Rational Numbers

Question 1.
Represent these numbers on the number line.
(i) $\frac { 7 }{ 4 }$
(ii) $\frac { -5 }{ 6 }$

Solution:
(i) For $\frac { 7 }{ 4 }$ , we make 7 markings of distance each on the right of zero and starting from 0. The seven marking is $\frac { 7 }{ 4 }$ .
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 13
The point P represents the rational number —.
(ii) For $\frac { -5 }{ 6 }$ , we make 5 markings of distance $\frac { 1 }{ 6 }$ each on the left of zero and starting from 0. The fifth marking $\frac { -5 }{ 6 }$ The point P represents the 6 rational number $\frac { -5 }{ 6 }$ .
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 14

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

Solution:
To represent $\frac { -2 }{ 11 } ,\frac { -5 }{ 11 } ,\frac { -9 }{ 11 }$ on a number line, draw a number line and mark a point O on it to represent zero. Now, mark a point P representing integers -1 on the left side of O on the number line.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 15
Divide the segment OP into eleven equal parts. Let A, B, C, D, E, F, G, H, I, J be the points of division so that OA=AB =BC = … = JP. By construction, OB is two-eleventh of OP so B represents $\frac { -2 }{ 11 }$ OE is five-eleventh of OP so E represents $\frac { -5 }{ 11 }$ and OI is nine-eleventh of OP so I represents $\frac { -9 }{ 11 }$ .

Question 3.
Write five rational numbers, which are smaller than 2.

Solution:
Five rational numbers less than 2 may be taken
$1,\frac { 1 }{ 2 } ,0,-1,\frac { -1 }{ 2 }$
(There can be many more such rational numbers.)

Question 4.
Find ten rational numbers between $\frac { -2 }{ 5 }$ and $\frac { 1 }{ 2 }$ .

Solution:
Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 16

Question 5.
Find five rational numbers between
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 17
Solution:
(i) Converting the given rational numbers with the same denominators

(ii) Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 19

(iii) Converting the given rational numbers with the same denominators
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 21

Question 6.
Write five rational numbers greater than – 2.

Solution:
Five rational numbers greater than -2 may be taken as
$-\frac { 3 }{ 2 } ,-1,\frac { -1 }{ 2 } ,0,\frac { 1 }{ 2 }$
There can be many more such rational numbers.