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

\( \frac{2}{100} \) x 5 = \( \frac{2 \times 5}{100} \) = \( \frac{10}{100} \) = 0.1 errors per hour

So, in an average hour, the machine will produce 5 - 0.1 = 4.9 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 4.9 = 83.3 error free parts were produced yesterday.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

If 79% of the town's 26,000 voters cast ballots the number of votes cast is:

(\( \frac{79}{100} \)) x 26,000 = \( \frac{2,054,000}{100} \) = 20,540

The mayor got 69% of the votes cast which is:

(\( \frac{69}{100} \)) x 20,540 = \( \frac{1,417,260}{100} \) = 14,173 votes.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

8y⁶ + 9y⁶
(8 + 9)y⁶
17y⁶