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

\( \frac{5}{100} \) x 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour

So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 4.75 = 71.3 error free parts were produced yesterday.

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

\( \frac{2}{5} \) ÷ \( \frac{4}{9} \) = \( \frac{2}{5} \) x \( \frac{9}{4} \)

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

\( \frac{2}{5} \) x \( \frac{9}{4} \) = \( \frac{2 x 9}{5 x 4} \) = \( \frac{18}{20} \) = \(\frac{9}{10}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

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.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).