SChand Composite Mathematics Class 7 Chapter 4 Rational Numbers Exercise 4A

  Exercise 4A

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Q1 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 1

Find five rational number equivalent to each of the following rational numbers:

(i) $\frac{3}{5}$

Sol :

$\frac{3 \times 2}{5 \times 2}=\frac{6}{10}$

$\frac{3 \times 3}{5 \times 3}=\frac{9}{15}$

$\frac{3 \times 4}{5 \times 4}=\frac{12}{20}$

$\frac{3 \times 5}{5 \times 5}=\frac{15}{25}$

$\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$

(ii) $\frac{-6}{11}$

Sol :

$\frac{-6 \times 2}{11 \times 2}=\frac{-12}{22}$

$\frac{-6 \times 3}{11 \times 3}=\frac{-18}{33}$

$\frac{-6 \times 4}{11 \times 4}=\frac{-24}{44}$

$\frac{-6 \times 5}{11 \times 5}=\frac{-30}{55}$

$\frac{-6 \times 6}{11 \times 6}=\frac{-36}{66}$

(iii) $\frac{7}{-10}$

Sol :

$\frac{7\times 2}{-10 \times 2}=\frac{14}{-20}$

$\frac{7 \times 3}{-10 \times 3}=\frac{21}{-30}$

$\frac{7 \times 4}{-10 \times 4}=\frac{28}{-40}$

$\frac{7 \times 5}{-10 \times 5}=\frac{35}{-50}$

$\frac{7 \times 6}{-10 \times 6}=\frac{42}{-60}$

(iv) $\frac{8}{15}$

Sol :

$\frac{8\times 2}{15 \times 2}=\frac{16}{30}$

$\frac{8 \times 3}{15 \times 3}=\frac{24}{45}$

$\frac{8 \times 4}{15 \times 4}=\frac{32}{60}$

$\frac{8 \times 5}{15 \times 5}=\frac{40}{75}$

$\frac{8 \times 6}{15 \times 6}=\frac{48}{90}$

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Q2 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 2

Write each of the following rational numbers with a positive denominator:

(i) $\frac{3}{-5}$

Sol :

$\frac{3}{-5} \times \frac{-1}{-1}=\frac{-3}{5}$

(ii) $\frac{8}{-17}$

Sol :

$\frac{8}{-17} \times \frac{-1}{-1}=\frac{-8}{17}$

(iii) $\frac{-21}{-25}$

Sol :

$\frac{-21}{-25} \times \frac{-1}{-1}=\frac{21}{25}$

(iv) $\frac{-40}{-59}$

Sol :

$\frac{-40}{-59} \times \frac{-1}{-1}=\frac{40}{59}$

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Q3 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 3

Express $\frac{-15}{16}$ as a rational number with:

(i) numerator=-30

Sol :

$\frac{-15}{16} \times \frac{2}{2}=\frac{-30}{32}$

(ii) numerator=75

Sol :

$\frac{-15}{16} \times \frac{-5}{-5}=\frac{75}{-80}$

(iii) denominator=48

Sol :

$\frac{-15}{16} \times \frac{3}{3}=\frac{-45}{48}$

(iv) denominator=-96

Sol :

$\frac{-15}{16} \times \frac{-6}{-6}=\frac{90}{-96}$

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Q4 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 4

Express $\frac{19}{-5}$ as a rational number with:

(i) numerator=-38

Sol :

$\frac{19}{-5} \times \frac{-2}{-2}=\frac{-38}{10}$

(ii) numerator=-95

Sol :

$\frac{19}{-5} \times \frac{-5}{-5}=\frac{-95}{25}$

(iii) denominator=-35

Sol :

$\frac{19}{-5} \times \frac{7}{7}=\frac{133}{-35}$

(iv) denominator=20

Sol :

$\frac{19}{-5} \times \frac{-4}{-4}=\frac{76}{20}$

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Q5 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 5

Express $\frac{-192}{240}$ as a rational number with numerator:

(i) 96

Sol :

$\frac{-192 \div -2}{240 \div -2} = \frac{96}{-120}$

(ii) -32

Sol :

$\frac{-192 \div 6}{240 \div 6} =\frac{-32}{40}$

(iii) 16

Sol :

$\frac{-192 \div -12}{240 \div -12} =\frac{16}{-20}$

(iv) -8

Sol :

$\frac{-192 \div 24}{240 \div 24} =\frac{-8}{10}$

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Q6 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 6

Express the following rational numbers in standard form:

(i) $\frac{-6}{15}$

Sol : $=\frac{-2}{5}$

(ii) $\frac{-18}{-24}$

Sol :  $\frac{3}{4}$

(iii) $\frac{21}{-35}$

Sol : $\frac{3}{-5}\times=\frac{-3}{5}$

(iv) $\frac{-36}{84}$

Sol : $\frac{-3}{7}$

(v) $\frac{-1302}{-1953}$

Sol : $\frac{2}{3}$

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Q7 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 7

Fill in the blanks :

(i) $\frac{-3}{4}=\frac{}{12}=\frac{}{28}$

Sol :

$\frac{-3\times 3}{4 \times 3}=\frac{-9}{12}$

$\frac{-3 \times 7}{4 \times 7}=\frac{-21}{28}$

(ii) $\frac{-5}{-8}=\frac{}{16}=\frac{25}{}$

Sol :

$\frac{-5 \times -2}{-8 \times -2}=\frac{10}{16}$

$\frac{-5 \times -5}{-8 \times -5}=\frac{25}{40}$

(iii) $\frac{7}{-9}=\frac{-14}{}=\frac{35}{}$

Sol :

$\frac{7 \times -2}{-9 \times -2}=\frac{-14}{18}$

$\frac{7 \times 5}{-9 \times 5}=\frac{35}{-45}$

(iv) $\frac{-8}{}=\frac{4}{13}=\frac{}{-65}$

Sol :

$\frac{-8 \div 2}{13 \times -2 =-26}=\frac{4}{13}$

$=\frac{4 \times -5}{13 \times -5}=\frac{-20}{-65}$

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Q8 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 8

Which of the two rational number is greater?

