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S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1E

Exercise 1E

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Question 1

The product of two rational numbers is $-12$. If one of the number is $-8$, find the other.

Sol :

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Question 2

Divide the sum of $\frac{3}{8}$ and $\frac{-5}{12}$ by the reciprocal of $\frac{-15}{8} \times \frac{16}{27}$.

Sol :

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Question 3

By what rational number should $\frac{-15}{56}$ be divided to get $\frac{-5}{7}$ ?

Sol :

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Question 4

The perimeter of an isosceles triangle is $10 \frac{3}{4} \mathrm{~cm}$. If one of its equal sides is $2 \frac{5}{6} \mathrm{~cm}$, find the third side.

Sol :

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Question 5

The area of a rectangular table top is $5 \frac{3}{8} \mathrm{~m}^{2}$. If one of the sides measures $2 \frac{1}{4} \mathrm{~m}$, find the length of the other side.

Sol :

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Question 6

A train covers $80 \frac{4}{5} \mathrm{~km}$ in 1 hour. How much distance will it cover is $4 \frac{3}{4}$ hours ?

Sol :

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Question 7

What is the perimeter of a quadrilateral whose four sides measure $3 \frac{1}{6} \mathrm{~cm}, 2 \frac{3}{4} \mathrm{~cm}, 4 \frac{5}{12} \mathrm{~cm}$ and $2 \frac{1}{2} \mathrm{~cm}$.

Sol :

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Question 8

If $\frac{1}{3}$ of a number exceeds its $\frac{2}{7}$ by 1 , find the number.

Sol :

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Question 9

Rohit travelled $1 \frac{1}{8} \mathrm{~km}$ from home to school, $\frac{5}{6} \mathrm{~km}$ from school to skating rink, $\frac{2}{3} \mathrm{~km}$ from skating rink to work and $\frac{5}{16} \mathrm{~km}$ from work to his home. How many km did Rohit travel?

Sol :

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Question 10

Concert tickets usually cost ₹ $120 \frac{4}{5}$ per person. For students they are priced at $\frac{1}{4}$ of the normal cost. How much will 6 tickets cost for students?

Sol :

Multiple Choice Questions (MCQs)

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Question 11

If a triangle has a base of $10 \frac{3}{4} \mathrm{~cm}$ and a height of $15 \frac{3}{4} \mathrm{~cm}$, what is its area?

(a) $150 \frac{9}{16} \mathrm{~cm}^{2}$

(b) $75 \frac{9}{32} \mathrm{~cm}^{2}$

(c) $84 \frac{21}{32} \mathrm{~cm}^{2}$

(d) $150 \frac{9}{32} \mathrm{~cm}^{2}$

Sol :

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Question 12

In the last three months Mr. Sharma lost $5 \frac{1}{2} \mathrm{~kg}$. gained $2 \frac{1}{4} \mathrm{~kg}$ and then lost $3 \frac{3}{4} \mathrm{~kg}$. If he now weighs $95 \mathrm{~kg}$, how much did Mr. Sharma weigh to begin with ?

(a) $100 \mathrm{~kg}$

(b) $102 \mathrm{~kg}$

(c) $106.5 \mathrm{~kg}$

(d) $104 \mathrm{~kg}$

Sol :

SChand New Learning Composite Mathematics Class 7 Chapter 1 Integers Exercise 1E

Exercise 1E

Question 1

Verify and name the property used.

(a) 18×(-15)=(-15)×18

(b) 15×[3×(-12)]=(15×3)×-12

(d) -12×[(-7)+5]=(-12)×(-7)+(-12)×5

Sol :

Question 2

Fill in the blanks :

(a) 28×__=28

(b) -16×__=16

(d) 0÷63=__

(e) -95÷__=-1

(f) -50×__=50

Question 3

Evaluate by using suitable properties:

(a) 37×(-58)+(-58)×(-27)

(b) -45×(103)

(d) 19×(-25)×(-4)×(-8)

(e) (-16)×(-39)

(f) (-68)×(-19)+68

SChand New Learning Composite Mathematics Class 6 Chapter 1 Knowing Our Numbers Exercise 1E

Exercise 1E

Question 1

(a) 57 nearest ten is 60

(b) 84 nearest ten is 80

(d) 869 nearest ten is 870

(e) 4539 nearest ten is 4540

(f) 8894 nearest ten is 8890

(g) 6397 nearest ten is 6400

(h) 82,035 nearest ten is 82040.

