​ Simplify: (i) 8/9 + -11/6 (ii) 3 + 5/-7 (iii) 1/-12 + 2/-15 (iv) -8/19 + -4/57 (v) 7/9 + 3/-4 (vi) 5/26 + 11/-39

Question

Simplify:

(i) \(\frac{8}{9} + \frac{-11}{6}\)

(ii) \(3 + \frac{5}{-7}\)

(iii) \(\frac{1}{-12} = \frac{2}{-15}\)

(iv) \(\frac{-8}{19} + \frac{-4}{57}\)

(v) \(\frac{7}{9} + \frac{3}{-4}\)

(vi) \(\frac{5}{26} + \frac{11}{-39}\)

(vii) \(\frac{-16}{9} + \frac{-5}{12}\)

(viii) \(\frac{-13}{8} + \frac{5}{36}\)

(ix) \(0 + \frac{-3}{5}\)

(x) \(1 + \frac{-4}{5}\)

Answer 1

(i) The L.C.M of 9 and 6 is 18

\(\frac{8}{9} = \frac{8\times 2}{9\times 2}\)

= \(\frac{16}{18}\)

And,

\(\frac{-11}{6} = \frac{-11\times 3}{6\times 3}\)

= \(\frac{-33}{18}\)

Therefore,

\(\frac{16}{18} - \frac{33}{18} = \frac{-17}{18}\)

(ii) \(\frac{3}{1}-\frac{5}{7}\)

\(\frac{7\times3-5}{7}\)

\(\frac{21-5}{7}\)

\(\frac{16}{7}\)

(iii) The L.C.M of -12 and -15 is 60

\(\frac{-1}{12}=\frac{-1\times 5}{12\times 5}\)

= \(\frac{-5}{60}\)

And,

\(\frac{2}{-15}=\frac{2\times 4}{-15\times 4}\)

= \(\frac{-8}{60}\)

Therefore,

\(\frac{-5}{60}-\frac{8}{60}=\frac{-13}{60}\)

(iv) The L.C.M of 19 and 57 is 57

\(\frac{-8}{19}=\frac{-8\times 3}{19\times 3}\)

= \(\frac{-24}{57}\)

And,

\(\frac{-4}{57}=\frac{-4\times 1}{57\times 1}\)

= \(\frac{-4}{57}\)

Therefore,

\(\frac{-24}{57}-\frac{4}{57}=\frac{-28}{57}\)

(v) The L.C.M of 9 and 4 is 36

\(\frac{7}{9}=\frac{7\times 4}{9\times 4}\)

= \(\frac{28}{36}\)

And,

\(\frac{3}{-4}=\frac{3\times 9}{-4\times 9}\)

= \(\frac{-27}{36}\)

Therefore,

\(\frac{28}{36}-\frac{27}{36}=\frac{-1}{36}\)

(vi) The L.C.M of 26 and -39 is 78

\(\frac{5}{26}=\frac{5\times 3}{26\times 3}\)

= \(\frac{15}{78}\)

And,

\(\frac{11}{-39}=\frac{11\times 2}{-39\times 2}\)

= \(\frac{-22}{78}\)

Therefore,

\(\frac{15}{78}-\frac{22}{78}=\frac{-7}{78}\)

(vii) The L.C.M of 9 and 12 is 108

\(\frac{-16}{9}=\frac{-16\times 12}{9\times 12}\)

= \(\frac{-192}{108}\)

And,

\(\frac{-5}{12}=\frac{-5\times 9}{12\times 9}\)

= \(\frac{-45}{108}\)

Therefore,

\(\frac{-192}{108}-\frac{45}{108}=\frac{-237}{108}\)

= \(\frac{-79}{36}\)

(viii) The L.C.M of 8 and 36 is 72

\(\frac{-13}{8}=\frac{-13\times 9}{8\times 9}\)

= \(\frac{-117}{72}\)

And,

\(\frac{5}{36}=\frac{5\times 2}{36\times 2}\)

= \(\frac{10}{72}\)

Therefore,

\(\frac{-117}{72}+\frac{10}{72}=\frac{-107}{72}\)

(ix) The L.C.M of 0 and 5 is 0

Therefore,

\(0-\frac{3}{5}=\frac{-3}{5}\)

(x) The L.C.M of 1 and 5 is 5

\(\frac{1}{1}=\frac{1\times 5}{1\times 5}\)

= \(\frac{5}{5}\)

And,

\(\frac{-4}{5}=\frac{-4\times 1}{5\times 1}\)

= \(\frac{-4}{5}\)

Therefore,

\(\frac{5}{5}-\frac{4}{5}=\frac{1}{5}\)