Get NCERT Solutions for Class 7 Mathematics: Chapter 9 – Rational Numbers. There are two exercises in this chapter and here we have provided solutions of all the questions of both the exercises. These solutions are based on the latest edition of Class 7 Maths NCERT textbook.

__NCERT Book for Class 7 Mathematics (PDF): Hindi & English__

**NCERT Solutions for Class 7 Mathematics: Chapter 9 – Rational Numbers**

**EXERCISE 9.1**

**1. **List five rational numbers between:

(i) –1 and 0

(ii) –2 and –1

(iii) - 4/5 and -2/3

(iv) 1/2 and 2/3

**Solutions:**

(i) −1 and 0

-2/3, -1/2, -2/5, -1/3, -2/7

(ii) −2 and −1

⇒ -2 = -12/6 & -1 = -6/6

Five rational numbers between −2 and −1:

-7/6, -8/6, -9/6, -10/6, -11/6

(iii) -4/5 and -2/3

⇒ -4/5 = (-4 × 9)/(5 × 9) = -36/45 & -2/3 = (-2 × 15)/(3 × 15) = -30/45

Five rational numbers between -4/5 and -2/3:

-35/45, -34/45, -33/45, -35/45, -31/45

(iv) 1/2 and 2/3

⇒ 1/2 = (1 × 18)/(2 × 18) = 18/36 & 2/3 = (2 × 12)/(3 × 12) = 24/36

Five rational numbers between 1/2 and 2/3:

19/36, 20/36, 21/36, 22/36, 23/36

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

(i) -3/5, -6/10, -9/15, -12/20, …

(ii) -1/4, -2/8, -3/12, …

(iii) -1/6, 2/-12, 3/-18, 4/-24, ……

(iv) -2/3, 2/-3, 4/-6, 6/-9, ……

**Solutions:**

(i) -3/5 -6/10 -9/15 -12/20,….

Can be rewritten as

-3/5, (-3 × 2)/(5 × 2), (-3 × 3)/(5 × 3), (-3 × 4)/(5 × 4)……

Based on the above pattern, the next four rational numbers are

(-3 × 5)/(5 × 5), (-3 × 6)/(5 × 6), (-3 × 7)/(5 × 7), (-3 × 8)/(5 × 8)….

-15/25, -18/30, -21/35, -24/40 ….

(ii) -1/4, -2/8, -3/12….

Can be rewritten as

-1/4, (-1 × 2)/(4 × 2), (-1 × 3)/(4 × 3) ….

Based on the above pattern, the next four rational numbers are

(-1 × 4)/(4 × 4), (-1 × 5)/(4 × 5), (-1 × 6)/(4 × 6), (-1 × 7)/(4 × 7)…..

-4/16, -5/20, -6/24, -7/28…

(iii) -1/6, 2/-12, 3/-18, 4/-24, ……

Can be rewritten as

-1/6, (1 × 2)/(-6 × 2), (1 × 3)/(-6 × 3), (1 × 4)/(-6 × 4)….

Based on the above pattern, the next four rational numbers are

(1 × 5)/(-6 × 5), (1 × 6)/(-6 × 6), (1 × 7)/(-6 × 7), (1 × 8)/(-6 × 8)….

5/-30, 6/-36, 7/-42, 8/-48 ….

(iv) -2/3, 2/-3, 4/-6, 6/-9, ……

Can be rewritten as

-2/3, 2/-3, (2 × 2)/(-3 × 2), (2 × 3)/(-3 × 3)…..

Based on the above pattern, the next four rational numbers are

(2 × 4)/(-3 × 4), (2 × 5)/(-3 × 5), (2 × 6)/(-3 × 6), (2 × 7)/(-3 × 7)….

8/-12, 10/-15, 12/-18, 14/-21 …..

**3. **Give four rational numbers equivalent to:

(i) -2/7

(ii) 5/-3

(iii) 4/9

**Solutions:**

(i) -2/7

Four rational numbers are

(-2 × 2)/(7 × 2), (-2 × 3)/(7 × 3), (-2 × 4)/(7 × 4), (-2 × 5)/(7 × 5)

-4/14, -6/21, -8/28, -10/35

(ii) 5/-3

Four rational numbers are

(5 × 2)/(-3 × 2), (5 × 3)/(-3 × 3), (5 × 4)/(-3 × 4), (5 × 5)/(-3 × 5)

10/-6, 15/-9, 20/-12, 25/-15

(iii) 4/9

Four rational numbers are

(4 × 2)/(9 × 2), (4 × 3)/(9 × 3), (4 × 4)/(9 × 4), (4 × 5)/(9 × 5)

8/18, 12/27, 16/36, 20/45

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

(i) 3/4

(ii) -5/8

(iii) -7/4

(iv) 7/8

**Solutions:**

**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.

**Solutions:**

P represents 7/3, Q represents 8/3, R represents -4/3, S represents -5/3.

