Exercise 1C
Q1 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers |
Chapter 1 | myhelper
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.
(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 :
Q2 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q3 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q4 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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.
Q5 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q6 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q7 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q8 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q9 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q10 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q11 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q12 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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)
Q13 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q14 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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 :
Q15 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
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)
Q16 | Ex-1C | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper
Question 16
Subtract the additive inverse of $\frac{5}{6}$ from the multiplicative
inverse of $\frac{-5}{7} \times \frac{14}{15}$
Sol :
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