(i) 71298 nearest ten is 71300

(j) 20193 nearest ten is 20190.

Question 2

(a) 624 nearest hundred 600

(b) 136 nearest hundred 100

(d) 4053 nearest hundred 4100

(e) 5974 nearest hundred 6000

(f) 20809 nearest hundred 20800

(g) 18994 nearest hundred 19000

(h) 79992 nearest hundred 80000

(i) 69927 nearest hundred 69900

(j) 12950 nearest hundred 13000

Question 3

(a) 3725 nearest hundred 4000

(b) 6498 nearest hundred 6000

(d) 5946 nearest hundred 6000

(e) 21586 nearest hundred 22000

(f) 69927 nearest hundred 70000

(g) 80279 nearest hundred 80000

(h) 25806 nearest hundred 26000

(i) 79634 nearest hundred 80000

(j) 40389 nearest hundred 40000

RS Aggarwal solution class 8 chapter 1 Rational Numbers Exercise 1E

Exercise 1E

Page-19

Q1 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 1:

Simplify:
(i) $\frac{4}{9} \div \frac{- 5}{12}$
(ii) $- 8 \div \frac{- 7}{16}$
(iii) $\frac{- 12}{7} \div (- 18)$
(iv) $\frac{- 1}{10} \div \frac{- 8}{5}$
(v) $\frac{- 16}{35} \div \frac{- 15}{14}$
(vi) $\frac{- 65}{14} \div \frac{13}{7}$

Answer 1:

$(i) \frac{4}{9} \div \frac{- 5}{12} = \frac{4}{9} \times \frac{12}{- 5} = \frac{4 \times 12}{9 \times - 5} = \frac{48}{- 45} = \frac{- 48}{45} = \frac{- 16}{15}$

$(ii) - 8 \div \frac{- 7}{16} = - 8 \times \frac{16}{- 7} = \frac{8 \times 16}{7} = \frac{128}{7}$

$(iii) \frac{- 12}{7} \div (- 18) = \frac{- 12}{7} \times \frac{1}{- 18} = \frac{12}{126} = \frac{12 \div 3}{126 \div 3} = \frac{4}{42} = \frac{4 \div 2}{42 \div 2} = \frac{2}{21}$

$(iv) \frac{- 1}{10} \div \frac{- 8}{5} = \frac{- 1}{10} \times \frac{5}{- 8} = \frac{5}{80} = \frac{5 \div 5}{80 \div 5} = \frac{1}{16} (v) \frac{- 16}{35} \div \frac{- 15}{14} = \frac{- 16}{35} \times \frac{14}{- 15} = \frac{32}{75} (vi) \frac{- 65}{14} \div \frac{13}{7} = \frac{- 65}{14} \times \frac{7}{13} = \frac{- 5}{2}$

Q2 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 2:

Verify whether the given statement is true or false:
(i) $\frac{13}{5} \div \frac{26}{10} = \frac{26}{10} \div \frac{13}{5}$
(ii) $- 9 \div \frac{3}{4} = \frac{3}{4} \div (- 9)$
(iii) $\frac{- 8}{9} \div \frac{- 4}{3} = \frac{- 4}{3} \div \frac{- 8}{9}$
(iv) $\frac{- 7}{24} \div \frac{3}{- 16} = \frac{3}{- 16} \div \frac{- 7}{24}$

Answer 2:

$(i) \frac{13}{5} \div \frac{26}{10} = \frac{26}{10} \div \frac{13}{5}$

$LHS \frac{13}{5} \div \frac{26}{10} = \frac{13}{5} \times \frac{10}{26} = \frac{130}{130} = 1$

$RHS \frac{26}{10} \div \frac{13}{5} = \frac{26}{10} \times \frac{5}{13} = \frac{130}{130} = 1$

