**Rd Sharma Solutions Class 8 Chapter 1 Rational Numbers**

Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of RD Sharma Class 8 Mathematics, Chapter 1, Rational Numbers. Here students can easily find Exercise wise solution for chapter 1, Rational Numbers. Students will find proper solutions for Exercise 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 and 1.8 Our teacher’s solved every problem with easily understandable methods so that every students can understand easily.

**Rational Numbers Exercise 1.1 Solution :**

**(i) Add -5/7 and 3/7**

= -5/7 + 3/7

= -5 + 3/7

= – 2/7

**(ii) Add -15/4 and 7/4**

= -15/4 and 7/4

= – 15/4 + 7/4

= – 15+7/4

= – 8/4

**(iii) -8/11 and -4/11**

= – 8/11 and – 4/11

= – 8/11 + – 4/11

= – 8 – 4/11

= – 12/11

**(iv) 6/13 and -9/13**

= 6/13 and -9/13

= 6/13 + -2/13

= 6-2/13

= 4/13

**Question no – (2) **

**Solution : **

**(ii) Add 5/-9 and 7/3**

5/-9 and 7/3

= 5/-9 +7/3

= -5+21/9

= -16/3

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

-3 and 3/5

= -3 + 3/5

= -15 + 3/5

= -12/5

**(iv) -7/27 and 11/18**

-7/27 and 11/18

= -7/27 + 11/18

= -14 + 33/54

= 19/54

**(v) 31/-4 and -5/8**

31/-4 and -5/8

= 31/-4 + -5/8

= – 62 – 5/8

= – 67/8

**(vi) 5/36 and -7/12**

5/36 and -7/12

= 5/36 + -7/12

= 5 – 21/36

= -16/36

= -4/9

**(vii) -5/16 and 7/24**

-5/16 and 7/24

= -5/16+7/24

= -15+14/48

= -1/48

**(viii) 7/-18 and 8/27**

= 7/-18 and 8/27

= -7/18 + 8/27

= -21+16/54

= -5/54

**Question no – (3) **

**Solution : **

**(i) 8/9 + -11/6**

8/9 + -11/6

= 8/9 – 11/6

= 16 – 33/18

= -17/18

**(ii) 3+ 5/-7**

3 + 5/-7

= 3 -5/7

= 21-5/7

= 16/7

**(iii) 1/-12 + 2/-15**

1/-12 + 2/-15

= -5-8/60

= -13/60

**(iv) -8/19 + -4/57**

-8/19 + -4/57

= -24 – 4/57

= -28/57

**(v) 7/9 + 3/-4**

7/9 + 3/-4

= 28 – 27/36

= 1/36

**(vi) 5/26 + 11/-39**

5/26 + 11/-39

= 15 – 22/78

= -7/7

**(viii) -13/8 + 5/36**

-13/8 + 5/36

= -117+10/72

= -107/72

**(ix) 0 + -3/5**

0 + -3/5

= – 3/5

**(x) 1 + -4/5**

1 + -4/5

= 5/-4/5

= 1/5

**Question no – (4) **

**Solution : **

**(i) -12/5 and 43/10**

– 12/5 and 43/10

= – 12/5 + 43/10

= -24 + 43/10

= -19/10

= – 1 9/10

**(ii) 24/7 and -11/4**

– 24/7 and -11/4

= 24/7 + -11/4

= 96 – 77/28

= 19/28

**(iii) -31/6 and -27/8**

– -31/6 and -27/8

= -31/6 + -27/8

= -124 – 81/24

= -205/24

= -8 13/24

**(iv) 101/6 and 7/8**

– 101 /6 and 7/8

= 101/6 + 7/8

= 404+21/24

= 425/24

= 17 17/24

**Rational Numbers Exercise 1.2 Solution :**

**Question no – (3) **

**Solution : **

**(i) -2/17**

= – (-2/17)

= 2/17

**(ii) -3/11**

The additive inverse of -3/11 is 3/11.

**(iii) -17/5**

= -17/5

= – (-17/5)

= 17/5

**(iv) -11/-25**

= -11/-25

= – (11/25)

= -11/25

**Question no – (6) **

**Solution : **

**(i) 11/12 + -17/3 + 11/2 + -25/2**

= (11/12 +-17/3) – (11/2 + 25/2)

= (11/12 – 17/3) (11+25/2)

= (44-68/12) – (36/2)

