## Chapter 9 Rational Numbers Exercise 9.1

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

= -1/1 and 0/1

= -1/1 x 10/10 = -10/10

= 0/1 x 10/10 = 0/10

= -9/10, -8/10, -7/10, -6/10, -5/10

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

Answer:

Answer:

= -2/1 and -1/1

= -2/1 x 10/10 = -20/10

= -1/1 x 10/10 = -10/10

= -19/10, -18/10, -17/10, -16/10, -15/10

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

Answer:

Answer:

= -4/5 and -2/3

= -4/5 x 10/10 = -40/50

= 0/1 x 10/10 = 0/10

= -9/10, -8/10, -7/10, -6/10, -5/10

**(iv) -1/2 and 2/3**

Answer:

Answer:

LCM of 2, 3 = 6

= -1/2 x 3/3 = -3/6

= 2/3 x 2/2 = 4/6

= -3/6 x 10/10 = -30/60

= 4/6 x 10/10 = 40/60

= -29/60, -28/60, -27/60, -26/60, -25/60

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

(i) -3/5, -6/10, -9/15, -12/20, …..

Answer:

(i) -3/5, -6/10, -9/15, -12/20, …..

Answer:

The numerator and denominator are multiples of 3, 5.

= -3 × 1/5 × 1 = -3/5

= -3 × 2/5 × 2 = -6/10

= -3 × 3/5 × 3 = -9/15

= -3 × 4/5 × 4 = -12/20

Next four rational numbers:

= -3 × 5/5 × 5 = -15/25

= -3 × 6/5 × 6 = -18/30

= -3 × 7/5 × 7 = -21/35

= -3 × 8/5 × 8 = -24/40

**(ii) -1/4, -2/8, -3/12, …..**

Answer:

Answer:

The numerator and denominator are multiples of 1, 4.

= -1 × 1/4 × 1 = -1/4

= -1 × 2/4 × 2 = -2/8

= -1 × 3/1 × 3 = -3/12

Next four rational numbers:

= -1 × 4/4 × 4 = -4/16

= -1 × 5/4 × 5 = -5/20

= -1 × 6/4 × 6 = -6/24

= -1 × 7/4 × 7 = -7/28

**(iii) -1/6, 2/-12, 3/-18, 4/-24 …..**

Answer:

Answer:

The numerator and denominator are multiples of 1, 6.

= -1 × 1/6 × 1 = -1/6

= 1 × 2/-6 × 2 = 2/-12

= 1 × 3/-6 × 3 = 3/-18

= 1 × 4/-6 × 4 = 4/-24

Next four rational numbers:

= 1 × 5/-6 × 5 = 5/-30

= 1 × 6/-6 × 6 = 6/-36

= 1 × 7/-6 × 7 = 7/-42

= 1 × 8/-6 × 8 = 8/-48

**(iv) -2/3, 2/-3, 4/-6, 6/-9 …..**

Answer:

Answer:

The numerator and denominator are multiples of 2, 3.

= -2 × 1/3 × 1 = -2/3

= 2 × 1/-3 × 1 = 2/-3

= 2 × 2/-3 × 2 = 4/-6

= 2 × 3/-3 × 3 = 6/-9

Next four rational numbers:

= 2 × 4/-3 × 4 = 8/-12

= 2 × 5/-3 × 5 = 10/-15

= 2 × 6/-3 × 6 = 12/-18

= 2 × 7/-3 × 7 = 14/-21

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

(i) -2/7

Answer:

(i) -2/7

Answer:

Four rational numbers equivalent to -2/7:

= -2 × 2/7 × 2 = -4/14

= -2 × 3/7 × 3 = -6/21

= -2 × 4/7 × 4 = -8/28

= -2 × 5/7× 5 = -10/35

**(ii) 5/-3**

Answer:

Answer:

Four rational numbers equivalent to 5/-3:

= 5 × 2/-3 × 2 = 10/-6

= 5 × 3/-3 × 3 = 15/-9

= 5 × 4/-3 × 4 = 20/-12

= 5 × 5/-3× 5 = 25/-15

**(iii) 4/9**

Answer:

Answer:

Four rational numbers equivalent to 4/9:

= 4 × 2/9 × 2 = 8/18

= 4 × 3/9 × 3 = 12/27

= 4 × 4/9 × 4 = 16/36

= 4 × 5/9× 5 = 20/45

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

(i) 3/4

Answer:

(i) 3/4

Answer:

**(ii) -5/8Answer:**

**(iii) -7/4Answer:**

**(iv) 7/8Answer:**

**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:**

The distance between A and B = 1 unit

= AP = PQ = QB = 1/3

= P = 2 + (1/3)

= (6 + 1)/ 3

= 7/3

Q = 2 + (2/3)

= (6 + 2)/ 3

= 8/3

The distance between U and T = 1 unit

= TR = RS = SU = 1/3

R = -1 - (1/3)

= (- 3 - 1)/ 3

= -4/3

S = -1 - (2/3)

= – 3 - 2)/ 3

= -5/3**Question 6: Which of the following pairs represent the same rational number?(i) (-7/21) and (3/9)Answer:**

= -7/21 = 3/9

= -1/3 = 1/3

Since, -1/3 ≠ 1/3

Therefore, -7/21 ≠ 3/9

So, the given pair doesn't represents the same rational number.

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

Answer:

Answer:

= -16/20 = 20/-25

= -4/5 = 4/-5

Since, -4/5 = -4/5

Therefore, -16/20 = 20/-25

So, the given pair is represents the same rational number.

