Class 7 Rational Numbers Exercise 8.2

1. Find the sum

(i)\(\dfrac{5}{4}+ \left(-\dfrac{11}{4}\right)\)

\(=\dfrac{5-11}{4}=\dfrac{-6}{4}=-\dfrac{3}{2}\)

✅ Answer: \(-\dfrac{3}{2}\)

(ii)\(\dfrac{5}{3}+\dfrac{3}{5}\)

LCM = 15

\(=\dfrac{25}{15}+\dfrac{9}{15}=\dfrac{34}{15}\)

✅ Answer: \(\dfrac{34}{15}\)

(iii)\(-\dfrac{9}{10}+\dfrac{22}{15}\)

LCM = 30

\(-\dfrac{27}{30}+\dfrac{44}{30}=\dfrac{17}{30}\)

✅ Answer: \(\dfrac{17}{30}\)

(iv)\(\dfrac{-3}{-11}+\dfrac{5}{9}\)

\(=\dfrac{3}{11}+\dfrac{5}{9}\)

LCM = 99

\(=\dfrac{27}{99}+\dfrac{55}{99}=\dfrac{82}{99}\)

✅ Answer: \(\dfrac{82}{99}\)

(v)\(-\dfrac{8}{19}+ \left(-\dfrac{2}{57}\right)\)

LCM = 57

\(-\dfrac{24}{57}-\dfrac{2}{57}=-\dfrac{26}{57}\)

✅ Answer: \(-\dfrac{26}{57}\)

(vi)\(-\dfrac{2}{3}+0=-\dfrac{2}{3}\)

✅ Answer: \(-\dfrac{2}{3}\)

(vii)\(-2\dfrac{1}{3}+4\dfrac{3}{5}\)

=\(\dfrac{-7}{3}+4\dfrac{23}{5}

=-\dfrac{34}{15}\)

✅ Answer: \(-\dfrac{2}{3}\)

2. Find 

(i) \(\dfrac{7}{24}-\dfrac{17}{36}\)

LCM = 72

\(=\dfrac{21}{72}-\dfrac{34}{72}=-\dfrac{13}{72}\)

✅ Answer: \(-\dfrac{13}{72}\)

(ii)\(\dfrac{5}{63}-\left(-\dfrac{6}{21}\right)\)

\(=\dfrac{5}{63}+\dfrac{18}{63}=\dfrac{23}{63}\)

✅ Answer: \(\dfrac{23}{63}\)

(iii)\(-\dfrac{6}{13}-\left(-\dfrac{7}{15}\right)\)

\(=-\dfrac{6}{13}+\dfrac{7}{15}\)

LCM = 195

\(=-\dfrac{90}{195}+\dfrac{91}{195}=\dfrac{1}{195}\)

✅ Answer: \(\dfrac{1}{195}\)

(iv)\(-\dfrac{3}{8}-\dfrac{7}{11}\)

LCM = 88

\(=-\dfrac{33}{88}-\dfrac{56}{88}=-\dfrac{89}{88}\)

✅ Answer: \(-\dfrac{89}{88}\)

(v)\(-2\dfrac{1}{9}-6\)

\(=-\dfrac{19}{9}-\dfrac{54}{9}

=-\dfrac{73}{9}\)

✅ Answer: \(-\dfrac{73}{9}\)

3. Find the product

(i)\(\dfrac{9}{2}\times\left(-\dfrac{7}{4}\right)=-\dfrac{63}{8}\)

(ii)\(\dfrac{3}{10}\times(-9)=-\dfrac{27}{10}\)

(iii)\(-\dfrac{6}{5}\times\dfrac{9}{11}=-\dfrac{54}{55}\)

(iv)\(\dfrac{3}{7}\times\left(-\dfrac{2}{5}\right)=-\dfrac{6}{35}\)

(v)\(\dfrac{3}{11}\times\dfrac{2}{5}=\dfrac{6}{55}\)

(vi)\(\dfrac{3}{-5}\times\dfrac{-5}{3}=1\)

4. Find the value

(i)\((-4)\div\dfrac{2}{3}=(-4)\times\dfrac{3}{2}=-6\)

(ii)\(-\dfrac{3}{5}\div2=-\dfrac{3}{10}\)

(iii)\(-\dfrac{4}{5}\div(-3)=\dfrac{4}{15}\)

(iv)\(-\dfrac{1}{8}\div\dfrac{3}{4}=-\dfrac{1}{6}\)

(v)\(-\dfrac{2}{13}\div\dfrac{1}{7}=-\dfrac{14}{13}\)

(vi)\(-\dfrac{7}{12}\div\left(-\dfrac{2}{13}\right)=\dfrac{91}{24}\)

(vii)\(\dfrac{3}{13}\div\left(-\dfrac{4}{65}\right)=-\dfrac{15}{4}\)