**Rational Numbers**

**Question 1.****List five rational numbers between(i)** -1 and 0

**(ii)**-2 and -1

**(iii)**and

**(iv)**– and

**Solution:**

**Question 2.****Write four more rational numbers in each of the following patterns :**

**Solution:**

**Question 3.****Give four rational numbers equivalent to(i)**

**(ii)**

**(iii)**

**Solution:**

**Question 4.****Draw the number line and represent the following rational numbers on it :(i)**

**(ii)**

**(iii)**

**(iv)**

**Solution:****(i)** In order to represent on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing 3 on the number line as shown. Now, divide the segment OP into four equal parts. Let A, B, C be the points of division so that OA = AB =BC = CP. By construction, OA is three- fourth of OP. So, A represents the rational number

**(ii)** In order to represent on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing -5 on it as shown. Now, divide the segment OP into eight equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. So, A represents the rational number .

**(iii)** In order to represent on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark a point P to represent -7 on the number line. Now,divide the segment OP into 4 equal parts. Let A, B, C be the points of division so that OA = AB = BC = CP. By construction, OA is one-fourth of OP. Therefore, A represents the rational number .

**(iv)** In order to represent on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P to represent 7 on the number line. Now, divide the segment OP into 8 equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. Therefore, A represents the rational number .

**Question 5.****The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.**

**Solution:**

**Question 6.****Which of the following pairs represents the same rational number ?**

**Solution:**

**Question 7.****Rewrite the following rational numbers in the simplest form :(i)**

**(ii)**

**(iii)**

**(iv)**

**Solution:**

**Question 8.****Fill in the boxes with the correct symbol out of >, <, and =.**

**Solution:**

**(i)**Clearly, is a negative rational number and is a positive rational number. We know that every negative rational number is less than every positive rational number. Therefore,

**(ii)**Clearly, denominators of the given rational numbers are positive. The denominators are 5 and 7. Their L.C.M. is 35. So, we first express each rational number with 35 as common denominator.

**(iii)** First- we write each one of the given rational numbers with positive denominator :

Clearly, denominator of is positive. The denominator of is negative. So, we express it with positive denominator as follows :

**(iv)** Clearly, the denominators of the given rational numbers are positive. The denominators are 5 and 4.

Their L.C.M. is 20. So, we first express each rational number with 20 as common denominator.

**(v)** First we write each one of the given rational numbers with positive denominator.

Clearly, denominator of is negative. So, expressing it with positive denominator as follows :

**(vi)** First we write each one of the given rational numbers with positive denominator.

**(vii)** Since every negative rational number is less than 0,

**Question 9.****Which is greater in each of the following :(i)** ,

**(ii)**,

**(iii)**,

**(iv)**,

**(v)**-3,-3

**Solution:**

**Question 10.****Write the following rational numbers in ascending order :**

**Solution:**