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**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

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

We may take any four of these.

**Ques 2:** Find any seven rational numbers between

**Ans:** Let us convert the given rational numbers having the same denominators.

We have

and

Now, the rational numbers between

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

Rational number between 1/5 and 7/20

Rational number between 7/20 and 1/2

Thus, the three rational numbers lie between .

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

**Ques 4: ****Write the rational number for each point labelled with a letter.**

**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.

The point A is 7/4

(ii) To represent 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.

The point B represents

**Ques 2: ****Represent on the number line.**

**Ans: **To represent on a number line, we make 11 markings each being equal to distance on the left of 0.

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:

**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

and

∴ The rational numbers between

We can take any 10 of them.

∴ Ten rational numbers between

(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

and

Now, any five rational numbers between

(ii) Converting with same denominators, we have

and

∴ Five rational numbers between

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

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

**Ans: **Five rational numbers greater than **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.

and

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

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