$TRUE$

(ii)

- 9 \div \frac{3}{4} = \frac{3}{4} \div (- 9)

$LHS - 9 \div \frac{3}{4} = - 9 \times \frac{4}{3} = \frac{- 36}{3} = - 12$

$RHS \frac{3}{4} ÷(-9) = \frac{3}{4} × \frac{1}{- 9} = \frac{3}{- 36} = \frac{- 1}{12}$

$FALSE$

(iii)

\frac{- 8}{9} \div \frac{- 4}{3} = \frac{- 4}{3} \div \frac{- 8}{9}

$LHS \frac{- 8}{9} \div \frac{- 4}{3} = \frac{- 8}{9} \times \frac{3}{- 4} = \frac{24}{36} = \frac{2}{3}$

$RHS \frac{- 4}{3} \div \frac{- 8}{9} = \frac{- 4}{3} \times \frac{9}{- 8} = \frac{36}{24} = \frac{3}{2}$

$FALSE$

(iv)

\frac{- 7}{24} \div \frac{3}{- 16} = \frac{3}{- 16} \div \frac{- 7}{24}

$LHS \frac{- 7}{24} \times \frac{- 16}{3} = \frac{112}{72}$

$RHS \frac{3}{- 16} \div \frac{- 7}{24} = \frac{3}{- 16} \times \frac{24}{- 7} = \frac{72}{112}$

$FALSE$

Q3 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 3:

Verify whether the given statement is true or false:
(i) $(\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2} = \frac{5}{9} \div (\frac{1}{3} \div \frac{5}{2})$
(ii) $\{(- 16) \div \frac{6}{5}\} \div \frac{- 9}{10} = (- 16) \div \{\frac{6}{5} \div \frac{- 9}{10}\}$
(iii) $(\frac{- 3}{5} \div \frac{- 12}{35}) \div \frac{1}{14} = \frac{- 3}{5} \div (\frac{- 12}{35} \div \frac{1}{4})$

Answer 3:

$(i) (\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2} = \frac{5}{9} \div (\frac{1}{3} \div \frac{5}{2})$

$LHS (\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2} = (\frac{5}{9} \times \frac{3}{1}) \times \frac{2}{5} = \frac{5 \times 3 \times 2}{9 \times 1 \times 5} = \frac{30}{45} = \frac{2}{3}$

$RHS \frac{5}{9} \div (\frac{1}{3} \div \frac{5}{2}) = \frac{5}{9} \div (\frac{1}{3} \times \frac{2}{5}) = \frac{5}{9} \div (\frac{2}{15}) = \frac{5}{9} \times (\frac{15}{2}) = \frac{75}{18} = \frac{25}{6}$

$LHS \neq RHS FALSE$

(ii)
$[(- 16) \div \frac{6}{5}] \div \frac{- 9}{10} = (- 16) \div [\frac{6}{5} \div \frac{- 9}{10}]$

$LHS = [(- 16) \div \frac{6}{5}] \div \frac{- 9}{10} = [(- 16) \times \frac{5}{6}] \times \frac{10}{- 9} = \frac{(- 16) \times 5 \times 10}{6 \times (- 9)} = \frac{800}{54} = \frac{400}{27}$

$RHS (- 16) \div (\frac{6}{5} \div \frac{- 9}{10}) = (- 16) \div (\frac{6}{5} \times \frac{10}{- 9}) = - 16 \div \{\frac{- 60}{45}\} = - 16 \times (\frac{- 45}{60}) = - 16 \times (\frac{- 3}{4}) = \frac{48}{4} = 12$

$LHS \neq RHS FALSE$

(iii)
$(\frac{- 3}{5} \div \frac{- 12}{35}) \div \frac{1}{14} = \frac{- 3}{5} \div (\frac{- 12}{35} \div \frac{1}{4})$

$LHS = (\frac{- 3}{5} \times \frac{35}{- 12}) \times 14 = \frac{(- 3) \times 35 \times 14}{5 \times (- 12)} = \frac{1470}{60} = \frac{49}{2}$

$RHS = \frac{- 3}{5} \div (\frac{- 12}{35} \div \frac{1}{4}) = \frac{- 3}{5} \div (\frac{- 12}{35} \times \frac{4}{1}) = \frac{- 3}{5} \div (\frac{- 12 \times 4}{35}) = \frac{- 3}{5} \div (\frac{- 48}{35}) = \frac{- 3}{5} \times \frac{35}{- 48} = \frac{3 \times 35}{5 \times 48} = \frac{105}{240} = \frac{7}{16}$

$LHS \neq RHS$

$FALSE$

Q4 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 4:

The product of two rational numbers is −9. If one of the numbers is −12, find the other.

