1. **State the problem:** A wire of length $\frac{7}{8}$ meter broke into two pieces. One piece is $\frac{1}{4}$ meter long. We need to find the length of the other piece. 2. **Formula used:** The total length of the wire equals the sum of the lengths of the two pieces. $$\text{Total length} = \text{Piece 1} + \text{Piece 2}$$ 3. **Apply the formula:** Let the length of the other piece be $x$. Then, $$\frac{7}{8} = \frac{1}{4} + x$$ 4. **Solve for $x$:** Subtract $\frac{1}{4}$ from both sides: $$x = \frac{7}{8} - \frac{1}{4}$$ 5. **Find common denominator:** The denominators are 8 and 4. Convert $\frac{1}{4}$ to eighths: $$\frac{1}{4} = \frac{2}{8}$$ 6. **Subtract:** $$x = \frac{7}{8} - \frac{2}{8} = \frac{5}{8}$$ 7. **Answer:** The other piece is $\frac{5}{8}$ meter long.