NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

Class 8 Mathematics by VP Classes

: NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

The document NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev is a part of the Course Class 8 Mathematics by VP Classes.

What is a Rational Number?

A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. 
  • Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero.
  • When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or repeating decimal. 

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

Let's have a look at NCERT Solutions of Rational Numbers!

Try These

Q1. Write the rational number for each point labelled with a letter.

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev 

Ans: 
(i) Here, the rational number for the point A is 1/5
The rational number for the point B is 4/5
The rational number for the point C is 5/5 or 1
The rational number for the point D is 8/5
The rational number for the point E is 9/5

(ii) The rational number for:
The point is F -2/6 or 1/3
The point G is -5/6
The point H is -7/6
The point I is -8/6 or -43
The point J is -11/6


Exercise 1.2

Q1. Represent these numbers on the number line.
(i) 7/4
(ii) -5/6

Ans: 
(i) To represent 7/4, we make 7 markings each of a distance equal to 1/4 on the right of 0. The 7th point represents the rational number 7/4 as shown in the figure.

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
The point A is 7/4
(ii) To represent (-5/6)  on the number line, we make 5 markings each of a distance equal to 1/6 on the left of 0. We consider the 5th point as shown in the figure.

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
The point B represents (-5/6)


Q2. Represent  -2/11, -5/11, -9/11 on the number line.
Ans: To represent -2/11, -5/11, -9/11 on a number line, we make 11 markings each being equal to distance 1/11  on the left of 0.

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

The point A represents (-2/11)
The point B represents (-5/11)
The point C represents (-9/11)


Q3. Write five rational numbers which are smaller than 2.
Ans: There can be unlimited rational numbers below 2.
Five of them are:
-1/2, -1, 0, 1/2, 1


Q4. Find ten rational numbers between -2/5 and 1/2
Ans: To convert -2/5 and 1/2 having the same denominators:

We have,
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

and,
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

∴ The rational numbers between 10/20 and -8/20

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

We can take any 10 of them.

∴ Ten rational numbers between -2/5 and 1/2 are:
 9/20, 8/20, 7/20, 6/20, 5/20, 4/20, 3/20, 2/20, 1/20, 0


Q5. Find five rational numbers between:
(i) 2/3 and 4/5
(ii) -3/2 and 5/3
(iii) 1/4 and 1/3

Ans: 
(i) Converting 2/3 and 4/5 having same denominators such that difference between the numerators is more than 5.

We have,
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

and,
 NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

Now, any five rational numbers between  40/60 and 48/60 are:
41/60, 42/60, 43/60, 44/60, 45/60

(ii) Converting -3/2 and 5/3  with same denominators
We have,
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
and,
 NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

∴ Five rational numbers between -3/2 and 5/3 are:
9/6, 8/6, 7/6, 0, -7/6.

(iii) Converting 1/4 and 1/2 to rational numbers with the same denominators, we have

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
∴ Five rational numbers between 1/4 and 1/2 are:
 15/32, 14/32, 13/32, 12/32, 11/32.


Q6. Write five rational numbers greater than -2.
Ans: Five rational numbers greater than -2 are:
-3/2, -1, -1/2, 0, 1/2.

Note: There can be countless rational numbers greater than -2.


Q7. Find ten rational numbers between 3/5 and 3/4
Ans: Converting 3/5 and 3/4 such that they have common denominators and their numerators have a difference of more than 10, i.e.

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
and,
NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

∴ Ten rational numbers between 3/5 and 3/4 are 

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

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