Answer 4:

$Let the number be x . Now, x \times (- 12) = - 9 \Rightarrow x = - 9 \div (- 12) \Rightarrow x = (- 9) \times \frac{1}{- 12} \Rightarrow x = \frac{- 9}{- 12} \Rightarrow x = \frac{3}{4}$

Q5 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 5:

The product of two rational numbers is $\frac{- 16}{9}$ . If one of the numbers is $\frac{- 4}{3}$ , find the other.

Answer 5:

$Let the number be x . Now, x \times \frac{- 4}{3} = \frac{- 16}{9} \Rightarrow x = \frac{- 16}{9} \div \frac{- 4}{3} \Rightarrow x = \frac{- 16}{9} \times \frac{3}{- 4} \Rightarrow x = \frac{- 16 \times 3}{9 \times (- 4)} \Rightarrow x = \frac{48}{36} \Rightarrow x = \frac{4}{3}$ .

Q6 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 6:

By what rational number should we multiply $\frac{- 15}{56}$ to get $\frac{- 5}{7}$ ?

Answer 6:

$Let the number be x . Now, x \times \frac{- 15}{56} = \frac{- 5}{7} \Rightarrow x = \frac{- 5}{7} \div \frac{- 15}{56} \Rightarrow x = \frac{- 5}{7} \times \frac{56}{- 15} \Rightarrow x = \frac{280}{105} \Rightarrow x = \frac{280 \div 5}{105 \div 5} \Rightarrow x = \frac{56}{21} \Rightarrow x = \frac{56 \div 7}{21 \div 7} \Rightarrow x = \frac{8}{3}$

Q7 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 7:

By what rational number should $\frac{- 8}{39}$ be multiplied to obtain $\frac{1}{26}$ ?

Answer 7:

$Let the number be x . Now, x \times \frac{- 8}{39} = \frac{1}{26} \Rightarrow x = \frac{1}{26} \div \frac{- 8}{39} \Rightarrow x = \frac{1}{26} \times \frac{39}{- 8} \Rightarrow x = \frac{39}{- 208} \Rightarrow x = \frac{39 \times - 1}{- 208 \times - 1} \Rightarrow x = \frac{- 39}{208} \Rightarrow x = \frac{- 39 \div 13}{208 \div 13} \Rightarrow x = \frac{- 3}{16}$

Q8 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 8:

By what number should $\frac{- 33}{8}$ be divided to get $\frac{- 11}{2}$ ?

Answer 8:

$Let the number be x . Now, \frac{- 33}{8} \div x = \frac{- 11}{2} \Rightarrow \frac{- 33}{8} \times \frac{1}{x} = \frac{- 11}{2} \Rightarrow \frac{1}{x} = \frac{- 11}{2} \div \frac{- 33}{8} \Rightarrow \frac{1}{x} = \frac{- 11}{2} \times \frac{8}{- 33} \Rightarrow \frac{1}{x} = \frac{88}{66} \Rightarrow \frac{1}{x} = \frac{4}{3} \Rightarrow x = \frac{3}{4} (Reciprocal of \frac{4}{3})$

Q9 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 9:

Divide the sum of $\frac{13}{5}$ and $\frac{- 12}{7}$ by the product of $\frac{- 31}{7}$ and $\frac{1}{- 2} .$

Answer 9:

$(\frac{13}{5} + \frac{- 12}{7}) \div (\frac{- 31}{7} \times \frac{1}{- 2}) = (\frac{91 - 60}{35}) \div (\frac{- 31}{- 14}) = (\frac{31}{35}) \div (\frac{31}{14}) = (\frac{31}{35}) \times (\frac{14}{31}) = \frac{14}{35} = \frac{14 \div 7}{35 \div 7} = \frac{2}{5}$

Q10 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 10:

Divide the sum of $\frac{65}{12}$ and $\frac{8}{3}$ by their difference.

