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

Class 8 Mathematics by Full Circle

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Class 8 : 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 Class 8 Course Class 8 Mathematics by Full Circle.
All you need of Class 8 at this link: Class 8

RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS

There can be indefinite number of rational numbers between two given rational numbers.
Ques 1: Write four rational numbers between 0 and –2.

Ans: We can write 0 as 0/10

We can write (–2) as  NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev 

Thus, the following rational numbers are between 0 and –2 are

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

We may take any four of these.

Ques 2: Find any seven rational numbers between NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

Ans: Let us convert the given rational numbers 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

Now, the rational numbers between NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

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

We can have any seven of these.

Note: Between any two integers, we need not necessarily get an integer but there will always lie a rational number. So, we can use the idea of mean to find the rational numbers between any two given rational numbers.

Ques 3: Find three rational numbers between  1/2 and 1/5

Ans: Rational number between  1/2 and 1/5

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

Rational number between 1/5 and 7/20

NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
Rational number between 7/20 and 1/2 

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

Thus, the three rational numbers NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev  lie between NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev.

REMEMBER

Even between two consecutive integers, there are countless rational numbers.

Ques 4: 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 

Ques 1: 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 NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev  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 NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

Ques 2: Represent  NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev on the number line.

Ans: To represent  NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev  on a number line, we make 11 markings each being equal to distance NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev  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)

Ques 3: Write five rational numbers which are smaller than 2.

Ans: There can be unlimited rational numbers below 2. Five of them are:

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

Ques 4: 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

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

∴ The rational numbers between NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

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

We can take any 10 of them.

∴ Ten rational numbers between NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

(i) 9/20  
(ii) 8/20
(iii) 7/20  
(iv) 6/20
(v) 5/20
(vi) 4/20
(vii) 3/20
(viii) 2/20
(ix) 1/20
(x) 0

Ques 5: 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  NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev

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

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

(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

Ques 6: Write five rational numbers greater than –2.

Ans: Five rational numbers greater than  NCERT Solutions(Part- 2)- Rational Numbers Class 8 Notes | EduRev
Note: There can be many rational numbers greater than –2.

Ques 7: 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, difference of more than 10, i.e.

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