Find the fourth proportional to :
15, 6, 7

Answer

To find the fourth proportional to the numbers 15, 6, and 7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the concept of fourth proportional**: The fourth proportional to three numbers \( a, b, c \) is a number \( d \) such that the ratio \( a:b = c:d \). In this case, we have \( a = 15 \), \( b = 6 \), and \( c = 7 \).

2. **Set up the proportion**: We can express the relationship as:
\[ \frac{15}{6} = \frac{7}{x} \]
where \( x \) is the fourth proportional we want to find.

3. **Cross-multiply**: To eliminate the fractions, we cross-multiply:
\[ 15 \cdot x = 6 \cdot 7 \]

4. **Calculate the right side**: Now, calculate \( 6 \cdot 7 \):
\[ 6 \cdot 7 = 42 \]
So, we have:
\[ 15x = 42 \]

5. **Solve for \( x \)**: To find \( x \), divide both sides by 15:
\[ x = \frac{42}{15} \]

6. **Simplify the fraction**: We can simplify \( \frac{42}{15} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
\[ x = \frac{42 \div 3}{15 \div 3} = \frac{14}{5} \]

7. **Convert to decimal**: Finally, convert \( \frac{14}{5} \) to a decimal:
\[ \frac{14}{5} = 2.8 \]

### Conclusion:
The fourth proportional to 15, 6, and 7 is \( x = 2.8 \).

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