Let's solve the problems from the image:

Problem 9:

$-\frac{3}{2} - \left( -\frac{1}{4} \right) - \left( -\frac{1}{4} \right)$ First, simplify the parentheses: $-\frac{3}{2} - \left( -\frac{1}{4} \right) = -\frac{3}{2} + \frac{1}{4}$ Since you're adding fractions, find a common denominator. The least common denominator (LCD) between 2 and 4 is 4. Rewrite $-\frac{3}{2}$ as $-\frac{6}{4}$: $-\frac{6}{4} + \frac{1}{4} + \frac{1}{4} = -\frac{6}{4} + \frac{2}{4} = -\frac{4}{4} = -1$

Problem 10:

$-4.1 - 5.5 - (-2.1)$ First, simplify the subtraction of a negative: $-4.1 - 5.5 + 2.1$ Now perform the arithmetic step by step: $-4.1 - 5.5 = -9.6$ $-9.6 + 2.1 = -7.5$

Problem 11:

$-0.03 - (-2.8) - 11.97$ First, simplify the subtraction of a negative: $-0.03 + 2.8 - 11.97$ Now perform the arithmetic: $-0.03 + 2.8 = 2.77$ $2.77 - 11.97 = -9.2$

Problem 12:

$-\frac{5}{10} - \frac{1}{5} - \left( -\frac{1}{2} \right)$ First, simplify the fractions: $-\frac{5}{10} = -\frac{1}{2}$ Now, simplify the parentheses: $-\frac{1}{2} - \frac{1}{5} + \frac{1}{2}$ Combine like terms: $-\frac{1}{2}$ and $+\frac{1}{2}$ cancel out, so you're left with: $-\frac{1}{5}$

Do you want any details or explanations for these steps?

Here are five follow-up questions to consider:

1. How do you add or subtract fractions with different denominators?
2. Why do two negative signs turn into a positive when subtracted?
3. How can you quickly simplify fractions in problems like #12?
4. What is the significance of common denominators in fraction problems?
5. How does arithmetic with decimals differ from fractions in multi-step problems?

Tip: Always look for opportunities to simplify expressions early, like combining terms or reducing fractions. This can make the rest of the problem easier!