A piece of wire `7/(8)` metre long broke into 2 pieces. One piece was `1/(4)` metre long. Find the length of the other piece.

Answer

To find the length of the other piece of wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total length of the wire and the length of the first piece.**
- The total length of the wire is \( \frac{7}{8} \) metre.
- The length of the first piece is \( \frac{1}{4} \) metre.

2. **Set up the equation to find the length of the second piece.**
- Let the length of the second piece be \( x \).
- According to the problem, the total length of the wire can be expressed as:
\[ \text{Length of first piece} + \text{Length of second piece} = \text{Total length of wire} \]
- This translates to:
\[ \frac{1}{4} + x = \frac{7}{8} \]

3. **Rearrange the equation to isolate \( x \).**
- To find \( x \), we can rearrange the equation:
\[ x = \frac{7}{8} - \frac{1}{4} \]

4. **Find a common denominator to perform the subtraction.**
- The denominators are 8 and 4. The least common multiple (LCM) of 8 and 4 is 8.
- Rewrite \( \frac{1}{4} \) with a denominator of 8:
\[ \frac{1}{4} = \frac{2}{8} \]

5. **Subtract the fractions.**
- Now substitute back into the equation:
\[ x = \frac{7}{8} - \frac{2}{8} \]
- Perform the subtraction:
\[ x = \frac{7 - 2}{8} = \frac{5}{8} \]

6. **Conclusion.**
- The length of the other piece of wire is \( \frac{5}{8} \) metre.

### Final Answer:
The length of the other piece of wire is \( \frac{5}{8} \) metre.

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