Exercise 8.2 (Revised) - Chapter 9 - Rational Numbers - Ncert Solutions class 7 - Maths

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Chapter 8 - Rational Numbers | NCERT Solutions for Class 7 Maths

Ex 8.2 Question 1.

Find the sum:
(i) $\frac{5}{4}+\left(\frac{-11}{4}\right)$
(ii) $\frac{5}{3}+\frac{3}{5}$
(iii) $\frac{-9}{10}+\frac{22}{15}$
(iv) $\frac{-3}{-11}+\frac{5}{9}$
(v) $\frac{-8}{19}+\frac{(-2)}{57}$
(vi) $\frac{-2}{3}+0$
(vii) $-2 \frac{1}{3}+4 \frac{3}{5}$

Answer:

(i) $\frac{5}{4}+\left(\frac{-11}{4}\right)=\frac{5-11}{4}=\frac{-6}{4}=\frac{-3}{2}$
(ii) $\frac{5}{3}+\frac{3}{5}=\frac{5 \times 5}{3 \times 5}+\frac{3 \times 3}{5 \times 3}=\frac{25}{15}+\frac{9}{15}$
[L.C.M. of 3 and 5 is 15]
$
=\frac{25+9}{15}=\frac{34}{15}=2 \frac{4}{15}
$
(iii) $\frac{-9}{10}+\frac{22}{15}=\frac{-9 \times 3}{10 \times 3}+\frac{22 \times 2}{15 \times 2}=\frac{-27}{30}+\frac{44}{30}$

[L.C.M. of 10 and 15 is 30 ]
$
=\frac{-27+44}{30}=\frac{17}{30}
$
(iv) $\frac{-3}{-11}+\frac{5}{9}=\frac{-3 \times 9}{-11 \times 9}+\frac{5 \times 11}{9 \times 11}=\frac{27}{99}+\frac{55}{99}$ [L.C.M. of 11 and 9 is 99 ]
$
=\frac{27+55}{99}=\frac{82}{99}
$

(v) $\frac{-8}{19}+\frac{(-2)}{57}=\frac{-8 \times 3}{19 \times 3}+\frac{(-2) \times 1}{57 \times 1}=\frac{-24}{57}+\frac{(-2)}{57}$ [L.C.M. of 19 and 57 is 57]
$
=\frac{-24-2}{57}=\frac{-26}{57}
$
(vi) $\frac{-2}{3}+0=\frac{-2}{3}$
(vii) $-2 \frac{1}{3}+4 \frac{3}{5}=\frac{-7}{3}+\frac{23}{5}=\frac{-7 \times 5}{3 \times 5}+\frac{23 \times 3}{5 \times 3}=\frac{-35}{15}+\frac{69}{15}$ [L.C.M. of 3 and 5 is 15] $=\frac{-35+69}{15}=\frac{34}{15}=2 \frac{4}{15}$

Ex 8.2 Question 2.

Find:
(i) $\frac{7}{24}-\frac{17}{36}$
(ii) $\frac{5}{63}-\left(\frac{-6}{21}\right)$
(iii) $\frac{-6}{13}-\left(\frac{-7}{15}\right)$
(iv) $\frac{-3}{8}-\frac{7}{11}$
(v) $-2 \frac{1}{9}-6$

Answer:

(i) $\frac{7}{24}-\frac{17}{36}=\frac{7 \times 3}{24 \times 3}-\frac{17 \times 2}{36 \times 2}=\frac{21}{72}-\frac{34}{72}$
[L.C.M. of 24 and 36 is 72]
$
=\frac{21-34}{72}=\frac{-13}{72}
$

(ii) $\frac{5}{63}-\left(\frac{-6}{21}\right)=\frac{5 \times 1}{63 \times 1}-\left(\frac{-6 \times 3}{21 \times 3}\right)=\frac{5}{63}-\frac{-18}{63}$ [L.C.M. of 63 and 21 is 63]
$
=\frac{5-(-18)}{63}=\frac{5+18}{63}=\frac{23}{63}
$
(iii) $\frac{-6}{13}-\left(\frac{-7}{15}\right)=\frac{-6 \times 15}{13 \times 15}-\left(\frac{-7 \times 13}{15 \times 13}\right)=\frac{-90}{195}-\left(\frac{-91}{195}\right)$ [L.C.M. of 13 and 15 is 195]
$
=\frac{-90-(-91)}{195}=\frac{-90+91}{195}=\frac{1}{195}
$
(iv) $\frac{-3}{8}-\frac{7}{11}=\frac{-3 \times 11}{8 \times 11}-\frac{7 \times 8}{11 \times 8}=\frac{-33}{88}-\frac{56}{88}$
[L.C.M. of 8 and 11 is 88]

