https://file.aiquickdraw.com/mathbot/file/1728621804515uq2zifpc.jpg

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!

Solve the following arithmetic problems:
9. -3/2 - (-1/4) - (-1/4)
10. -4.1 - 5.5 - (-2.1)
11. -0.03 - (-2.8) - 11.97
12. -5/10 - 1/5 - (-1/2)

Learn how to solve arithmetic problems involving fractions, decimals, and negative numbers with step-by-step guidance. Problems include simplifying expressions like -3/2 - (-1/4) and -4.1 - 5.5 - (-2.1). Suitable for students in Grades 7-8.

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