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

(i) -7/21 and 3/9

(ii) -16/20 and 20/-25

(iii) -2/-3 and 2/3

(iv) -3/5 and -12/20

(v) 8/-5 and -24/15

(vi) 1/3 and -1/9

(vii) -5/-9 and 5/-9

**Solutions:**

(i) -7/21 and 3/9

⇒ -7/21 = -1/3 and 3/9 = 1/3

Clearly, -1/3 ≠ 1/3.

(ii) -16/20 and 20/-25

⇒-16/20 = -4/5 and -20/25 = -4/5

Clearly, it represents same rational numbers.

(iii) -2/-3 and 2/3

⇒ -2/-3 = 2/3

Clearly, it represents same rational numbers.

(iv) -3/5 and -12/20

-12/20 = -3/5

Clearly, it represents same rational numbers.

(v) 8/-5 and -24/15

⇒ -24/15 = -8/5 and 8/-5 = -8/5

Clearly, it represents same rational numbers.

(vi) 1/3 and -1/9

Here, 1/3 ≠ -1/9

Clearly, it does not represent same rational numbers.

(vii) -5/-9 and 5/-9

⇒ -5/-9 = 5/9

Since, 5/9 ≠ -5/9

Clearly, it does not represent same rational numbers.

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

(i) -8/6

(ii) 25/45

(iii) -44/72

(iv) -8/10

**Solutions:**

(i) -8/6 = (-4 × 2)/(3 × 2) = -4/3

(ii) 25/45 = (5 × 5)/(9 × 5) = 5/9

(iii) -44/72 = (-11 × 4)/(18 × 4) = -11/18

(iv) -8/10 = (-4 × 2)/(5 × 2) = -4/5

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

**Solutions:**

(i) We have,

-5/7 = (-5 × 3)/(7 × 3) = -15/21 and 2/3 = (2 × 7)/(3 × 7) = 14/21

Now, −15 < 14,

So, (-5/7) < (2/3)

(ii) We have,

-4/5 = (-4 × 7)/(5 × 7) = -28/35 and -5/7 = (-5 × 5)/(7 × 5) = -25/35

Now, −28 < −25

So, (-4/5) < (-5/7)

(iii) We have,

14/-16 = (7 × 2)/(-8 × 2) = 7/-8 = -7/8

So, (-7/8) = (14/-16)

(iv) We have,

-8/5 = (-8 × 4)/(5 × 4) = -32/20 and -7/4 = (-7 × 5)/(4 × 5) = -35/20

Now, −32 > −35,

So, -8/5 > (-7/4)

(v) We have,

-1/3 = (-1 × 4)/(3 × 4) = -4/12 and -1/4 = (-1 × 3)/(4 × 3) = -3/12

Now, −4 < −3,

So, (-1/3) < (-1/4)

(vi) (5/-11) = (-5/11)

(vii) 0 > (-7/6)

**9. **Which is greater in each of the following:

(i) 2/3, 5/2

(ii) -5/6, -4/3

(iii) -3/4, 2/-3

(iv) -1/4, 1/4

(v) -3 2/7, -3 4/5

**Solutions:**

(i) 2/3 and 5/2 can be rewritten as

2/3 = (2 × 2)/(3 × 2) = 4/6 and 5/2 = (5 × 3)/(2 × 3) = 15/6

Now, 15 > 4, so, 5/2 is greater.

(ii) -4/3 can be rewritten as

-4/3 = (-4 × 2)/(3 × 2) = -8/6

Now, -5 > - 8, so, -5/6 is greater.

(iii) -3/4 and 2/-3 can be rewritten as

-3/4 = (-3 × 3)/(4 × 3) = -9/12 and -2/3 = (-2 × 4)/(3 × 4) = -8/12

Now, -8 > - 9, so, -2/7 is greater.

(iv) -1/4, 1/4

Clearly, 1/4 > -1/4

(v) We have, -23/7 and -19/5. These can be rewritten as

-23/7 = (-23 × 5)/(7 × 5) = -115/35 and -19/5 = (-19 × 7)/(5 × 7) = -133/35

As -115 > - 133, first number is greater.

