Question

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

Answer 1

Hint: In this problem, we need to subtract the length of the broken piece of rod from the original length of the rod to obtain the length of the other piece. While solving the two fractions, first take the LCM of the denominators and then further simplify it.

Complete step by step solution:
The original length of the rod is \[\dfrac{7}{8}\] meter.
Let the length of the other broken piece of the rod be x.
According to the question,
\[
  \,\,\,\,\,\,\,\dfrac{1}{4} + x = \dfrac{7}{8} \\
   \Rightarrow x = \dfrac{7}{8} - \dfrac{1}{4} \\
   \Rightarrow x = \dfrac{{7 - 2}}{8} \\
   \Rightarrow x = \dfrac{5}{8}meter \\
\]

Thus, the length of the other piece of the rod is \[\dfrac{5}{8}\] meter.

Note: To subtract the two fractions having the same denominator, just subtract the numerators of the fraction and put denominators as it is. When we need to subtract two fractions having different denominators, first make the denominators equal by multiplying some factors and then subtract the numerators.