S.chand publication New Learning Composite mathematics solution of class 7 Chapter 3 Rational numbers Exercise 3C

 Exercise 3C

Question 1

(a) $\frac{1}{5}+\frac{2}{-5}$

Sol :

$=\frac{1}{5}+\frac{-2}{5}$

$=\frac{1-2}{5}=-\frac{1}{5}$

(b) $1\frac{3}{8}+3\frac{7}{8}$

Sol :

$=\frac{11}{8}+\frac{31}{8}$

$=\frac{11+31}{8}=\frac{42}{8}$

$=5\frac{1}{4}$

(c) $\frac{-1}{4}+\frac{3}{-4}$

Sol :

$=\frac{-1}{4}+\frac{-3}{4}$

$=\frac{-1-3}{4}=\frac{-4}{4}$

=-1

(d) $\frac{-1}{10}+\left(\frac{-7}{10}\right)$

Sol :

$=\frac{-1-7}{10}=\frac{-3}{10}$

$=-\frac{4}{5}$

(e) $1\frac{3}{4}+\left(-1\frac{1}{4}\right)$

Sol :

$=\frac{7}{4}-\frac{5}{4}=\frac{7-5}{4}$

$=\frac{2}{4}=\frac{1}{2}$

(f) $1\frac{7}{12}+\frac{11}{-12}$

Sol :

$=\frac{19}{12}+\frac{-11}{12}=\frac{19-11}{12}$

$=\frac{8}{12}=\frac{2}{3}$

(g) $\frac{-4}{15}+\frac{-4}{15}$

Sol :

$=-\frac{4}{15}-\frac{4}{15}-\frac{4}{15}$

$=\frac{-4-4-4}{15}$

$=-\frac{4}{5}$

(h) $\frac{17}{-30}+\frac{7}{30}+1\frac{7}{30}$

Sol :

$=-\frac{17}{30}+\frac{7}{30}+\frac{37}{30}$

$=\frac{-17+7+37}{30}=\frac{27}{30}=\frac{9}{10}$

Question 2

Subtract

(a) -$\frac{5}{6}$ from $\frac{1}{6}$

Sol :

$=\frac{1}{6}-\left(-\frac{5}{6}\right)$

$=\frac{1}{6}+\frac{5}{6}$

$=\frac{5+1}{6}=\frac{6}{6}$

=1

(b) $\frac{7}{8}$ from $\frac{3}{-8}$

Sol :

$=\frac{-3}{8}-\frac{7}{8}$

$=\frac{-3-7}{8}$

$=\frac{-10}{8}=-1\frac{1}{4}$

(c) $-1\frac{3}{4}$ from $-2\frac{1}{4}$

Sol :

$=\frac{-9}{4}+\frac{7}{4}$

$=\frac{-9+7}{4}$

$=-\frac{2}{4}=-\frac{1}{2}$

(d) $-1\frac{3}{10}$ from $7\frac{1}{10}$

Sol :

$=\frac{-71}{10}+\frac{13}{10}$

$=\frac{-58}{10}=-5\frac{4}{5}$

Question 3

Simplify :

(a) $-\frac{15}{22}+\left(\frac{7}{-22}\right)$

Sol :

$=\frac{-15-7}{22}=\frac{-22}{22}$

=-1

(b) $-1\frac{4}{29}+2\frac{7}{29}+\frac{18}{-22}$

Sol :

$=-\frac{33}{29}+\frac{65}{29}-\frac{18}{29}$

$=\frac{-33+65-18}{29}$

$=\frac{14}{29}$

Question 4

$\frac{8}{17}-x$ for $x=\frac{5}{-17}$

Sol :

$=\frac{8}{17}-\frac{5}{-17}$

$=-\frac{8}{17}+\frac{5}{17}$

$=\frac{-8+5}{17}=\frac{-13}{17}$