Ch 9 : Rational Numbers

                                                      Rational Numbers

 

Exercise 9.1

Question 1:

List five rational numbers between:
(i) − 1 and 0 (ii) − 2 and − 1
(iii) (iv)

Answer:

(i) −1 and 0

(ii) −2 and −1

Five rational numbers are

(iii)

Five rational numbers are

(iv)

Five rational numbers are



Question 2:

Write four more rational numbers in each of the following patterns:
(i) (ii)
(iii) (iv)

Answer:

(i)

It can be observed that the numerator is a multiple of 3 while the denominator is a multiple of 5 and as we increase them further, these multiples are increasing. Therefore, the next four rational numbers in this pattern are

(ii)

The next four rational numbers in this pattern are

(iii)

The next four rational numbers in this pattern are

(iv)

The next four rational numbers in this pattern are

Question 3:

Give four rational numbers equivalent to:
(i) (ii) (iii)

Answer:

(i)
Four rational numbers are

(ii)
Four rational numbers are

(iii)
Four rational numbers are



Question 4:

Draw the number line and represent the following rational numbers on it:
(i) (ii)
(iii) (iv)

Answer:

(i)
This fraction represents 3 parts out of 4 equal parts. Therefore, each space between two integers on number line must be divided into 4 equal parts.
can be represented as

(ii)
This fraction represents 5 parts out of 8 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 8 equal parts.
can be represented as

(iii)
This fraction represents 1 full part and 3 parts out of 4 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 4 equal parts.
can be represented as

(iv)
This fraction represents 7 parts out of 8 equal parts. Therefore, each space between two integers on number line must be divided into 8 equal parts.
can be represented as



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.

Answer:

Distance between U and T = 1 unit
It is divided into 3 equal parts.
TR = RS = SU =
R =
S =
Similarly,
AB = 1 unit
It is divided into 3 equal parts.
P =
Q =

Question 6:

Which of the following pairs represent the same rational number?
(i) (ii) (iii)
(iv) (v) (vi)
(vii)

Answer:

(i)

As, therefore, it does not represent same rational numbers.
(ii)


Therefore, it represents same rational numbers.
(iii)

Therefore, it represents same rational numbers.
(iv)

Therefore, it represents same rational numbers.
(v)

Therefore, it represents same rational numbers.
(vi)
As, therefore, it does not represent same rational numbers.
(vii)





Question 7:

Rewrite the following rational numbers in the simplest form:
(i) (ii)
(iii) (iv)

Answer:

(i)
(ii)
(iii)
(iv)

Question 8:

Fill in the boxes with the correct symbol out of >, <, and =
(i) (ii) (iii)
(iv) (v) (vi)
(vii)

Answer:

(i)

As −15 < 14,
Therefore,
(ii)

As −28 < −25
Therefore,
(iii) Here,
Therefore,
(iv)

As −32 > −35,
Therefore,
(v)

As −4 < −3,
Therefore,
(vi)
(vii)

Question 9:

Which is greater in each of the following?
(i) (ii) (iii)
(iv) (v)

Answer:

(i)
By converting these into like fractions,

As 15 > 4, therefore, is greater.
(ii)

(iii)

By converting these into like fractions,

(iv)

(v)

By converting these into like fractions,





Question 10:

Write the following rational numbers in ascending order:
(i) (ii) (iii)

Answer:

(i)
As −3 < −2 < −1,

(ii)
By converting these into like fractions,

As −12 < −3 < −2,

(iii)
By converting these into like fractions,

As −42 < −21 < −12,

  Exercise 9.2

Question 1:

Find the sum:
(i) (ii) (iii)
(iv) (v) (vi)
(vii)

 Answer:

(i)
(ii)
L.C.M of 3 and 5 is 15.

(iii)
L.C.M of 10 and 15 is 30.

(iv)
L.C.M of 11 and 9 is 99.

(v)
L.C.M of 19 and 57 is 57.

(vi)
(vii) =
L.C.M of 3 and 5 is 15.

Question 2:

Find
(i) (ii) (iii)
(iv) (v)

 Answer:

(i)
L.C.M of 24 and 36 is 72.

(ii)
L.C.M of 63 and 7 is 63.

(iii)
L.C.M of 13 and 15 is 195.

(iv)
L.C.M of 8 and 11 is 88.

(v)
L.C.M of 9 and 1 is 9.

  

Question 3:

Find the product:
(i) (ii) (iii)
(iv) (v) (vi)

 Answer:

  (i)
(ii)
(iii)
(iv)
(v)
(vi)


Question 4:

Find the value of:
(i) (ii) (iii)
(iv) (v) (vi)
(vii)

 Answer:

(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)