Answer 10:

$(\frac{65}{12} + \frac{8}{3}) \div (\frac{65}{12} - \frac{8}{3}) = (\frac{65}{12} + \frac{32}{12}) \div (\frac{65}{12} - \frac{32}{12}) = (\frac{97}{12}) \div (\frac{33}{12}) = \frac{97}{12} \times \frac{12}{33} = \frac{97}{33}$

Q11 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 11:

Fill in the blanks:
(i) $\frac{9}{8} \div (. . .) = \frac{- 3}{2}$
(ii) $(. . .) \div (\frac{- 7}{5}) = \frac{10}{19}$
(iii) $(. . .) \div (- 3) = \frac{- 4}{15}$
(iv) $(- 12) \div (. . .) = \frac{- 6}{5}$

Answer 11:

$(i) Let \frac{9}{8} \div x = \frac{- 3}{2} \Rightarrow \frac{9}{8} \times \frac{1}{x} = \frac{- 3}{2} \Rightarrow \frac{1}{x} = \frac{- 3}{2} \div \frac{9}{8} \Rightarrow \frac{1}{x} = \frac{- 3}{2} \times \frac{8}{9} \Rightarrow \frac{1}{x} = \frac{- 24}{18} \Rightarrow \frac{1}{x} = \frac{- 4}{3} \Rightarrow x = \frac{- 3}{4} [Reciprocal of \frac{- 4}{3}]$

$(ii) Let x \div (\frac{- 7}{5}) = \frac{10}{19} \Rightarrow x \times (\frac{5}{- 7}) = \frac{10}{19} \Rightarrow x = (\frac{10}{19}) \div (\frac{5}{- 7}) \Rightarrow x = \frac{10}{19} \times \frac{- 7}{5} \Rightarrow x = \frac{- 70}{95} \Rightarrow x = \frac{- 14}{19}$

$(iii) Let x \div (- 3) = \frac{- 4}{15} \Rightarrow x \times (\frac{1}{- 3}) = \frac{- 4}{15} \Rightarrow x = \frac{- 4}{15} \times (- 3) \Rightarrow x = \frac{12}{15} \Rightarrow x = \frac{4}{5}$

$(iv) Let (- 12) \div x = \frac{- 6}{5} \Rightarrow (- 12) \times \frac{1}{x} = \frac{- 6}{5} \Rightarrow \frac{1}{x} = \frac{- 6}{5} \div (- 12) \Rightarrow \frac{1}{x} = \frac{- 6}{5} \times \frac{1}{- 12} \Rightarrow \frac{1}{x} = \frac{1}{10} \Rightarrow x = 10$

Q12 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Question 12:

(i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?

Answer 12:

(i) No, rational numbers are not closed under division in general.

$\frac{a}{0} = \infty$ ; it is not a rational number.

(ii) No

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c} Also, \frac{c}{d} \div \frac{a}{b} = \frac{c}{d} \times \frac{b}{a} = \frac{c b}{d a} Thus, \frac{a}{b} \div \frac{c}{d} \neq \frac{c}{d} \div \frac{a}{b}$

Therefore, division is not commutative.

(iii) No, rational numbers are not associative under division.

$\frac{a}{b} \div (\frac{c}{d} \div \frac{e}{f}) \neq (\frac{a}{b} \div \frac{c}{d}) \div \frac{e}{f}$

(iv) No, we cannot divide 1 by 0. The answer will be $\infty$ , which is not defined.

Exercise 1E

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Exercise 1E

Question 1

Question 2

Question 3

Exercise 1E

Question 1

Question 2

Question 3

Exercise 1E

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Q1 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Q9 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Q10 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Q11 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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Q12 | Ex-1E | Rational Numbers | Class 8 | RS AGGARWAL | Chapter 1 | myhelper

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