Problem: Divide the sum of -16/35 and 14/15 by the quotient of -12/7 and -18.

Solution:
To solve this problem, we need to follow the order of operations, also known as PEMDAS (parentheses, exponents, multiplication, division, addition, and subtraction).

Step 1: Simplify the fractions

-16/35 and 14/15 are both proper fractions. To add or subtract fractions, we need a common denominator. The least common multiple of 35 and 15 is 105. Therefore, we need to convert both fractions to have a denominator of 105.

-16/35 = -48/105
14/15 = 98/105

Step 2: Find the sum of the fractions

To find the sum of -48/105 and 98/105, we simply add the numerators and keep the denominator the same:

-48/105 + 98/105 = 50/105

Step 3: Simplify the quotient

To simplify the quotient of -12/7 and -18, we divide the numerator by the denominator:

-12/7 ÷ -18 = 2/21

Step 4: Divide the sum by the quotient

To divide 50/105 by 2/21, we multiply the first fraction by the reciprocal of the second fraction:

50/105 ÷ 2/21 = 50/105 x 21/2 = 1050/210 = 5

Therefore, the final answer is 5.

Answer: The sum of -16/35 and 14/15 divided by the quotient of -12/7 and -18 is 5.