i) The denominators are 4 and 8 . The LCM of 4 and 8 is 8.
We rewrite the given fraction in order to get the same denominator
\(\frac{-3}{4}=\frac{(3\times2)}{(4\times2)}=\frac{6}{8}\) and \(=\frac{-5}{8}\)
\(\frac{-5}{8}=\frac{(-5\times1)}{(8\times1)} \)
Hence the denominators are same.Now,
\(\frac{6}{8}+\frac{-5}{8} \)
= \(\frac{6+(-5)}{8}=\frac{(6-5)}{8}\)
= \(\frac{1}{8} \)
ii) We convert the denominators in to positive numbers
\(\frac{5}{-9} =\frac{(5\times-1)}{(-9\times-1)}\)
= \(\frac{-5}{9}\)
The denominators are 9 and 3.The LCM for 9 and 3 is 9
We rewrite the given fraction in order to get the same denominator.
\(\frac{-5}{9}=\frac{(-5\times1)}{(9\times1)}\)
= \(\frac{-5}{9}\) and \(\frac{7}{3}\)
\(=\frac{(7\times3)}{(3\times3)}\)
= \(\frac{21}{9}\)
Since the denominators are same now we can add them directly.We get
\(\frac{-5}{9}\) + \(\frac{21}{9}=\frac{(-5+21)}{9}\)
= \(\frac{16}{9}\)
iii) The denominators are 1 and 5.The L.C.M of 1 and 5 is 5.
We rewrite the given fraction in order to get the same denominator.We get
\(\frac{-3}{1}=\frac{(3\times5)}{(1\times5)}\)
= \(\frac{-15}{5}\) and \(\frac{3}{5}\)
\(=\frac{(3\times1)}{(5\times1)}\)
= \(\frac{3}{5}\)
Since the denominators are same now we can add them directly.We get
\(\frac{-15}{5}+\frac{3}{5}=\frac{(-15+3)}{5}\)
= \(\frac{-12}{5}\)
iv) The denominators are 27 and 18. The L.C,M of 27 and 18 is 54.
We rewrite the given fraction in order to get the same denominator.We get
\(\frac{-7}{27}=\frac{(-7\times2)}{(27\times2)}\)
= \(\frac{-14}{54}\) and \(\frac{11}{18}\)
\(=\frac{(11\times3)}{(18\times3)}\)
= \(\frac{33}{54}\)
Since, the denominators are same we can add them directly
\(\frac{-14}{54} + \frac{33}{54}=\frac{(-14+33)}{54}\)
= \(\frac{19}{54}\)
v) Firstly we convert the denominators to positive numbers.
\(\frac{31}{-4}=\frac{(31\times-1)}{(-4\times-1)}\)
= \(\frac{-31}{4}\)
The denominators are 4 and 8. The L.C.M of 4 and 8 is 8
We rewrite the given fraction in order to get the same denominator. We get
\(\frac{-31}{4}=\frac{(-31\times2)}{(4\times2)}\\=\frac{-62}{8}\)
\(\frac{5}{8}=\frac{(-5\times1)}{(8\times1)}\\=\frac{-5}{8}\)
Since the denominators are same we can add them directly as
\(\frac{-62}{8}+\frac{(-5)}{8}=\frac{(-62+(-5))}{8}\\\frac{(-62-5)}{8}=\frac{-67}{8}\)
vi) : The denominators are 36 and 12. The L.C.M of 36 and 12 is 36.
We rewrite the given fraction in order to get the same denominator.We get
\(\frac{-5}{36}=\frac{(5\times1)}{(36\times1)}\\=\frac{5}{36}\)
\(\frac{-7}{12}=\frac{(-7\times3)}{(12\times3)}\\\frac{-21}{36}\)
Now, the denominators are same we can add them directly.We get
\(\frac{5}{36} + \frac{-21}{36}=\frac{(5+(-21))}{36}\\\frac{5-21}{36}=\frac{16}{36}\\\frac{-4}{9}\)
