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

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

\( \frac{3}{6} \) ÷ \( \frac{1}{5} \) = \( \frac{3}{6} \) x \( \frac{5}{1} \)

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

\( \frac{3}{6} \) x \( \frac{5}{1} \) = \( \frac{3 x 5}{6 x 1} \) = \( \frac{15}{6} \) = 2\(\frac{1}{2}\)

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

\( \frac{9}{100} \) x 8 = \( \frac{9 \times 8}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour

So, in an average hour, the machine will produce 8 - 0.72 = 7.28 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 7.28 = 152.9 error free parts were produced yesterday.

The factors of 16 are [1, 2, 4, 8, 16] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 76 have in common.

If 65% of the town's 25,000 voters cast ballots the number of votes cast is:

(\( \frac{65}{100} \)) x 25,000 = \( \frac{1,625,000}{100} \) = 16,250

The mayor got 63% of the votes cast which is:

(\( \frac{63}{100} \)) x 16,250 = \( \frac{1,023,750}{100} \) = 10,238 votes.