An electrician had $ 5 \frac{4}{7} \mathrm{~cm} $ of wire with him. He used $ 2 \frac{2}{5} \mathrm{~cm} $ of wire to complete a particular job. How much wire is remaining with him after completing the job?
Given:
An electrician had \( 5 \frac{4}{7} \mathrm{~cm} \) of wire with him. He used \( 2 \frac{2}{5} \mathrm{~cm} \) of wire to complete a particular job.
To do:
We have to find the length of the wire remaining with him after completing the job.
Solution:
Total length of the wire with the electrician $=5\frac{4}{7}\ cm$
$=\frac{5\times7+4}{7}\ cm$
$=\frac{35+4}{7}\ cm$
$=\frac{39}{7}\ cm$
Length of the wire used for the job $=2\frac{2}{5}\ cm$
$=\frac{2\times5+2}{5}\ cm$
$=\frac{10+2}{5}\ cm$
$=\frac{12}{5}\ cm$
Length of the wire remaining with him after completing the job $=$ Total length of the wire with the electrician $-$ Length of the wire used for the job
$=\frac{39}{7}-\frac{12}{5}$
$=\frac{39\times5-12\times7}{35}$
$=\frac{195-84}{35}$
$=\frac{111}{35}\ cm$
$=3\frac{6}{35}\ cm$.
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