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It is written in the question that the total length of the piece of wire is $\dfrac{7}{8}\,m$

Further it is broken into two pieces. The length of one piece is given as $\dfrac{1}{4}\,m$

Now we know that the sum of two pieces is equal to the total length of the actual wire.

$\dfrac{1}{4}\,m$$ + $Length of second piece$ = $$\dfrac{7}{8}\,m$

Length of second piece$ = \dfrac{7}{8} - \dfrac{1}{4} = \dfrac{{7 - 2}}{8} = \dfrac{5}{8}$

So Length of second piece is $\dfrac{5}{8}$ meters

Suppose the length of wire was $ = $$\dfrac{7}{8}\,m$ and it got broken into two equal pieces. So now the length of one of both the pieces can be obtained by dividing original length by $2$

So the length of each piece $ = \dfrac{7}{{8 \times 2}} = \dfrac{7}{{16}}$ meters.