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

Exercise 1C

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Q1 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper

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Question 1

Answer True (T) or False (F) :
(i) $\frac{10}{21} \div \frac{8}{9}=\frac{8}{9} \div \frac{10}{21}$
(ii) Addition distributes over multiplication in rational numbers.
(iii) The reciprocal of $-5$ is $\frac{1}{5}$.
(iv) $\frac{3}{4} \div \frac{-8}{7}$ is a rational number.
(v) $0 \times \frac{4}{5}=\frac{4}{5} \times 0$ implies that 0 is the multiplicative identity for rational numbers.

Sol :

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Question 2

Multiply :

(i) $\frac{6}{7}$ by $\frac{2}{3}$

(ii) $\frac{-9}{11}$ by $\frac{22}{63}$

(iii) $\frac{-12}{13}$ by $\frac{-5}{18}$

(iv) $\frac{-90}{11}$ by $\frac{-55}{72}$

(v) $5 \frac{1}{7}$ by $-2 \frac{1}{3}$

(vi) $\frac{18}{35}$ by $-3 \frac{1}{8}$

Sol :

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Question 3

Simplify:

(i) $\left(\frac{-6}{7} \times \frac{-28}{18}\right)+\left(\frac{-11}{13} \times \frac{65}{22}\right)$

(ii) $\left(\frac{-4}{5} \times \frac{15}{8}\right)+\left(\frac{-1}{3} \times \frac{-9}{7}\right)-\left(\frac{2}{9} \times \frac{27}{14}\right)$

Sol :

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Question 4

Fill in the blanks :

(i) $\frac{-18}{37} \times \frac{11}{40}=\frac{11}{40} \times$

(ii) $-19 \times \frac{-5}{12}=\frac{-5}{12} \times$

(iii) $\left(\frac{6}{11} \times \frac{-20}{21}\right) \times\left(\frac{-7}{8}\right)=\ldots . . \times\left(\frac{-20}{21} \times \frac{-7}{8}\right)$

(iv) $\frac{-21}{40} \times\left(\frac{3}{7} \times \frac{17}{-24}\right)=\left(\frac{-21}{40} \times \frac{17}{-24}\right) \times \ldots .$

(v) $\frac{2}{9} \times\left(\frac{-4}{9}+\frac{6}{17}\right)=\frac{2}{9} \times \ldots . .+\ldots . . \times \frac{6}{17}$

Sol :

Verify the statements given in Q5 to Q7. Also name the properties of multiplication illustrated by these statements.

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Question 5

(i) $\frac{4}{5} \times \frac{7}{9}=\frac{7}{9} \times \frac{4}{5}$

(ii) $\frac{8}{7} \times \frac{9}{-10}=\frac{9}{-10} \times \frac{8}{7}$

Sol :

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Question 6

(i) $\left(\frac{3}{4} \times \frac{1}{2}\right) \times \frac{5}{7}=\frac{3}{4} \times\left(\frac{1}{2} \times \frac{5}{7}\right)$

(ii) $\left(-\frac{7}{6} \times \frac{-2}{5}\right) \times \frac{3}{8}=\frac{-7}{6} \times\left(\frac{-2}{5} \times \frac{3}{8}\right)$

Sol :

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Question 7

(i) $\frac{2}{3} \times\left(\frac{4}{5}+\frac{7}{8}\right)=\left(\frac{2}{3} \times \frac{4}{5}\right)+\left(\frac{2}{3} \times \frac{7}{8}\right)$

(ii) $\frac{-6}{15} \times\left(\frac{7}{8}+\frac{-5}{12}\right)=\left(\frac{-6}{15} \times \frac{7}{8}\right)+\left(\frac{-6}{15} \times \frac{-5}{12}\right)$

Sol :

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Question 8

Use the distributivity of multiplication of rational numbers over addition to simplify :

(i) $\frac{7}{4} \times\left(\frac{5}{8}+\frac{1}{2}\right)$

(ii) $\frac{-3}{8} \times\left(\frac{4}{7}+\frac{-11}{7}\right)$

(iii) $\frac{-2}{5} \times\left(\frac{3}{8}-25\right)$

Sol :

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Question 9

Find the multiplicative inverse, $i \cdot e_{\text {s }}$, the reciprocal of

(i) 6

(ii) $-23$

(iii) $\frac{11}{20}$

(iv) $\frac{-19}{16}$

(v) $\frac{11}{-5}$

(vi) $\frac{-7}{-8}$

(vii) $\frac{4}{5} \times \frac{15}{8}$

(viii) $0 \times \frac{2}{9}$

Sol :

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Question 10

Match the mathematical sentence in Column A with the property illustrated by the statement in Column B.

Column A	Column B
(i) $\frac{1}{3} \times 0=0$ (ii) $\frac{-2}{5} \times 1=\frac{-2}{5}$ (iii) $\frac{1}{4} \times 4=1$ (iv) $\frac{-6}{7} \times \frac{2}{3}=-\frac{4}{5}$ (v) $0 \times-\frac{7}{8}=\frac{-7}{8} \times 0$	(a) Property of 1 (b) Closure Property (c) Property of 0 (d) Commutative Property (e) Multiplicative Inverse

Sol :

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Question 11

Divide :

(i) $\frac{5}{9}$ by 15

(ii) $\frac{7}{18}$ by $\frac{-14}{51}$

(iii) $\frac{10}{33}$ by $\frac{2}{-11}$

(iv) $-18$ by $\frac{(-36)}{37}$

(v) $\frac{-24}{50}$ by $\frac{-4}{75}$

Sol :

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Question 12

Evaluate :

(i) $\left(\frac{5}{9} \div \frac{15}{36}\right) \div\left(-\frac{5}{6}\right)$

(ii) $\left(\frac{-3}{29} \div \frac{9}{87}\right) \div \frac{-1}{7}$

Sol :

Multiple Choice Questions (MCQs)

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Question 13

Which property of multiplication is not involved in the following :

$32 \times \frac{1}{4}=(8 \times 4) \times \frac{1}{4}=8 \times\left(4 \times \frac{1}{4}\right)=8 \times 1=8$

(a) Associative property

(b) Multiplicative inverse property

(c) Commutative property

(d) Property of 1

Sol :

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Question 14

$(-36) \times\left(\frac{-35}{76}\right) \times\left(\frac{19}{15}\right) \times\left(\frac{3}{-2}\right)^{-1}$ equals

(a) -64

(b) -14

(c) 14

(d) 64

Sol :

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Question 15

Which of the following statements is true ?

(a) $\frac{16}{21} \div\left(\frac{-4}{9} \div \frac{8}{9}\right)=\left(\frac{16}{21} \div \frac{-4}{5}\right) \div \frac{8}{9}$

(b) $\left(\frac{9}{20}-\frac{17}{40}\right) \div \frac{10}{3}=\left(\frac{9}{20} \div \frac{10}{3}\right)-\left(\frac{17}{40} \div \frac{10}{3}\right)$

(c) $0 \div-\frac{13}{14}=0$

Sol :

High Order Thinking Skills (HOTS)

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Question 16

Subtract the additive inverse of $\frac{5}{6}$ from the multiplicative inverse of $\frac{-5}{7} \times \frac{14}{15}$

Sol :