# Rational Numbers

## NCERT Exercise 1.2

Question 1: Represent these numbers on the number line.

(i) 7/4

(ii) -5/6

Question 2: Represent (-2)/(11), (-5)/(11), (-9)/(11) on the number line.

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

Solution: Some of the five rational numbers smaller than 2 can be written as follows:

1, 1/2, 0, -1/2, -1

Alternate method:

Given number 2 can be written as 6/3

And thus, some of the five rational numbers smaller than 2 can be written as follows:

5/3, 4/3, 1, 2/3, 1/3

Question 4: Find ten rational numbers between -2/5 and 1/2

Solution: Given numbers can be written as (-2xx2)/(5xx2) and (1xx5)/(2xx5)

=(-4)/(10) and (5)/(10)

Thus, some five rational numbers between given rational numbers may be (-3)/(10), (-2)/(10), (-1)/(10), 0 and (1)/(10)

Question 5: Find five rational numbers between

(i) 2/3 and 4/5

Solution: Given numbers can be written as (2xx15)/(3xx15) and (4xx9)/(5xx9)

=(30)/(45) and (36)/(45)

Thus, some of the five rational numbers between given rational numbers will be (31)/(45), (32)/(45), (33)/(45), and (35)/(45)

(ii) -3/2 and 5/3

Solution: Given numbers can be written as (-3xx3)/(2xx3) and (5xx2)/(3xx2)

=-9/6 and (10)/(6)

Thus, some of the five rational numbers between given rational numbers will be -8/6, -7/6, -1, -5/6, -4/6

Alternate method:

Some of the five rational numbers between given rational numbers -3/2 and 5/3 will be -2/2 i.e. -1, -1/2, 0, 1/2 and 1

Question 6: Write five rational numbers greater than – 2

Solution: Some of the five rational numbers greater than – 2 will be -1, 0, 1, 2 and 3

Question 7: Find ten rational numbers between 3/5 and 3/4

Solution: Given numbers can be written as (3xx20)/(5xx20) and (3xx25)/(4xx25)

=(60)/(100) and (75)/(100)

Thus, some of the ten rational numbers between given rational numbers will be (61)/(100), (62)/(100), (63)/(100), (64)/(100), (65)/(100), (66)/(100), (67)/(100), (68)/(100), (69)/(100), (70)/(100)