SChand Composite Mathematics Class 7 Chapter 2 Fractions Exercise 2B

 Exercise 2B

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Q1 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 1

Multiply :-

(i) $\frac{2}{3} \times 11$

Sol :

$=\frac{22}{3}=7\frac{1}{3}$

(ii) $\frac{4}{9} \times 15$

Sol :

$=\frac{4}{3} \times 5$

$=\frac{20}{3}=6\frac{2}{3}$

(iii) $1 \frac{5}{11} \times 12$

Sol :

$=\frac{1 \times 11+5}{11} \times 12$

$=\frac{16}{11} \times 12=\frac{192}{11}$

$=17\frac{5}{11}$

(iv) $\frac{37}{12} \times 21$

Sol :

$=\frac{37}{12} \times 21=\frac{37}{4}\times 7$

$=\frac{259}{4}=64\frac{3}{4}$

(v) $\frac{5}{7} \times 2 \frac{1}{10}$

Sol :

$=\frac{5}{7} \times \frac{2 \times 10+1}{10}$

$=\frac{5}{7} \times \frac{21}{10}$

$=\frac{3}{2}=1\frac{1}{2}$

(vi) $6 \frac{9}{10} \times 1 \frac{1}{23}$

Sol :

$=\frac{6 \times 10+9}{10} \times \frac{1\times 23+1}{23}$

$=\frac{69}{10}\times \frac{24}{23}$

$=\frac{36}{5}=7\frac{1}{5}$

(vii) $3 \frac{1}{2} \times 14 \frac{1}{2}$

Sol :

$=\frac{3 \times 2+1}{2} \times \frac{14 \times 2+1}{2}$

$=\frac{7}{2} \times \frac{29}{2}=\frac{203}{4}$

$=50\frac{3}{4}$

(viii) $6 \frac{1}{7} \times 5 \frac{5}{6}$

Sol :

$=\frac{6 \times 7+1}{7} \times \frac{5 \times 6+5}{6}$

$=\frac{43}{7} \times \frac{35}{6}$

$=\frac{215}{6}=35\frac{5}{6}$

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Q2 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 2

Find the product of :

(i) $\frac{3}{5} \times \frac{15}{16} \times \frac{4}{7}$

Sol :

$=\frac{9}{28}$

(ii) $2 \frac{1}{7} \times 2 \frac{4}{9} \times \frac{7}{22}$

Sol :

$=\frac{2\times 7+1}{7} \times  \frac{2 \times 9+4}{9} \times \frac{7}{22}$

$=\frac{15}{7} \times \frac{22}{9} \times \frac{7}{22}$

$=\frac{5}{3}=1\frac{2}{3}$

(iii) $9 \frac{2}{3} \times 1 \frac{1}{29} \times \frac{6}{15} \times 7 \frac{1}{5}$

Sol :

$=\frac{29}{3} \times \frac{30}{29} \times \frac{6}{15} \times \frac{36}{5}$

$=\frac{2 \times 2 \times 36}{5}=\frac{144}{5}=28\frac{4}{5}$

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Q3 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 3

Find the value of :

(i) $\frac{3}{4}$ of 32 kg

Sol :

$=\frac{3}{4} \times 32$ kg

=3×8=24 kg

(ii) $\frac{2}{7}$ of 1 week

Sol :

1 week=7 days

$=\frac{2}{7} \times 7$ 

=2 days

(iii) $\frac{5}{8}$ of 20 m

Sol :

$=\frac{5}{8} \times 20=\frac{25}{2}=12\frac{1}{2}$

(iv) $\frac{7}{8}$ of 1 day

Sol :

1 day = 24 hour

$=\frac{7}{8} \times 24$

=7×3=21 hour

(v) $\frac{4}{5}$ of ₹ 90

Sol :

$=\frac{4}{5} \times 90$

=4×18=72 ₹

(vi) $\frac{4}{9}$ of $\frac{1}{24}$

Sol :

$=\frac{4}{9} \times \frac{1}{24}=\frac{1}{54}$

(vii) $\frac{1}{3}$ of $\frac{15}{16}$

Sol :

$=\frac{1}{3} \times \frac{15}{16}=\frac{5}{16}$

(viii) $\frac{7}{9}$ of 45

Sol :

$=\frac{7}{9} \times 45$

=35

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Q4 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 4

Simplify :

(i) $\left(2 \frac{4}{5}+1 \frac{3}{10}\right) \times 1\frac{1}{2}$

Sol :

$=\left(\frac{2 \times 5+4}{5}+\frac{1 \times 10+3}{10}\right) \times \frac{1 \times 2+1}{2}$

