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

\( \frac{3}{8} \) x \( \frac{2}{9} \) = \( \frac{3 x 2}{8 x 9} \) = \( \frac{6}{72} \) = \(\frac{1}{12}\)

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

9\( \sqrt{6} \) x 8\( \sqrt{6} \)
(9 x 8)\( \sqrt{6 \times 6} \)
72\( \sqrt{36} \)

Now we need to simplify the radical:

72\( \sqrt{36} \)
72\( \sqrt{6^2} \)
(72)(6)
432

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

\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.6 = 101.2 error free parts were produced yesterday.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.