# 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)`