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

(i) -3/5, -2/5, -1/5

(ii) 1/3, -2/9, -4/3

(iii) -3/7, -3/2, -3/4

**Solutions:**

(i) -3/5, -2/5, -1/5

Here, −3 < −2 < −1,

So, -3/5 < -2/5 < -1/5

(ii) 1/3, -2/9, -4/3 can be rewritten as

⇒ (-1 × 3)/(3 × 3), -2/9, (-4 × 3)/(3 × 3)

⇒ -3/9, -2/9, -12/9

Now, −12 < −3 < −2,

So, -4/3 < -1/3 < -2/9

(iii) -3/7, -3/2, -3/4 can be rewritten as

⇒ (-3 × 4)/(7 × 4), (-3 × 14)/(2 × 14), (-3 × 7)/(4 × 7)

⇒ -12/28, -42/28, -21/28

Now −42 < −21 < −12,

So, -3/2 < -3/4 < -3/7

__EXERCISE 9.2__

**1. **Find the sum:

**Solutions:**

(i) (4/5) + (-11/4) = (4/5) – (11/4) = (16 - 55)/20 = -39/20

(ii) (5/3) + (3/5)

(5/3) + (3/5) = (5 × 5)/(3 × 5) + (3 × 3)/(5 × 3) = (25/15) + (9/15) = (25 + 9)/15 = 34/15

(iii) (-9/10) + (22/15)

(-9/10) + (22/15) = (-9 × 3)/(10 × 3) + (22 × 2)/(15 × 2) = (-27/30) + (44/30) = (-27 + 44)/30 = 17/30

(iv) -3/-11 + (5/9) = (3/11) + (5/9)

(3/11) + (5/9) = (3 × 9)/(11 × 9) + (5 × 11)/(9 × 11) = (27/99) + (55/99) = (27 + 55)/99 = 82/99

(v) (-8/19) + [(-2)/57] = (-8/19) – (2/57)

(-8/19) – (2/57) = (8 × 3)/(19 × 3) – (2/57) = (-24/57) – (2/57) = (-24 - 2)/57 = -26/57

(vi) (-2/3) + 0 = -2/3

(vii) (-7/3) + (23/5) = (-7 × 5)/(3 × 5) + (23 × 3)/(5 × 3) = (-35/15) + (69/15) = (-35 + 69)/15 = 34/15

**2. **Find

**Solutions: **

(i) (7/24) – (17/36)

(7/24) – (17/36) = (7 × 3)/(24 × 3) – (17 × 2)/(36 × 2) = (21/72) – (34//72) = (21 - 34)/72 = -13/72

(ii) (5/63) – [(-6)/12] = (5/63) + (2/7)

(5/63) + (2/7) = (5/63) + (2 × 9)/(7 × 9) = (5/63) + (18/63) = (5 + 18)/63 = 23/63

(iii) (-6/13) – (-7/15) = (-6/13) + (7/15) = (-6x15)/195 + (7x13)/195 = 1/195

(iv) (-3/8) – (7/11)

(-3/8) – (7/11) = (-33-56)/88 = -89/88

(v) (-19/9) – (6/1) = (-19/9) – (6 × 9)/(1 × 9) = (-19/1) – (54/9) = (-19 - 54)/9 = -73/9

**3. **Find the product:

**Solutions:**

(i) (9/2) ×** **(-7/4) = -63/8

(ii) (3/10) × (-9) = -27/10

(iii) (-6/5) × (9/11) = -54/55

(iv) (3/7) × (-2/5) = -6/35

(v) (3/11) × (2/5) = 6/55

(vi) (3/-5) × (-5/3) = 1

**4. **Find the value of:

**Solutions:**

(i) -4 ÷ (2/3) = -4 × (3/2) = -6

(ii) (-3/5) ÷ 2 = (-3/5) × (1/2) = -3/10

(iii) (-4/5) ÷ (-3) = (-4/5) × (1/-3) = 4/15

(iv) (-1)/8 ÷ (3/4) = (-1/8) × (4/3) = -1/6

(v) (-2/13) ÷ (1/7) = (-2/13) ×** **7 = -14/13

(vi) (-7/12) ÷ (-2/13) = (-7/12) × (13/-2) = 91/24

(vii) (3/13) ÷ (-4/65) = (3/13) × (65/-4) =-15/4