amount due is the original amount + the accumulated interest:

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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{4 x 4}{6 x 4} \) + \( \frac{9 x 3}{8 x 3} \)

\( \frac{16}{24} \) + \( \frac{27}{24} \)

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

\( \frac{16 + 27}{24} \) = \( \frac{43}{24} \) = 1\(\frac{19}{24}\)

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

\( \frac{2}{100} \) x 6 = \( \frac{2 \times 6}{100} \) = \( \frac{12}{100} \) = 0.12 errors per hour

So, in an average hour, the machine will produce 6 - 0.12 = 5.88 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 5.88 = 105.8 error free parts were produced yesterday.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{6!}{5!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{6}{1} \)
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