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 add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 3}{8 x 3} \) + \( \frac{5 x 2}{12 x 2} \)

\( \frac{24}{24} \) + \( \frac{10}{24} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{24 + 10}{24} \) = \( \frac{34}{24} \) = 1\(\frac{5}{12}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{10\sqrt{36}}{5\sqrt{9}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{36}{9}} \)
2 \( \sqrt{4} \)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{11 + 5 + 10 + 6}{4} \) = \( \frac{32}{4} \) = 8

The factors of 16 are [1, 2, 4, 8, 16] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 60 have in common.