(i) Since, the denominators of given rational numbers are negative therefore, we will make them positive.
\(\frac{7}{-18} = \frac{7\times-1}{-18\times-1} = \frac{-7}{18}\)
Now,
since, the denominators of given rational numbers are different therefore, we take their LCM.
LCM of 18 and 27 = 54
\(\frac{-7}{18} = \frac{-7\times3}{18\times3} = \frac{-21}{54}\)
And
\(\frac{8}{27} = \frac{8\times2}{27\times2} = \frac{16}{54}\)
Now,
\(\frac{-7}{18}+\frac{8}{27}\)
= \(\frac{-21}{54}+\frac{16}{54}\)
= \(\frac{-21+16}{54}\)
= \(\frac{-5}{54}\)
(ii) Since, the denominators of given rational numbers are negative therefore, we will make them positive.
\(\frac{1}{-12} = \frac{1\times-1}{-12\times-1} = \frac{-1}{12}\)
And,
\(\frac{2}{-15} = \frac{2\times-1}{-15\times-1} = \frac{-2}{15}\)
Now,
since, the denominators of given rational numbers are different therefore, we take their LCM. LCM of 12 and 15 = 60
\(\frac{-1}{12} = \frac{-1\times5}{12\times5} = \frac{-5}{60}\)
And
\(\frac{-2}{15} = \frac{-2\times4}{15\times4} = \frac{-8}{60}\)
Now,
\(\frac{-5}{60}+\frac{8}{60}\)
= \(\frac{-5+(8)}{60}\)
= \(\frac{-5-8}{60}\)
= \(\frac{-13}{60}\)
(iii) We can write \(-1\) as \(\frac{-1}{1}.\)
Now,
since, the denominators of given rational numbers are different therefore, we take their LCM.
LCM of 1 and 4 = 4
\(\frac{-1}{1} = \frac{-1\times4}{1\times4} = \frac{-4}{4}\)
And
\(\frac{3}{4} = \frac{3\times1}{4\times1} = \frac{3}{4}\)
Now,
\(-1+\frac{3}{4}\)
= \(\frac{-4+3}{4}\)
= \(\frac{-1}{4}\)
(iv) We can write 2 as \(\frac{2}{1.}\)
Now,
since, the denominators of given rational numbers are different therefore, we take their
LCM. LCM of 1 and 4 = 4
\(\frac{2}{1} = \frac{2\times4}{1\times4} = \frac{8}{4}\)
And
\(\frac{-5}{4} = \frac{-5\times1}{\times1} = \frac{-5}{4}\)
Now,
\(2+\frac{-5}{4}\)
= \(\frac{8+(-5)}{4}\)
= \(\frac{8-5}{4}\)
= \(\frac{3}{4}\)
(v) \(0+\frac{-2}{5}\)
On adding, any number to 0 we get the same number.
Therefore,
\(0+\frac{-2}{5}= \frac{-2}{5}\)
