Gujarat BoardEnglish MediumSTD 8MATHSRational Numbers1 Mark
Question
Add the following rational numbers. $\frac{1}{-12}\ \text{and}\ \frac{2}{-15}$
✓
Answer
We will first write each of the given numbers with positive denominators.
$\frac{1}{-12}=\frac{1\times(-1)}{-12\times(-1)}$
$=\frac{-1}{12}$
and $\frac{2}{-15}=\frac{2\times(-1)}{-15\times(-1)}$
$=\frac{-2}{15}$
The denominators of the given rational number are $12$ and $15.$
$LCM$ of $12, 15$ is $60$
Now,
$\frac{-1}{12}=\frac{-1\times5}{12\times5}$
$=\frac{-5}{60}$
and $\frac{-2}{15}=\frac{2\times4}{15\times4}$
$=\frac{-8}{60}$
$\therefore\frac{1}{-12}+\frac{2}{-15}$
$=\frac{-5}{60}+\frac{-8}{60}$
$=\frac{-5+(-8)}{60}$
$=\frac{-5-8}{60}$
$=\frac{-13}{60}$
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