Show that the numbers 25, 36, 5, 6 are not in proportion ?

Answer

To show that the numbers 25, 36, 5, and 6 are not in proportion, we will use the method of comparing the products of the extremes and the means.

### Step-by-Step Solution:

1. **Identify the Ratios**:
We need to compare the ratios \( \frac{25}{36} \) and \( \frac{5}{6} \).

2. **Identify the Extremes and Means**:
- The extremes are the first and last numbers in the ratios:
- Extremes: 25 and 6
- The means are the two middle numbers in the ratios:
- Means: 36 and 5

3. **Calculate the Product of the Extremes**:
- Multiply the extremes:
\[ \text{Product of extremes} = 25 \times 6 = 150 \]

4. **Calculate the Product of the Means**:
- Multiply the means:
\[ \text{Product of means} = 36 \times 5 = 180 \]

5. **Compare the Products**:
- Now we compare the two products:
\[ 150 \neq 180 \]

6. **Conclusion**:
Since the product of the extremes (150) is not equal to the product of the means (180), we conclude that the numbers 25, 36, 5, and 6 are not in proportion.