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Question
Add the following rational numbers:
\[\frac{3}{4} and \frac{- 5}{8}\]
Solution
\[\text{Clearly, denominators of the given numbers are positive}.\]
\[\text{The L.C.M. of denominators}\ 4\ \text{and}\ 8\ \text{is}\ 8.\]
\[\text{Now, we will express} \frac{3}{4}\text{in the form in which it takes the denominator is} 8 . \]
\[\frac{3 \times 2}{4 \times 2} = \frac{6}{8}\]
\[\frac{3}{4} + \frac{- 5}{8}=\frac{6}{8}+\frac{- 5}{8}\]
\[ = \frac{6 + ( - 5)}{8}\]
\[ = \frac{6 - 5}{8}\]
\[ = \frac{1}{8}\]
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