Find the A.M. between:
(i) 3.7 and 5.5 (ii) 6 and -8

Answer

To find the arithmetic mean (A.M.) between two numbers, we use the formula:

\[ \text{A.M.} = \frac{a + b}{2} \]

where \(a\) and \(b\) are the two numbers.

### Solution Steps:

**(i) Finding A.M. between 3.7 and 5.5:**

1. **Identify the numbers:**
- Let \(a = 3.7\) and \(b = 5.5\).

2. **Add the numbers:**
\[ a + b = 3.7 + 5.5 \]

3. **Calculate the sum:**
- Adding the whole numbers: \(3 + 5 = 8\)
- Adding the decimal parts: \(0.7 + 0.5 = 1.2\)
- Therefore, \(3.7 + 5.5 = 8 + 1.2 = 9.2\).

4. **Divide the sum by 2:**
\[ \text{A.M.} = \frac{9.2}{2} \]

5. **Calculate the final result:**
- Performing the division: \(9.2 \div 2 = 4.6\).

Thus, the arithmetic mean between 3.7 and 5.5 is **4.6**.

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**(ii) Finding A.M. between 6 and -8:**

1. **Identify the numbers:**
- Let \(a = 6\) and \(b = -8\).

2. **Add the numbers:**
\[ a + b = 6 + (-8) \]

3. **Calculate the sum:**
- \(6 - 8 = -2\).

4. **Divide the sum by 2:**
\[ \text{A.M.} = \frac{-2}{2} \]

5. **Calculate the final result:**
- Performing the division: \(-2 \div 2 = -1\).

Thus, the arithmetic mean between 6 and -8 is **-1**.

### Final Answers:
- (i) A.M. between 3.7 and 5.5 is **4.6**.
- (ii) A.M. between 6 and -8 is **-1**.

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