(i) $\frac{-7}{12} \text{ or } \frac{5}{12}$

Sol : <

(ii) $\frac{-3}{14} \text{ or } \frac{-6}{7}$

Sol : >

(iii) $\frac{-7}{13} \text{ or } 0$

Sol : <

(iv) $\frac{-22}{-33} \text{ or } \frac{45}{-65}$

Sol : >

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Q9 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 9

Which of the two rational number is smaller?

(i) $\frac{-5}{8} \text{ or } \frac{3}{-8}$

Sol : <

(ii) $\frac{8}{17} \text{ or } \frac{-9}{-17}$

Sol : <

(iii) $\frac{19}{-5} \text{ or } 1$

Sol : <

(iv) $\frac{-11}{1111} \text{ or } \frac{1}{-103}$

Sol : <

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Q10 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 10

Which of the symbols '=' , < or > . Should replace the blank space.

(i) $\dfrac{5}{4} \Box{} 1$

Sol : >

(ii) $\dfrac{-1}{2} \Box \dfrac{-3}{5}$

Sol : >

(iii) $\dfrac{-3}{4} \Box{} \dfrac{-2}{3}$

Sol : <

(iv) $\left(-2\dfrac{3}{7}\right) \Box{} \left(-2\dfrac{3}{5}\right)$

Sol :  >

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Q11 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 11

Arrange in order from least to greatest.

(i) $\frac{1}{3} , \frac{3}{7} , \frac{2}{5}$

Sol :

LCM of 3, 7 , 5 is 105

$\frac{1 \times 35}{3 \times 35} =\frac{35}{105}$

$\frac{3 \times 15}{7 \times 15} =\frac{45}{105}$

$\frac{2 \times 21}{5 \times 21} =\frac{42}{105}$

$\frac{35}{105}<  \frac{42}{105}< \frac{45}{105}$

$\frac{1}{3} < \frac{2}{5} < \frac{3}{7}$

(ii) $\frac{-9}{6} , \frac{-4}{3} , \frac{-17}{12}$

Sol :

L.C.M of 6 , 3 , 12 is 12

$\frac{-9 \times 2}{6 \times 2} =\frac{-18}{12}$

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

$\frac{-17 \times 1}{12 \times 1} =\frac{-17}{12}$

$\frac{-18}{12} <  \frac{-17}{12} < \frac{-16}{12}$

$\frac{-9}{6} < \frac{-17}{12} <  \frac{-4}{3}$

(iii) $\frac{-3}{5} , \frac{7}{-10} , \frac{-5}{6}$

Sol :

L.C.M of 5 , 10 , 6 is 30

$\frac{-3 \times 6}{5 \times 6}  =\frac{-18}{30}$

$\frac{7 \times -3}{-10 \times -3} =\frac{-21}{30}$

$\frac{-5 \times 5}{6 \times 5} =\frac{-25}{30}$

$\frac{-25}{30} < \frac{-21}{30} < \frac{-18}{30}$

$\frac{-5}{6} < \frac{7}{-10} < \frac{-3}{5}$

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Q12 | Ex-4A | Class 7 | Rational Numbers |S.Chand | Composite Mathematics | myhelper

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Question 12

Arrange in descending order.

(i) $\frac{3}{4} , \frac{11}{8} , \frac{9}{16} , \frac{33}{16}$

Sol :

L.C.M of 4 , 16 , 16 is 16

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

$\frac{11 \times 2}{8 \times 2}=\frac{22}{16}$

$\frac{9 \times 1}{16 \times 1}=\frac{9}{16}$

$\frac{33 \times 1}{16 \times 1} =\frac{33}{16}$

$\frac{33}{16} > \frac{22}{16} > \frac{12}{16} > \frac{9}{16}$

$\frac{33}{16} > \frac{11}{8} > \frac{3}{4} > \frac{9}{16}$

(ii) $\frac{1}{7} , \frac{-1}{3} , \frac{-2}{8}$

Sol :

L.C.M of 7 , 3 , 8 is 168

$\frac{1 \times 24}{7 \times 24} =\frac{24}{168}$

$\frac{-1 \times 56}{3 \times 56} =\frac{-56}{168}$

$\frac{-2 \times 21}{8 \times 21}=\frac{-42}{168}$

$\frac{24}{168} > \frac{-42}{168} >\frac{-56}{168}$

$\frac{1}{7}>  \frac{-2}{8} > \frac{-1}{3}$

(iii) $\frac{3}{-5} ,  \frac{-7}{10} , \frac{8}{-10} , \frac{-17}{15}$

Sol :

L.C.M of 5 , 10 , 15 is 30

$\frac{3 \times -6}{-5 \times -6}=\frac{-18}{30}$

$\frac{-7 \times 3}{10 \times 3}=\frac{-21}{30}$

$\frac{8 \times -3}{-10 \times -3}=\frac{-24}{30}$

$\frac{-17 \times 2}{15 \times 2}=\frac{-34}{30}$

$\frac{-18}{30} >\frac{-21}{30}>\frac{-24}{30}>\frac{-34}{30}$

$\frac{3}{-5} > \frac{-7}{10} >  \frac{8}{-10} > \frac{-17}{15}$