Solve a:(-b):c: Evaluating Sequential Division with Given Values

Let's start with the first option.

Insert the given values into the expression:

$3:(-(-9)):2=$

First, solve what's inside of the parentheses, maintaining the appropriate sign given that a minus multiplied by a minus equals a plus:

$3:9:2=$

Solve the exercise from left to right.

Write the division as a simple fraction:

$\frac{3}{9}:2=$

Break down 9 into a multiplication problem:

$\frac{3}{3\times3}:2=$

Reduce the 3 in both the numerator and the denominator:

$\frac{1}{3}:2=$

Convert the division to a multiplication, remembering to switch between the numerator and denominator accordingly:

$\frac{1}{3}:\frac{2}{1}=\frac{1}{3}\times\frac{1}{2}=\frac{1}{3\times2}=\frac{1}{6}$

Let's continue with the second option.

Substitute the given values into the expression:

$-4:(-16):3=$

Solve the exercise from left to right, writing the division as a simple fraction:

$\frac{-4}{-16}:3=$

Note that we are dividing two negative numbers, hence the result must be a positive number:

$\frac{4}{16}:3=$

Break down 16 into a multiplication problem:

$\frac{4}{4\times4}:3=$

Let's reduce the 4 in both the numerator and denominator and we obtain the following:

$\frac{1}{4}:3=$

Convert the division to a multiplication, remembering to switch between the numerator and denominator:

$\frac{1}{4}:3=\frac{1}{4}:\frac{3}{1}=\frac{1}{4}\times\frac{1}{3}=\frac{1}{4\times3}=\frac{1}{12}$

Therefore, the final answer is:

$1=\frac{1}{6},2=\frac{1}{12}$