Question

 Add the following rational numbers:

(i) \(\frac{-5}{7}\, and\)\(\, \frac{3}{7}\)

(ii) \(\frac{-15}{4}\, and\, \frac{7}{4}\)

(iii) \(\frac{-8}{11}\, and\, \frac{-4}{11}\)

(iv) \(\frac{6}{13} \,and\, \frac{-9}{13}\)

Answer 1

(i) Clearly,

Denominators of the given numbers are positive

The L.C.M. of denominator 7 and 7 is 7

We have,

\(\frac{-5}{7}\, +\, \frac{3}{7}\)

\(=\, \frac{-5+3}{7}\)

\(=\, \frac{-2}{7}\)

(ii) Clearly,

Denominators of the given numbers are positive

The L.C.M. of denominators 4 and 4 is 4

We have,

\(\frac{-15}{4}\, +\, \frac{7}{4}\)

\(=\, \frac{-15+7}{4}\)

\(=\, \frac{-8}{4}\)

\(=\, -2\)

(iii) Clearly,

Denominators of the given numbers are positive

The L.C.M. of denominator 11 and 11 is 11

We have,

\(\frac{-8}{11}\, +\, \frac{-4}{11}\)

\(=\, \frac{-8-4}{11}\)

\(=\, \frac{-12}{11}\)

(iv) Clearly,

Denominators of the given numbers are positive

The L.C.M. of denominator 13 and 13 is 13

We have,

\(\frac{6}{13}\, +\, \frac{-9}{13}\)

\(=\, \frac{6-9}{13}\)

\(=\, \frac{-3}{13}\)