$
=\frac{-33-56}{88}=\frac{-89}{88}=-1 \frac{1}{88}
$
(v) $-2 \frac{1}{9}-6=\frac{-19}{9}-\frac{6}{1}=\frac{-19 \times 1}{9 \times 1}-\frac{6 \times 9}{1 \times 9}$ [L.C.M. of 9 and 1 is 9 ]
$
=\frac{-19}{9}-\frac{54}{9}=\frac{-19-54}{9}=\frac{-73}{9}=-8 \frac{1}{9}
$

Ex 8.2 Question 3.

Find the product:
(i) $\frac{9}{2} \times\left(\frac{-7}{4}\right)$
(ii) $\frac{3}{10} \times(-9)$
(iii) $\frac{-6}{5} \times \frac{9}{11}$
(iv) $\frac{3}{7} \times\left(\frac{-2}{5}\right)$
(v) $\frac{3}{11} \times \frac{2}{5}$
(vi) $\frac{3}{-5} \times \frac{5}{3}$

Answer:

(i) $\frac{9}{2} \times\left(\frac{-7}{4}\right)=\frac{9 \times(-7)}{2 \times 4}=\frac{-63}{8}=-7 \frac{7}{8}$
(ii) $\frac{3}{10} \times(-9)=\frac{3 \times(-9)}{10}=\frac{-27}{10}=-2 \frac{7}{10}$
(iii) $\frac{-6}{5} \times \frac{9}{11}=\frac{(-6) \times 9}{5 \times 11}=\frac{-54}{55}$
(iv) $\frac{3}{7} \times\left(\frac{-2}{5}\right)=\frac{3 \times(-2)}{7 \times 5}=\frac{-6}{35}$

(v) $\frac{3}{11} \times \frac{2}{5}=\frac{3 \times 2}{11 \times 5}=\frac{6}{55}$
(vi) $\frac{3}{-5} \times\left(\frac{-5}{3}\right)=\frac{3 \times(-5)}{-5 \times 3}=1$

Ex 8.2 Question 4.

Find the value of:
(i) $(-4) \div \frac{2}{3}$
(ii) $\frac{-3}{5} \div 2$
(iii) $\frac{-4}{5} \div(-3)$

(iv) $\frac{-1}{8} \div \frac{3}{4}$
(v) $\frac{-2}{13} \div \frac{1}{7}$
(vi) $\frac{-7}{12} \div\left(\frac{2}{13}\right)$
(vii) $\frac{3}{13} \div\left(\frac{-4}{65}\right)$

Answer:

(i) $(-4) \div \frac{2}{3}=(-4) \times \frac{3}{2}=(-2) \times 3=-6$
(ii) $\frac{-3}{5} \div 2=\frac{-3}{5} \times \frac{1}{2}=\frac{(-3) \times 1}{5 \times 2}=\frac{-3}{10}$
(iii) $\frac{-4}{5} \div(-3)=\frac{(-4)}{5} \times \frac{1}{(-3)}=\frac{(-4) \times 1}{5 \times(-3)}=\frac{4}{15}$
(iv) $\frac{-1}{8} \div \frac{3}{4}=\frac{-1}{8} \times \frac{4}{3}=\frac{(-1) \times 1}{2 \times 3}=\frac{-1}{6}$
(v) $\frac{-2}{13} \div \frac{1}{7}=\frac{-2}{13} \times \frac{7}{1}=\frac{(-2) \times 7}{13 \times 1}=\frac{-14}{13}=-1 \frac{1}{13}$
(vi) $\frac{-7}{12} \div\left(\frac{-2}{13}\right)=\frac{-7}{12} \times \frac{13}{(-2)}=\frac{(-7) \times 13}{12 \times(-2)}=\frac{-91}{24}=3 \frac{19}{24}$
(vii) $\frac{3}{13} \div\left(\frac{-4}{65}\right)=\frac{3}{13} \times \frac{65}{(-4)}=\frac{3 \times(-5)}{1 \times 4}=\frac{-15}{4}=-3 \frac{3}{4}$