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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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 = 0.09 x $600
i = $54

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 5 = \( \frac{6 \times 5}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour

So, in an average hour, the machine will produce 5 - 0.3 = 4.7 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 4.7 = 79.9 error free parts were produced yesterday.

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

\( \frac{1}{7} \) ÷ \( \frac{1}{9} \) = \( \frac{1}{7} \) x \( \frac{9}{1} \)

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

\( \frac{1}{7} \) x \( \frac{9}{1} \) = \( \frac{1 x 9}{7 x 1} \) = \( \frac{9}{7} \) = 1\(\frac{2}{7}\)

The greatest common factor (GCF) is the greatest factor that divides two integers.