Ncert solutions mathematics class 8 Solutions for Chapter 1 rational numbers

Exercises in Chapter 1 rational numbers Grade 8

Exercise 1.1

Exercise 1.2

Exercise 1.2.2

Questions in Exercise 1.1

Which of the following is the multiplicative inverse of $\frac{1}{5}$ ?

State whether the given mathematical statement is TRUE or FALSE:

-(-x) = x for x = $\frac{11}{15}$

Which of the following is the multiplicative inverse of $-\frac{13}{19}$ ?

Fill in the blanks.

The reciprocal of − 5 is __________.

Which of the following is the multiplicative inverse of -1?

Name the property/identity used in:

$\frac{-19}{29}\times\frac{29}{-19}=1$

Which of the following is the multiplicative inverse of $\frac{-5}{8}\times\frac{-3}{7}$ ?

Which of the following is the multiplicative inverse of $-1\times\frac{-2}{5}$ ?

Which property allows you to compute

$\frac{1}{3}\times\left(6\times\frac{4}{3})\right)as\ \left(\frac{1}{3}\times6\right)\times\frac{4}{3}$ ?

Name the property/identity used in:

$-\frac{13}{17}\times\frac{-2}{7}=\frac{-2}{7}\times\frac{-13}{17}$

Name the property/identity used in:

$\frac{-4}{5}\times1=1\times\frac{-4}{5}=-\frac{4}{5}$

State whether the following statement is TRUE or FALSE:

$\frac{8}{9}$ the multiplication inverse of $-1\ \frac{1}{8}$

Multiply $\frac{6}{13}$ by the reciprocal of $-\frac{7}{16}$ and select the correct option.

State whether the following statement is TRUE or FALSE:

0.3 the multiplicative inverse of $3\ \frac{1}{3}$

Which of the following are rational numbers that are equal to their reciprocals?

Fill in the blanks.

Zero has __________ reciprocal.

Which of the following rational number is equal to its negative counterpart?

Which of the following is a rational number that does not have a reciprocal?

Fill in the blanks.

The reciprocal of a positive rational number is __________.

Fill in the blanks.

The product of two rational numbers is always a __________.

Fill in the blanks.

The numbers __________ and __________ are their own reciprocals.

Fill in the blanks:

Reciprocal of $\frac{1}{x}$ , where x ≠ 0 is _________.

Q1) Using appropriate properties find.

(i) $-\frac{2}{3}\ \times\ \frac{3}{5}\ +\ \frac{5}{2}-\frac{3}{5}\times\frac{1}{6}$

(ii) $\frac{2}{5}\times\left(-\frac{3}{7}\right)-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}$

$\begin{aligned} &\text { Using appropriate properties find. }\\ &\text { (i) }-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6} \end{aligned}$

$\text { (ii) } \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$

Write the additive inverse of each of the following.

$\frac{2}{8}$

$\frac{-5}{9}$

$\frac{-6}{-5}$

$\frac{2}{-9}$

Using appropriate properties find the value of:

$\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$

Which of the following is the additive inverse of $\frac{-6}{-5}$ ?

Using appropriate properties find the value of $-\frac{2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6}$

Which of the following is the multiplicative inverse of -13?

Which of the following is the additive inverse of $-\frac{5}{9}$ ?

Which of the following is the additive inverse of $\frac{2}{-9}$ ?

Which of the following is the additive inverse of $\frac{2}{8}$ ?

Which of the following is the additive inverse of $\frac{19}{-16}$ ?

State whether the given mathematical statement is TRUE or FALSE:

-(-x) = x for x = $-\frac{13}{17}$

Q2) Write the additive inverse of each of the following.

(i) $\frac{2}{8}$

(ii) $\frac{-5}{9}$

(iii) $\frac{-6}{-5}$

(iv) $\frac{2}{-9}$

(v) $\frac{19}{-6}$

Using appropriate properties find.

$\text { (i) }-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}$

$\text { (ii) } \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$

Write the additive inverse of each of the following.

$(i) \frac{2}{8} (iv) \frac{2}{-9} (ii) \frac{-5}{9} (iii) \frac{-6}{-5} (v) \frac{19}{-6}$

Q3) Verify that – (– x) = x for

(i) x= $\frac{11}{15}$

(ii) x= - $\frac{13}{17}$

Verify that : -(-x) = x for.

$(i) x=\frac{11}{15} (ii) x=-\frac{13}{17}$

Q4) Find the multiplicative inverse of the following.

(i) – 13

(ii) $\frac{-13}{19}$

(iii) $\frac{1}{5}$

(iv) $\frac{-5}{8}\times\ \frac{-3}{7}$

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

(vi) -1

Q5) Name the property under multiplication used in each of the following.

