To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{9 x 3}{3 x 3} \) - \( \frac{3 x 1}{9 x 1} \)

\( \frac{27}{9} \) - \( \frac{3}{9} \)

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

\( \frac{27 - 3}{9} \) = \( \frac{24}{9} \) = 2\(\frac{2}{3}\)

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

\( \frac{6}{100} \) x 6 = \( \frac{6 \times 6}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour

So, in an average hour, the machine will produce 6 - 0.36 = 5.64 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 5.64 = 90.2 error free parts were produced yesterday.

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 2) ÷ 5 x 5 - 5²
P: 4 + (5) ÷ 5 x 5 - 5²
E: 4 + 5 ÷ 5 x 5 - 25
MD: 4 + \( \frac{5}{5} \) x 5 - 25
MD: 4 + \( \frac{25}{5} \) - 25
AS: \( \frac{20}{5} \) + \( \frac{25}{5} \) - 25
AS: \( \frac{45}{5} \) - 25
AS: \( \frac{45 - 125}{5} \)
\( \frac{-80}{5} \)
-16

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{11 + 9 + 14 + 6}{4} \) = \( \frac{40}{4} \) = 10