$=\left(\frac{14}{5}+\frac{13}{10}\right) \times \frac{3}{2}$

L.C.M of 5 and 10 is 10

$=\left ( \frac{14\times 2+13 \times 1}{10} \right) \times \frac{3}{2}$

$=\frac{28+13}{10} \times \frac{3}{2}$

$=\frac{41}{10} \times \frac{3}{2}=\frac{122}{20}=6\frac{2}{20}$

(ii) $1 \frac{5}{6} \times 2 \frac{3}{4}+1 \frac{5}{6} \times 1 \frac{3}{4}$

Sol :

$=\frac{1 \times 6+5}{6}+\frac{2 \times 4+3}{4}+\frac{1 \times 6+5}{6} \times \frac{1 \times 4+3}{4}$

$=\frac{121}{24}+\frac{77}{24}=\frac{198}{24}$

$=8\frac{6}{24}=8\frac{1}{4}$

(iii) $\left(2 \frac{3}{4}-1 \frac{1}{3}\right) \times \frac{3}{4}$

Sol :

$=\left(\frac{2 \times 4+3}{4}-\frac{1 \times 3+1}{3} \right) \times \frac{3}{4}$

$=\left(\frac{11}{4}-\frac{4}{3} \right) \times \frac{3}{4}$

L.C.M of 4 and 3 is 12

$=\left( \frac{11 \times 3-4 \times 4}{12} \right) \times \frac{3}{4}$

$=\frac{33-16}{12} \times \frac{3}{4}$

$=\frac{17}{12} \times \frac{3}{4}=\frac{17}{16}=1\frac{1}{16}$

(iv) $3 \frac{1}{4} \times 2 \frac{1}{3}-1 \frac{1}{4} \times \frac{1}{5}$

Sol :

$= \frac{3 \times +1}{4} \times  \frac{2 \times 3+1}{3}- \frac{1\times 4+1}{4} \times \frac{1}{5}$

$=\frac{13}{4} \times \frac{7}{3}-\frac{5}{4} \times \frac{1}{5}$

$=\frac{91}{12}-\frac{1}{4}$

L.C.M of 12 and 4 is 12

$=\frac{91-3}{12}=\frac{88}{12}$

$=\frac{22}{3}=7\frac{1}{3}$

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Q5 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 5

Find the difference between $\frac{3}{5}$ of 30 km and $\frac{2}{3}$ of 30 km

Sol :

A.T.Q

$=\frac{2}{3} \times 30$ km - $\frac{3}{5}\times 30$

=(2×10 - 3×6) km

= 20 - 18 = 2 km

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Q6 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 6

Write down the reciprocal of :

(i) $\frac{3}{5}$

Sol :

$=\frac{5}{3}$

(ii) $\frac{1}{3}$

Sol :

$=\frac{3}{1}$

(iii) 5

Sol :

$=\frac{1}{5}$

(iv) $2 \frac{1}{5}$

Sol :

$= \frac{2 \times 5+1}{5}=\frac{11}{5}$

$=\frac{5}{11}$

(v) $\frac{61}{9}$

Sol :

$\frac{9}{61}$

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Q7 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 7

Divide :

(i) $20 \div \frac{1}{5}$

Sol :

$=20 \times \frac{5}{1}$

=100

(ii) $8 \div 2 \frac{1}{3}$

Sol :

$=8 \div \frac{2 \times 3 +1}{3}$

$=8 \div \frac{7}{3}=8 \times \frac{3}{7}$

$=\frac{24}{7}=3\frac{3}{7}$

(iii) $2 \frac{3}{5} \div 3 \frac{1}{2}$

Sol :

$=\frac{2 \times 5+3}{5} \div  \frac{3 \times 2+1}{2}$

$=\frac{13}{5} \div  \frac{7}{2}$

$=\frac{13}{5} \times  \frac{2}{7}=\frac{26}{35}$

(iv) $8 \frac{2}{3} \div 5 \frac{7}{9}$

Sol :

$=\frac{8 \times 3+2}{3} \div  \frac{5 \times 9+7}{9}$

$=\frac{26}{3} \div  \frac{52}{9}$

$=\frac{26}{3} \times  \frac{9}{52}$

$=\frac{3}{2}=1\frac{1}{2}$

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Q8 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 8

Find

(i) $\frac{5}{8} \times 1 \frac{1}{2} \div \frac{15}{16}$

Sol :

$=\frac{5}{8} \times \frac{1 \times 2+1}{2} \times \frac{16}{15}$

$=\frac{5}{8} \times \frac{3}{2} \times \frac{16}{15}$

$=1$

(ii) $1 \frac{13}{27} \times 2 \frac{11}{12} \div 3 \frac{1}{9}$

Sol :

$= \frac{1 \times 27+13}{27} \times \frac{2 \times 12+11}{12} \div  \frac{3 \times 9+1}{9}$

$= \frac{40}{27} \times \frac{35}{12} \div  \frac{28}{9}$

$= \frac{40}{27} \times \frac{35}{12} \times \frac{9}{28}$

$=\frac{50}{36}=\frac{25}{18}=1\frac{7}{18}$

(iii) $1 \frac{1}{24} \times 2 \frac{1}{4} \div 1 \frac{1}{14}$

Sol :

