NCERT Solutions Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

NCERT Solutions Class 7 Mathematics
Chapter – 9 (Rational Numbers)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 9 Rational Numbers Exercise 9.1 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 9 Rational Numbers

• NCERT Solution Class 7 Maths Exercise – 9.2

Exercise – 9.1

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

Solution –

(i) -1 and 0
Converting each of rational numbers as a denominator 5 + 1 = 6,
we have
-1 = = and =

< < < < < <

or

-1 < < < < < < 0

Hence,
the Five Rational numbers between -1 and 0 are  , , , and   

(ii) -2 and -1
Converting each of rational numbers as a denominator 5 + 1 = 6,
We have
-2 = = and = = -1

< < < < < <

or

-2 < < < < < < -1

Hence,
the Five Rational numbers between -2 and -1 are , , , and  

(iii)  and
Converting each of the rational numbers as a denominator (L.C.M. of 5 and 3) = 15,
we have
=  = and =

Since there is only one integer i.e. -11 between -12 and -10, we have to find equivalent rational numbers.

= = and =

< < < < < <

or

< < < < < <

Hence,
the Five Rational numbers between   and are , , , and  

(iv) and

Converting each of the rational numbers in their equivalent rational numbers,
we have

= = and  =  =

Since there is only one integer i.e. 3 between 4, we have to find equivalent rational numbers.

=  = and = =

∴ < < < < < <

or

∴  < < < <  < <

Hence,
the Five Rational numbers between   and   are , , , and

 

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

(i)

(ii)

(iii)

(iv)

Solution –

(i)

In the above question, we can observe that the numerator and denominator are the multiples of 3 and 5.

=

Then, next four rational numbers in this pattern are,

=

=

(ii)

In the above question, we can observe that the numerator and denominator are the multiples of 1 and 4.

=

Then, next four rational numbers in this pattern are,

=

=

(iii)

In the above question, we can observe that the numerator and denominator are the multiples of 1 and 6.

=

Then, next four rational numbers in this pattern are,

=

=

(iv)

In the above question, we can observe that the numerator and denominator are the multiples of 2 and 3.

=

Then, next four rational numbers in this pattern are,

=

=

3. Give four rational numbers equivalent to:

(i)                            (ii)                          (iii)

Solution –

(i)

The four rational numbers equivalent to are,

=

=

(ii)

The four rational numbers equivalent to are,

=

=

(iii)

The four rational numbers equivalent to are,

=

=

4. Draw the number line and represent the following rational numbers on it:

(i)                  (ii)

(iii)           (iv)

Solution –

(i)

We know that   is greater than 0 and less than 1.
∴ it lies between 0 and 1. It can be represented on number line as,

(ii)

We know that is less than 0 and greater than -1.
∴ it lies between 0 and -1. It can be represented on number line as,

(iii)

Now above question can be written as, =  

We know that is Less than -1 and greater than -2.
∴ it lies between -1 and -2. It can be represented on number line as,

(iv)

We know that 7/8 is greater than 0 and less than 1.
∴ it lies between 0 and 1. It can be represented on number line as,

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 –
The distance between A and B = 1 unit
And it is divided into 3 equal parts = AP = PQ = QB =
P = 2 + = =

Q = 2 + = =

Similarly,
The distance between U and T = 1 unit
And it is divided into 3 equal parts = TR = RS = SU =
R = – 1 – = =

S = – 1 –  = =

6. Which of the following pairs represent the same rational number?

(i) and

(ii) and

(iii)   and

(iv) and

Solution –

(i) and

LCM of 21 and 9 = 189

⇒ and

⇒  and

Since – 63 ≠ 63,

So,   and   pair is not represents the same rational number.

(ii) and

LCM of 20 and 25 = 100

⇒ and

⇒  and  

⇒ and

Since – 80 = 80,

So,   and   pair is represents the same rational number.

(iii)   and

Here, we have the same numerator and denominator. So = and represents the same rational number.

(iv) and

LCM of 5 and 20 = 20

⇒ and

⇒   and  

Since – 12 = – 12,

So,   and pair is represents the same rational number.

(v) and

LCM of 5 and 15 = 15

⇒ and

⇒  and

⇒ and

Since 24 = 24,

So, and  pair is represents the same rational number.

(vi) and

LCM of 3 and 9 = 9

⇒ and

⇒  and

Since 3 ≠ -1,

So, and pair is not represents the same rational number.

(vii) and

⇒ = and

Since 5 ≠ -5,

So, and  pair is not represents the same rational number.

7. Rewrite the following rational numbers in the simplest form:

(i)                     (ii)

Solution –

(i)

⇒ =   [ HCF of 8 and 6 = 2]

(ii)

⇒ =   [ HCF of 25 and 45 = 5]

(iii)

⇒ =   [ HCF of 44 and 72 = 4]

(iv)

⇒  =   [ HCF of 8 and 10 = 2]

 

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

(i) [ ]                        (ii) [ ]             (iii)  [ ]

(iv) [ ]                  (v) [ ]              (vi) [ ]

(vii) 0 [ ]

Solution –

(i) [ ]
The LCM of the denominators 7 and 3 is 21
∴ = =

and

= =

Now, -15 < 14

So, <

Hence, [<]

(ii) [ ]

The LCM of the denominators 5 and 7 is 35

∴ = =

and

= =

Now, -28 < -25

So, <

Hence, [<]

(iii)  [ ]

can be simplified further,
Then,
             ——- [∵ Divide both numerator and denominator by 2]

So, =

Hence, [=]

(iv) [ ]    

The LCM of the denominators 5 and 4 is 20

∴ = =

and

= =

Now,  – 32 > – 35

So, >

Hence,  [>]

(v) [ ]      

The LCM of the denominators 3 and 4 is 12
∴ = =

and

= =

Now, – 4 < – 3

So, <

Hence, [<]

(vi) [ ]

Since, =

Hence, [=]

(vii) 0 [ ]

Since every negative rational number is less than 0.
We have  0 [>]

9. Which is greater in each of the following:

(i) ,                     (ii) ,            (iii) ,          

(iv) ,             (v) ,

Solution –

(i) ,
The LCM of the denominators 3 and 2 is 6

⇒ ,

⇒ ,

⇒ 4 < 15

So, <

∴ <

Hence, is greater.

(ii) ,
The LCM of the denominators 6 and 3 is 6

⇒ ,

⇒ ,

⇒ -5 > -8

So, >

∴ >

Hence, is greater.

(iii) ,
The LCM of the denominators 4 and 3 is 12

⇒ ,

⇒ ,

⇒ -9 < -8

So, <

∴ <

Hence, is greater.

(iv) ,

∴ Each Positive number is greater than its negative 

So, <

Hence is greater

(v) ,

⇒ ,

The LCM of the denominators 7 and 5 is 35

⇒ ,

⇒ ,

Now, -115 > -133

So, >

∴ >  

Hence, is greater.

10. Write the following rational numbers in ascending order:

(i) , ,                (ii) , ,                         (iii) , ,

Solution –

(i) , ,

The given rational numbers are in form of like fraction,
Hence,

(ii) , ,

LCM of 3, 9, and 3 is 9

⇒ , ,

⇒ , ,

Since  <  <  

Hence, < <

(iii) , ,

LCM of 7, 2, and 4 is 28

⇒ , ,

⇒ , ,

Since < <

Hence, < <