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

Answer:

Answer:

= -2/-3 = 2/3

= 2/3= 2/3

Since, 2/3 = 2/3

Therefore, -2/-3 = 2/3

So, the given pair is represents the same rational number.

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

Answer:

Answer:

= -3/5 = – 12/20

= -3/5 = -3/5

Since, -3/5 = -3/5

Therefore, -3/5= -12/20

So, the given pair is represents the same rational number.

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

Answer:

Answer:

= 8/-5 = -24/15

= 8/-5 = -8/5

Since, -8/5 = -8/5

Therefore, 8/-5 = -24/15

So, the given pair is represents the same rational number.

**(vi) (1/3) and (-1/9)**

Answer:

Answer:

= 1/3 = -1/9

Since, 1/3 ≠ -1/9

Therefore, 1/3 ≠ -1/9

So, the given pair doesn't represents the same rational number.

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

**Answer:**

= -5/-9 = 5/-9

Since, 5/9 ≠ -5/9

Therefore, -5/-9 ≠ 5/-9

So, the given pair doesn't represents the same rational number.

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

(i) -8/6

Answer:-4/3

(i) -8/6

Answer:

**(ii) 25/45**

Answer:5/9

Answer:

**(iii) -44/72**

Answer:-11/18

Answer:

**(iv) -8/10**

Answer:-4/5

Answer:

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

(i) -5/7 [ ] 2/3

Answer:

(i) -5/7 [ ] 2/3

Answer:

LCM of 3, 7 = 21

= -5/7 = -5 × 3/7 × 3 = -15/21

= 2/3 = 2 × 7/3 × 7 = 14/21

-15 < 14

So, -15/21 < 14/21

Therefore, -5/7 [<] 2/3

**(ii) -4/5 [ ] -5/7**

Answer:

Answer:

LCM of 5, 7 = 35

= -4/5 = -4 × 7/5 × 7 = -28/35

= -5/7 = -5 × 5/7 × 5 = -25/35

-28 < -25

So, -28/35 < - 25/35

Therefore, -4/5 [<] -5/7

**(iii) -7/8 [ ] 14/-16**

Answer:

Answer:

= 7/-8

So, -7/8 = -7/8

Therefore, -7/8 [=] 14/-16

**(iv) -8/5 [ ] -7/4**

Answer:

Answer:

LCM of 4, 5 = 20

= -8/5 = -8 × 4/5 × 4 = -32/20

= -7/4 = -7 × 5/4 × 5 = -35/20

-32 > – 35

So, -32/20 > -35/20

Therefore, -8/5 [>] -7/4

**(v) 1/-3 [ ] -1/4**

Answer:

Answer:

LCM of 3, 4 = 12

= -1/3 = -1 × 4/3 × 4 = -4/12

= -1/4 = -1 × 3/4 × 3 = -3/12

-4 < -3

So, -4/12 < -3/12

Therefore, 1/-3 [<] -1/4

**(vi) 5/-11 [ ] -5/11**

Answer:

Answer:

= -5/11 = -5/11

Therefore, 5/-11 [=] -5/11

**(vii) 0 [ ] -7/6**

Answer:

Answer:

= 0 [>] -7/6

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

(i) 2/3, 5/2

Answer:

(i) 2/3, 5/2

Answer:

LCM of 2, 3 = 6

= 2/3 = 2 × 2/3 × 2 = 4/6

= 5/2 = 5 × 3/2 × 3 = 15/6

4 < 15

So, 4/6 < 15/6

= 2/3 < 5/2

Therefore, 5/2 is greater.

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

Answer:

Answer:

LCM of 3, 6 = 6

= -5/6 = -5 × 1/6 × 1 = -5/6

= -4/3 = -4 × 2/3 × 2 = -12/6

-5 > -12

So, -5/6 > -12/6

So, -5/6 > -12/6

Therefore, -5/6 is greater.

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

Answer:

Answer:

LCM of 3, 4 = 12

= -3/4 = -3 × 3/4 × 3 = -9/12

= -2/3 = -2 × 4/3 × 4 = -8/12

-9 < -8

So, (-9/12) < (- 8/12)

So, -3/4 < 2/-3

Therefore, 2/-3 is greater.

**(iv) -1/4, 1/4**

Answer:

Answer:

So, -1/4 < 1/4

Therefore, 1/4 is greater.

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

Answer:

Answer:

-3 2/7 = -23/7

-3 4/5 = -19/5

LCM of 5, 7 = 35

= -23/7 = -23 × 5/7 × 5 = -115/35

= -19/5 = -19 × 7/5 × 7 = (133/35

-115 > -133

So, -115/35 > - 133/35

= -3 2/7 > -3 4/5

Therefore, -3 2/7 is greater.

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

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

Answer:

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

Answer:

= -3/5 < -2/5 < -1/5

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

Answer:

Answer:

LCM of 3, 3, 9 = 9

= -1/3 = -1 × 3/3 × 9 = -3/9

= -2/9 = -2 × 1/9 × 1 = -2/9

= -4/3 = -4 × 3/3 × 3 = -12/9

= -12/9 < -3/9 < -2/9

= -4/3 < -1/3 < -2/9

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

Answer:

Answer:

LCM of 2, 4, 7 = 28

= -3/7 = -3 × 4/7 × 4 = -12/28

= -3/2 = -3 × 14/2 × 14 = -42/28

= -3/4 = -3 × 7/4 × 7 = -21/28

= -42/28 < -21/28 < -12/28

= -3/2 < -3/4 < -3/7

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