Add the following rational numbers. 1 -12 and 2 -15

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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