Questions and Solutions for NCERT Class 8th Mathematics Chapter 1 -Exercise 1.1

Questions and Solutions for NCERT Class 8 Mathematics Chapter 1 Exercise 1.1, Stepwise Solutions for NCERT Class 8th Mathematics, Solutions for NCERT Class 8th Mathematics Chapter 1,  Class 8th Mathematics Chapter 1: Rational Numbers, Class 8th Maths solutions, ncert class 8th class solutions, cbse 8th class solutions, 8th class maths solutions, 8th class maths solutions pdf, 8th maths solution, ncert solutions, download ncert maths solutions

NCERT Class 8th Mathematics Chapter 1 – Rational Numbers Solutions Exercise 1.1 Solutions

                                                                       Exercise 1.1
Q1. Using appropriate properties find:
(i)

$–\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}–\frac{3}{5}\times \frac{1}{6}$

(ii)

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

Sol:(i)

$–\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}–\frac{3}{5}\times \frac{1}{6}$

=

$–\frac{2}{3}\times \frac{3}{5}–\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$

(Using Commutativity of rationa numbers)
=

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

( By Distributivity)
=

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

=

$\left(–\frac{3}{5}\right)\times \left(\frac{5}{6}\right)+\frac{5}{2}$

=

$\frac{–1}{2}+\frac{5}{2}$

=

$\frac{4}{2}$

= 2
(ii)

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

(Using Commutativity of rational numbers)
=

$\frac{2}{5}\times \left(\frac{–3}{7}+\frac{1}{14}\right)–\frac{1}{4}$

( By Distributivity)
=

$\frac{2}{5}\times \left(\frac{–3\times 2+1}{14}\right)–\frac{1}{4}$

=

$\frac{2}{5}\times \left(\frac{–5}{14}\right)–\frac{1}{4}$

=

$\frac{–1}{7}–\frac{1}{4}$

=

$\frac{–4–7}{28}$

=

$\frac{–11}{28}$

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)

$\frac{19}{–6}$

Sol: (i)

$\frac{2}{8}$

Additive inverse =

$\frac{–2}{8}$

(ii)

$\frac{–5}{9}$

Additive inverse =

$\frac{5}{9}$

(iii)

$\frac{–6}{–5}$

Additive inverse =

$\frac{–6}{5}$

(iv)

$\frac{2}{–9}$

Additive inverse =

$\frac{2}{9}$

(v)

$\frac{19}{–6}$

Additive inverse =

$\frac{19}{6}$

Q3.Verify that: –(-x)=x for
(i) x=

$\frac{11}{15}$

(ii) x=

$\frac{–13}{17}$

Sol: (i) x=

$\frac{11}{15}$

The additive inverse of x=

$\frac{11}{15}$

is -x=

$\frac{–11}{15}$

as

$\frac{11}{15}+\left(–\frac{11}{15}\right)$

=0
This equality

$\frac{11}{15}+\left(–\frac{11}{15}\right)$

=0 represent that the additive inverse of

$\frac{–11}{15}$

is

$\frac{11}{15}$

or it can be said that
-(

$\frac{–11}{15}$

)=

$\frac{11}{15}$

i.e, -(-x)=x
(ii) x=

$\frac{–13}{17}$

The additive inverse of x=

$\frac{–13}{17}$

is -x=

$\frac{13}{17}$

as

$\frac{–13}{17}+\frac{13}{17}$

=0
This equality

$\frac{–13}{17}+\frac{13}{17}$

=0 represent that the additive inverse of

$\frac{13}{17}$

is

$\frac{–13}{17}$

or it can be said that
-(

$\frac{–13}{17}$

)=

$\frac{13}{17}$

i.e, -(-x)=x
Q4. Write the Multiplicative inverse of each of the following :
(i) -13 (ii)

$\frac{–13}{19}$

(iii)

$\frac{1}{5}$

(iv)

$\frac{–5}{8}\times \frac{–3}{7}$

(v)

$\frac{15}{56}$ $–1\times \frac{–2}{5}$

(vi) -1

Sol: (i) -13
Multiplicative inverse =

$\frac{1}{–13}$

(ii)

$\frac{–13}{19}$

Multiplicative inverse=

$\frac{–19}{13}$

(iii)

$\frac{1}{5}$

Multiplicative inverse= 5
(iv)

$\frac{–5}{8}\times \frac{–3}{7}$

=

$\frac{15}{56}$

Multiplicative inverse=

$\frac{56}{15}$

(v)

$–1\times \frac{–2}{5}$

=

$\frac{2}{5}$

Multiplicative inverse=

$\frac{5}{2}$

(vi) -1
Multiplicative inverse= -1
Q5. Name the property under multiplication used in each of the following:
(i)

$\frac{–4}{5}\times 1=1\times \frac{{\displaystyle –4}}{{\displaystyle 5}}=\frac{{\displaystyle –4}}{{\displaystyle 5}}$

(ii)

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

(iii)

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

Sol: (i)

$\frac{–4}{5}\times 1=1\times \frac{{\displaystyle –4}}{{\displaystyle 5}}=\frac{{\displaystyle –4}}{{\displaystyle 5}}$

1 is the Multiplicative Identity.
(ii)

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

Commutativity Property
(iii)

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

Multipicative inverse
Q6. Multiply

$\frac{6}{13}$

by the reciprocal of

$\frac{–7}{16}$

.
Sol:

$\frac{6}{13}$

×(Reciprocal of

$\frac{–7}{16}$

=

$\frac{6}{13}$

×(

$\frac{–16}{7}$

)
=

$\frac{–96}{91}$

Q7.Tell what property allows you to compute

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

.

Sol: Associativity Property
Q8. I s

$\frac{8}{9}$

the multiplicative inverse of

$–1\frac{1}{8}$

? Why or why not?
Sol: If it is the multipilicative inverse , then the product should be 1.
However, here the product is not 1 as
=

$\frac{8}{9}$

×(

$–1\frac{1}{8}$

)

=

$\frac{8}{9}$

×(

$\frac{–9}{8}$

)
=-1≠1
Q9. Is 0.3 the multiplicative inverse of

$3\frac{1}{3}$

? Why or why not?
Sol: If it is the multipilicative inverse , then the product should be 1.
=0.3×

$3\frac{1}{3}$

=

$\frac{3}{10}$

×

$\frac{10}{3}$

= 1
Here the product is 1 . Hence 0.3 is the multiplicative inverse of

$3\frac{1}{3}$

.
Q10.Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational number that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Sol:
(i) 0 is rational number but its reciprocal is not defined.
(ii) 1 and -1 are rational number that are equal to their reciprocals.
(iii) 0 is 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≠0 is___.
(v)The product of two rational numbers is always a ____.
(vi)The reciprocal of a positive rational number is ____.
Sol:
(i) No
(ii) 1,-1
(iii)

$\frac{–1}{5}$

(iv) x
(v)Rational number
(vi) Positive rational number

Rational Numbers Solutions Exercise 1.2 Solutions

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• NCERT Class 8th Mathematics Solutions – Detailed Chapter Wise Solution