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 - 7 = 17 hours yesterday so you would expect that 17 x 5.64 = 95.9 error free parts were produced yesterday.

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{5} \) ÷ \( \frac{2}{5} \) = \( \frac{1}{5} \) x \( \frac{5}{2} \)

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

\( \frac{1}{5} \) x \( \frac{5}{2} \) = \( \frac{1 x 5}{5 x 2} \) = \( \frac{5}{10} \) = \(\frac{1}{2}\)

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).

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.