(i) $\frac{-4}{5}\times1=1\times\frac{-4}{5}=\ \frac{-4}{5}$

(ii) $\frac{-13}{17}\times\frac{-2}{7}=\ \frac{-2}{7}\times\ \frac{-13}{17}$

(iii) $\frac{-19}{29}\ \times\ \frac{29}{-19}=\ 1$

Find the multiplicative inverse of the following.

$(i) -13 (ii) \frac{-13}{19} (iii) \frac{1}{5} (iv) \frac{-5}{8} \times \frac{-3}{7} \quad(v)-1 \times \frac{-2}{5} \quad(v i)-1$

Name the property under multiplication used in each of the following

$(i) \frac{-4}{5} \times 1=1 \times \frac{-4}{5}=\frac{-4}{5} (ii) \frac{-13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17} (iii) \frac{-19}{29} \times \frac{29}{-19}=1$

Q6) Multiply $\frac{6}{13}$ by the reciprocal of $\frac{-7}{16}$

Q7) Tell what property allows you to compute $\frac{1}{3}\times\left(6\times\frac{4}{3}\right)\ as\ \left(\frac{1}{3}\ \times6\right)\ \times\frac{4}{3}$

$\text { Multiply } \frac{b}{13} \text { by the reciprocal of } \frac{-7}{16}$

Q8) Is $\frac{8}{9}$ the multiplicative inverse of $-1\frac{1}{8}$ ? Why or why not?

$\text { Tell what property allows you to compute } \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \text { as }\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}$

$\text { Is } \frac{8}{9} \text { the multiplicative inverse of }-1 \frac{1}{8} ? \text { Why or why not? }$

Q9) Is 0.3 the multiplicative inverse of $3\frac{1}{3}$ ? Why or Why not?

$\text { Is } 0.3 \text { the multiplicative inverse of } 3 \frac{1}{3} ? \text { Why or why not? }$

Q10) Write.

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

Write.

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocal.

(iii) The rational number that is equal to its negative.

Q11)Fill in the blanks.

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocals.

(iii) The reciprocal of – 5 is ______.

(iv) Reciprocal of $\frac{1}{x}$ , where x $\ne$ 0 is __________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

Fill in the blanks.

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocal

(iii) The reciprocal of – 5 is ________.

(iv) Reciprocal of 𝟏/𝒙, where x ≠ 0 is ________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

Questions in Exercise 1.2

Which is the rational number between $-\frac{2}{5}\ and\ \frac{1}{2}$ ?

Which is the rational number between $\frac{2}{3}\ and\ \frac{4}{5}$ ?

Which are the rational numbers greater than -2?

Which of the followig rational number is smaller than 2?

Observe the following number line. Which point corresponds to $-\frac{5}{6}$ ?

Observe the following number line. Which point corresponds to $\frac{7}{4}$ ?

Observe the following number line. Which point corresponds to $-\frac{9}{11}$ ?

Observe the following number line. Which point corresponds to $-\frac{5}{11}$ ?

Which is the rational number between $\frac{3}{5}\ and\ \frac{3}{4}$ ?

Which is the rational number between $\frac{1}{4}\ and\ \frac{1}{2}$ ?

Which is the rational number between $-\frac{3}{2}\ and\ \frac{5}{3}$ ?

Represent these numbers on the number line. $(i) \frac{7}{4} (ii) \frac{-5}{6}$

$\text { Represent } \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} \text { on the number line. }$

Write five rational numbers which are smaller than 2.

Find ten rational numbers between $\frac{-2}{5} \text { and } \frac{1}{2}$

Find five rational numbers between. $(i) \frac{2}{3} and \frac{4}{5} (ii) \frac{-3}{2} and \frac{5}{3} (iii) \frac{1}{4} and \frac{1}{2}$

Write five rational numbers greater than -2.

$\text { Find ten rational numbers between } \frac{3}{5} \text { and } \frac{3}{4}$

Questions in Exercise 1.2.2

Q1)Represent these numbers on the number line.

(i) $\frac{7}{4}$

(ii) $\frac{-5}{6}$

Q2) Represent $\frac{-2}{11},\ \frac{-5}{11},\ \frac{-9}{11}$ on the number line.

Q3)Write five rational numbers which are smaller than 2.

Q4) Find ten rational numbers between, $\frac{-2}{5}\ \&\ \frac{1}{2}$

Q5) Find five rational numbers between.

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

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

(iii) $\frac{1}{4}\ \&\ \frac{1}{2}$

Q6) Write five rational numbers greater than –2.

Q7) Find ten rational numbers between $\frac{3}{5}\ and\ \frac{3}{4}$

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Chapters in this book

Rational Numbers

Linear Equations in One Variable

Understanding Quadrilaterals

Practical Geometry

Data Handling

Squares and Square Roots

Cubes and Cube Roots

Comparing Quantities

Algebraic Expressions and Identities

Visualising Solid Shapes

Mensuration

Exponents and Powers

Direct and Inverse Proportions

Factorisation

Introduction to Graphs

Playing with Numbers