Add the following rational numbers: (i) 3/4 and -3/5 (ii) 5/8 and -7/12 (iii) -8/9 and 11/6 (iv) 7/-18 and 7/24

Question

Add the following rational numbers:

(i) \(\frac{3}{4}\) and \(\frac{-3}{5}\)

(ii) \(\frac{5}{8}\) and \(\frac{-7}{12}\)

(iii) \(\frac{-8}{9}\) and \(\frac{11}{6}\)

(iv) \(\frac{-5}{16}\) and \(\frac{7}{24}\)

Answer 1

(i) Since, 

the denominators of given rational numbers are different therefore, we take their LCM. LCM of 4 and 5 = 20

\(\frac{3}{4}\) = \(\frac{3\times5}{4\times5} = \frac{15}{20}\)

And

\(\frac{-3}{5}\) = \(\frac{-3\times4}{5\times4} = \frac{-12}{20}\)

Now,

= \(\frac{3}{4}+\frac{-3}{5}\)

= \(\frac{15}{20}+\frac{-12}{20}\)

= \(\frac{15+(-12)}{20}\)

= \(\frac{15-12}{20}\)

= \(\frac{3}{20}\)

(ii) Since, 

the denominators of given rational numbers are different therefore, we take their LCM. LCM of 8 and 12 = 24

 \(\frac{5}{8}\) = \(\frac{5\times3}{8\times3} = \frac{15}{24}\)

And

 \(\frac{-7}{12}\) = \(\frac{-7\times2}{12\times2} = \frac{-14}{24}\)

Now,

\(\frac{5}{8}+\frac{-7}{12}\)

= \(\frac{15}{24}+\frac{-14}{24}\)

= \(\frac{15+(-14)}{24}\)

= \(\frac{15-14}{24}\)

= \(\frac{1}{24}\)

(iii) Since, 

the denominators of given rational numbers are different therefore, we take their LCM. LCM of 9 and 6 = 18

 \(\frac{-8}{9}\) = \(\frac{-8\times2}{9\times2} = \frac{-16}{18}\)

And

\(\frac{11}{6}\) = \(\frac{11\times3}{6\times3} = \frac{33}{18}\)

Now,

\(\frac{-8}{9}+\frac{11}{6}\)

= \(\frac{-16}{18}+\frac{33}{18}\)

= \(\frac{-16+33}{18}\)

= \(\frac{17}{18}\)

(iv) Since, 

the denominators of given rational numbers are different therefore, we take their LCM. LCM of 16 and 24 = 48

 \(\frac{-5}{16}\) = \(\frac{-5\times3}{16\times3} = \frac{-15}{48}\)

And
\(\frac{7}{24}\) = \(\frac{7\times2}{24\times2} = \frac{14}{48}\)

Now,

\(\frac{-5}{16}+\frac{7}{24}\)

= \(\frac{-15}{48}+\frac{14}{48}\)

= \(\frac{-15+14}{48}\)

= \(\frac{-1}{48}\)