Check whether the following numbers are in proportion or not :
`2, 2(1)/(2), 3, 3 (1)/(2)`

Answer

To determine whether the numbers \(2\), \(2\frac{1}{2}\), \(3\), and \(3\frac{1}{2}\) are in proportion, we will use the property that states: **the product of the extremes is equal to the product of the means**.

### Step-by-Step Solution:

1. **Identify the numbers**:
The given numbers are \(2\), \(2\frac{1}{2}\), \(3\), and \(3\frac{1}{2}\).

2. **Convert mixed numbers to improper fractions**:
- \(2\frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)
- \(3\frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}\)

So, the numbers can be rewritten as:
- \(2\), \(\frac{5}{2}\), \(3\), \(\frac{7}{2}\)

3. **Identify extremes and means**:
- **Extremes**: \(2\) and \(\frac{7}{2}\)
- **Means**: \(\frac{5}{2}\) and \(3\)

4. **Calculate the product of extremes**:
\[ \text{Product of extremes} = 2 \times \frac{7}{2} = \frac{14}{2} = 7 \]

5. **Calculate the product of means**:
\[ \text{Product of means} = \frac{5}{2} \times 3 = \frac{15}{2} \]

6. **Compare the products**:
- Product of extremes: \(7\)
- Product of means: \(\frac{15}{2} = 7.5\)

7. **Conclusion**:
Since \(7 \neq 7.5\), the product of the extremes is not equal to the product of the means. Therefore, the numbers \(2\), \(2\frac{1}{2}\), \(3\), and \(3\frac{1}{2}\) are **not in proportion**.