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A piece of wire \[\dfrac{7}{8}\] meter long broke into two pieces. One piece was \[\dfrac{1}{4}\] meter long. How long is the other piece?

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Last updated date: 19th Jul 2024
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Answer
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Hint: we have to determine the unknown value of the length of another piece, so just subtract the known value from the total length.
Given: total length of wire= 7/8 meter and length of one piece= 1/4 meter
To find: length of other piece=x

Complete step by step answer:
Step 1: we have total length of the wire equal to \[\dfrac{7}{8}\]meter
Now let us suppose that the unknown length of the wire be ‘x’, and the length of another piece of the wire is given as \[\dfrac{1}{4}\]meter long.
Therefore, the total length of the wire is equal to the sum of the length of the both broken pieces, that is
Total length of the wire = length of one piece of wire + length of other piece of wire
Step 2: substituting the values, we get
Total length of the wire = length of one piece of wire + length of other piece of wire
\[\dfrac{7}{8} = \dfrac{1}{4} + x\]
Rearranging the terms such that we get unknown value on one side of equality and other terms on other side of equality
\[x = \dfrac{7}{8} - \dfrac{1}{4}\]
Step 3: further simplifying, we get
\[x = \dfrac{7}{8} - \dfrac{1}{4}\]
\[x = \dfrac{{7 \times 4 - 1 \times 8}}{{8 \times 4}}\]
\[x = \dfrac{{28 - 8}}{{32}}\]
\[x = \dfrac{{20}}{{32}}\]
Reducing to its simplest form, we get
\[x = \dfrac{{20 \div 4}}{{32 \div 4}}\]
\[x = \dfrac{5}{8}\]
Hence, the value of unknown length of other piece is equal to \[\dfrac{5}{8}\]

Note: The total length of the wire is equal to the sum of the individual length of all its broken pieces and the unknown length of any broken piece can be obtained by subtracting all other known length of the pieces from the total length of the wire.