$=\frac{1 \times 24+1}{24} \times  \frac{2 \times 4+1}{4} \div \frac{1\times 14+1}{14}$

$=\frac{25}{24} \times  \frac{9}{4} \div \frac{15}{14}$

$=\frac{35}{16}=2\frac{3}{16}$

(iv) $1 \frac{1}{8} \div 2 \frac{1}{4} \times 4 \frac{1}{3}$

Sol :

$=\frac{1 \times 8+1}{8} \div \frac{2 \times 4+1}{4} \times \frac{4 \times 3+1}{3}$

$=\frac{9}{8} \div \frac{9}{4} \times \frac{13}{3}$

$=\frac{9}{8} \times \frac{4}{9} \times \frac{13}{3}$

$=\frac{13}{6}=2\frac{1}{6}$

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Q9 | Ex-2B |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 9

Simplify :

(i) $\frac{2}{3}$ of $\frac{3}{4}+\frac{4}{5}$

Sol :

$=\left( \frac{2}{3} \times \frac{3}{4}\right) + \frac{4}{5}$

$=\frac{1}{2} + \frac{4}{5}=\frac{1\times 5+4\times 2}{10}$

$=\frac{5+8}{10}=\frac{13}{10}=1\frac{3}{10}$

(ii) $\frac{2}{3}-\frac{3}{4} \times \frac{4}{5}$

Sol :

$=\frac{2}{3}-\frac{3}{5}=\frac{10-9}{15}=\frac{1}{15}$

(iii) $\frac{2}{3}$ of $\frac{3}{4} \div \frac{4}{5}$

Sol :

$=\frac{2}{3} \times \frac{3}{4} \times \frac{5}{4}=\frac{5}{8}$

(iv) $\frac{2}{3} \times\left(\frac{3}{4}-\frac{1}{8}\right) \div \frac{3}{4}$

Sol :

$=\frac{2}{3} \times \left(\frac{6-1}{8}\right) \times \frac{4}{3}$

$=\frac{2}{3} \times \frac{5}{8} \times \frac{4}{3}=\frac{5}{9}$

(v) $\frac{4}{5}$ of $\left(\frac{4}{9}+\frac{2}{3}\right) \div 2 \frac{2}{3}$

Sol :

$=\frac{4}{5} \times \left( \frac{4+6}{9}\right) \times \frac{3}{8}$

$=\frac{4}{5} \times \frac{10}{9} \times \frac{3}{8}=\frac{1}{3}$

(vi) $\left(\frac{1}{2}+\frac{1}{3}\right) \div 1 \frac{5}{6} \times 11-3 \frac{1}{2}$

Sol :

$=\left(\frac{1}{2}+\frac{1}{3}\right) \div \frac{1 \times 6+5}{6} \times 11- \frac{3 \times 2+1}{2}$

$=\left(\frac{1\times 3+1 \times 2}{6}\right) \div \frac{11}{6} \times 11- \frac{7}{2}$

$=\left(\frac{3+2}{6}\right) \times  \frac{6}{11} \times 11- \frac{7}{2}$

$=\frac{5}{1}-\frac{7}{2}=\frac{10-7}{2}=\frac{3}{2}=1\frac{1}{2}$

(vii) $\frac{3}{4}+\frac{1}{2} \times 2 \frac{1}{2}-\frac{2}{3} \times \frac{7}{8} \div 1 \frac{1}{4}$

Sol :

$=\frac{3}{4} + \frac{1}{2} \times  \frac{5}{2}-\frac{2}{3} \times \frac{7}{8} \times \frac{4}{5}$

$=\frac{3}{4}+\frac{5}{4}-\frac{7}{15}=\frac{45+75-28}{60}$

$=\frac{92}{60}=1\frac{32}{60}=1\frac{8}{15}$

(viii) $\frac{3}{4}+\frac{2}{3} \times \frac{5}{8} \div \frac{5}{6}-\frac{1}{8}$

Sol :

$=\frac{3}{4}+\frac{2}{3}\times \frac{5}{8} \times \frac{6}{5}-\frac{1}{8}$

$=\frac{3}{4}+\frac{1}{2}-\frac{1}{8}=\frac{6+4-1}{8}=\frac{9}{8}=1\frac{1}{8}$

(ix) $108 \div 36 \text { of } \frac{1}{3}+\frac{2}{5} \times 3 \frac{3}{4}$

Sol :

$=108 \div 36 \times \frac{1}{3}+\frac{2}{5} \times \frac{15}{4}$

$=108 \times \frac{1}{36} \times \frac{1}{3}+\frac{2}{5}  \times \frac{15}{4}$

$=\frac{1}{1}+\frac{3}{2}=\frac{1 \times 2+3 \times 1}{2}$

$=\frac{2+3}{2}=2\frac{1}{2}$