If `(3)/(2) = (18)/(12) =(24)/(16) =alpha` then find the value of `alpha`.

Answer

To find the value of \( \alpha \) given that \( \frac{3}{2} = \frac{18}{12} = \frac{24}{16} = \alpha \), we can calculate each ratio step by step.

### Step 1: Calculate \( \frac{3}{2} \)
The first ratio is straightforward:
\[ \alpha = \frac{3}{2} \]

### Step 2: Calculate \( \frac{18}{12} \)
Next, we simplify \( \frac{18}{12} \):
\[ \frac{18}{12} = \frac{18 \div 6}{12 \div 6} = \frac{3}{2} \]
So, \( \alpha = \frac{18}{12} = \frac{3}{2} \).

### Step 3: Calculate \( \frac{24}{16} \)
Now, we simplify \( \frac{24}{16} \):
\[ \frac{24}{16} = \frac{24 \div 8}{16 \div 8} = \frac{3}{2} \]
Thus, \( \alpha = \frac{24}{16} = \frac{3}{2} \).

### Conclusion
Since all three ratios simplify to \( \frac{3}{2} \), we conclude that:
\[ \alpha = \frac{3}{2} \]

### Final Answer
The value of \( \alpha \) is \( \frac{3}{2} \).

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