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Let's solve each of the problems step by step:

### 2. \(- 2 \dfrac{1}{2} + 0.83\)
1. Convert the mixed fraction \(- 2 \dfrac{1}{2}\) into an improper fraction:
   \[
   - 2 \dfrac{1}{2} = -\left(\frac{5}{2}\right)
   \]
2. Express the decimal \(0.83\) as a fraction. It is approximately:
   \[
   0.83 \approx \frac{83}{100}
   \]
3. Find the least common denominator (LCD) for \(\frac{5}{2}\) and \(\frac{83}{100}\). The LCD is 100.
   \[
   -\frac{5}{2} = -\frac{250}{100}
   \]
4. Now add the two fractions:
   \[
   -\frac{250}{100} + \frac{83}{100} = \frac{-250 + 83}{100} = \frac{-167}{100} = -1.67
   \]
   
   Final answer: \(-1.67\).

---

### 3. \(- 3 \dfrac{1}{3} + (- 4.6)\)
1. Convert \(- 3 \dfrac{1}{3}\) to an improper fraction:
   \[
   - 3 \dfrac{1}{3} = -\left(\frac{10}{3}\right)
   \]
2. Express \(-4.6\) as a fraction:
   \[
   - 4.6 = -\frac{46}{10}
   \]
3. Simplify \(-\frac{46}{10}\) by dividing both numerator and denominator by 2:
   \[
   -\frac{46}{10} = -\frac{23}{5}
   \]
4. Find the LCD for \(\frac{10}{3}\) and \(\frac{23}{5}\). The LCD is 15.
   \[
   -\frac{10}{3} = -\frac{50}{15}, \quad -\frac{23}{5} = -\frac{69}{15}
   \]
5. Add the two fractions:
   \[
   -\frac{50}{15} + -\frac{69}{15} = -\frac{119}{15}
   \]
6. Simplify the improper fraction:
   \[
   -\frac{119}{15} = -7.93\overline{3}
   \]
   
   Final answer: approximately \(-7.93\overline{3}\).

---

### 5. \(- 4.82 - \frac{2}{5}\)
1. Convert \(- 4.82\) to a fraction:
   \[
   - 4.82 = -\frac{482}{100}
   \]
2. Simplify the fraction by dividing by 2:
   \[
   -\frac{482}{100} = -\frac{241}{50}
   \]
3. Convert \(\frac{2}{5}\) so that it has the same denominator as \(\frac{241}{50}\):
   \[
   \frac{2}{5} = \frac{20}{50}
   \]
4. Subtract the two fractions:
   \[
   -\frac{241}{50} - \frac{20}{50} = -\frac{261}{50}
   \]
5. Simplify the improper fraction:
   \[
   -\frac{261}{50} = -5.22
   \]
   
   Final answer: \(-5.22\).

---

### 6. \(9.23 - (- 2 \dfrac{1}{4})\)
1. Convert \(2 \dfrac{1}{4}\) to an improper fraction:
   \[
   2 \dfrac{1}{4} = \frac{9}{4}
   \]
2. Express \(- 9.23\) as a fraction:
   \[
   - 9.23 = -\frac{923}{100}
   \]
3. The negative sign outside the parentheses makes the second term positive:
   \[
   9.23 - (- 2 \dfrac{1}{4}) = 9.23 + 2 \dfrac{1}{4}
   \]
4. Add the two values:
   \[
   9.23 + 2.25 = 11.48
   \]
   
   Final answer: \(11.48\).

---

Let me know if you'd like further details, clarifications, or solutions for any other problems.

### 5 Related Questions:
1. How do you convert mixed numbers to improper fractions?
2. What is the process to find the least common denominator (LCD)?
3. How can fractions be simplified after addition or subtraction?
4. What are the steps to convert decimals into fractions?
5. Why do we need to find a common denominator before adding or subtracting fractions?

### Tip:
Always simplify fractions to their lowest terms after performing arithmetic operations for more accurate and clear results.

Add & Subtract Rational Numbers Practice: Solve problems such as -2 1/2 + 0.83, -3 1/3 + (-4.6), -4.82 - 2/5, and 9.23 - (-2 1/4).

Practice adding and subtracting rational numbers with problems involving mixed numbers, improper fractions, and decimals. Examples include -2 1/2 + 0.83 and 9.23 - (-2 1/4), covering essential math concepts for Grades 6-8.

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