The product of two decimals is 261.36. If one of them is 17.6, find the other.

Answer

To find the other decimal when the product of two decimals is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the product of two decimals is 261.36, and one of the decimals is 17.6. We need to find the other decimal, which we will call \( x \).

2. **Set Up the Equation**: We can express the relationship as:
\[ 17.6 \times x = 261.36 \]

3. **Isolate \( x \)**: To find \( x \), we need to divide both sides of the equation by 17.6:
\[ x = \frac{261.36}{17.6} \]

4. **Perform the Division**: Now we will calculate \( \frac{261.36}{17.6} \). To make the division easier, we can eliminate the decimals by multiplying both the numerator and the denominator by 10:
\[ x = \frac{2613.6}{176} \]

5. **Calculate the Division**: Now, we perform the division:
- 176 goes into 2613.6.
- 176 goes into 2613 about 14 times (since \( 176 \times 14 = 2464 \)).
- Subtract \( 2464 \) from \( 2613 \) to get \( 149 \).
- Bring down the 6 to make it \( 1496 \).
- 176 goes into 1496 about 8 times (since \( 176 \times 8 = 1408 \)).
- Subtract \( 1408 \) from \( 1496 \) to get \( 88 \).
- Bring down the next digit (0) to make it \( 880 \).
- 176 goes into 880 about 5 times (since \( 176 \times 5 = 880 \)).
- Subtract \( 880 \) from \( 880 \) to get \( 0 \).

Thus, we find:
\[ x = 14.85 \]

6. **Conclusion**: The other decimal is \( 14.85 \).

### Final Answer:
The other decimal is **14.85**.