The fourth proportional of 9, 8, and 18 is____.

Options

A. 16
B. 9
C. 72
D. None of these

Explanation

To find the fourth proportional of the numbers 9, 8, and 18, we can use the concept of ratios. The fourth proportional \( d \) can be found using the formula:

\[ \frac{a}{b} = \frac{c}{d} \]

Where:
- \( a = 9 \)
- \( b = 8 \)
- \( c = 18 \)
- \( d \) is what we need to find.

### Step 1: Set up the ratio
We start by setting up the equation based on the given values:

\[ \frac{9}{8} = \frac{18}{d} \]

### Step 2: Cross-multiply
Next, we cross-multiply to eliminate the fractions:

\[ 9 \cdot d = 18 \cdot 8 \]

### Step 3: Calculate the right side
Now, we calculate the right side of the equation:

\[ 18 \cdot 8 = 144 \]

So, we have:

\[ 9d = 144 \]

### Step 4: Solve for \( d \)
To find \( d \), we divide both sides of the equation by 9:

\[ d = \frac{144}{9} \]

### Step 5: Simplify the fraction
Now, we simplify \( \frac{144}{9} \):

\[ d = 16 \]

### Conclusion
Thus, the fourth proportional of 9, 8, and 18 is:

\[ \boxed{16} \]

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