= 24/12 – 18

= 2 – 18

= -16

**(iii) 3/5 + 7/3 + 9/ 5+ -13/15 + -7/3**

= (3/5 + 9/5) + (7/3 – 7/3) + -13/15

= 3 + 9/5 + 0 – 13/15

= 12/5 – 13/15

= 36 -13/15

= 23/15

**(iv) 4/13 + -5/8 + -8/13 + 9/13**

4/13 + -5/8 + -8/13 + 9/13

= (4/13+-8/13+9/13) – 5/8

= (4/13+9/13-8/13) -5/8

= (4+9-8/13) – 5/8

= (13-8/13) – 5/8

= 5/13 -5/8

= 40-65/104

= -25/104

**(v) 2/3 + -4/5 + 1/3 + 2/5**

2/3 + -4/5 + 1/3 + 2/5

= (2/3 + 1/3) + (2/5 – 4/5)

= (2+1/3) + (2-4/5)

= (3/3) + (-2/5)

= 1 – 2/5

= 5-2/5

= 3/5

**(vi) 1/8 + 5/12 + 2/7 + 7/12 + 9/7 + -5/16**

1/8 + 5/12 + 2/7 + 7/12 + 9/7 + -5/16

= (5/12 + 7/12) + (2/7 + 9/7) + 1/8 – 5/16

= (5+7/12) + (2+5/7) + 1/8 – 5/16

= 12/12 + 11/7 + 1/8 – 5/16

= 88 + 7/ 56 – 5/16

= 95/56 – 5/16

= 190-35/112

= 55/112

**Rational Numbers Exercise 1.3 Solution : **

**Question no – (1)**

**Solution : **

**(i) 3/8, 5/8**

3/8 from 5/8

= 5/8 – 3/8

= 5 – 3/8

= 2/8

= 1/4

**(ii) -7/9, 4/9**

-7/9 from 4/9

= 4/9 – (-7/5)

= 4/9 + 7/9

= 11/9

**(iii) -2/11, -9/11**

-2/11 from -9/11

= -9/11 – (-2/11)

= -9 + 2/11

= – 7/11

**(iv) 11/13, -4/13**

11/13 from -4/13

= -4/13 – 11/13

= -4 – 11/13

= -15/13

**(v) 1/4, -3/8**

1/4 from -3/8

= -3/8 – 1/4

= -3 – 2/8

= -5/8

**(vi) -2/3, 5/6**

-2/3, 5/6

= 5/6 – (-2/3)

= 5/6+2/3

= 5 + 4/6

= 6/9

= 2/3

**(vii) -6/7, -13/14**

-6/7 from -13/14

= -13/14 – (-6/7)

= -13 + 12/14

= -1/14

**(viii) -8/33, -7/22**

-8/33 from -7/22

= -7/22 – (- 8/33)

= -21+16/66

= -5/66

**Question no – (2)**

**Solution : **

**(i) 2/3 – 3/5**

2/3 – 3/5

= 10-9/15

= 1/15

**(ii) -4/7 – 2/-3**

– 4/7 – 2/-3

= -12+14/21

= 2/21

**(iii) 4/7 – -5/-7**

4/7 – (-5/-7)

= 4-5/7

= -1/7

**(iv) -2 – 5/9**

-2 – 5/9

= -18 – 5/9

= -23/9

**(v) -4/13 – -5/26**

-4/13 – (-5/26)

= -8 + 5/26

= -3/26

**(vi) -5/14 – -2/7**

-5/14 – (-2/7)

= -5+4/14

= -1/14

**(vii) 13/15 – 12/25**

13/15 – 12/25

= 65 – 36/75

= 29/75

**(viii) -6/13 – -7/13**

-6/13 – (-7/13)

= -6 + 7/13

= -1/13

**(ix) 7/24 – 19/36**

7/24 – 19/36

= 21-138/72

= -17/72

**(x) 5/63 – -8/21**

5/63 – (-8/21)

= 5 + 24/63

= 29/63

**Question no – (4) **

**Solution : **

As per the question –

a + b = 5/9

Given, = a = 1/3

**∴** b = 5/9 -1/3

= 5 – 3/9

= 2/9

So, the other number is 2/9.

**Question no – (5) **

**Solution : **

As per the question,

a + b = -4/3

Given, a = -5

**∴** b = -4/3 – (-5)

= -4+15/3

= 11/3

So, the other number is 11/3.

**Question no – (6) **

**Solution : **

a + b = -8

Give, a = -15/7

**∴** b = -8 – (-15/7)

= -56 + 15/7

= -41/7

**∴** The other number is -41/7

**Question no – (7) **

**Solution : **

= 5/7 – (- 7/8)

= 5/9 + 7/8

= 40 + 63/72

= 103/72

**Question no – (8) **

**Solution : **

According to question,

= -5/11 + x = 26/33

Or -5/11x/11

= 26/33

Or – 15 + 33x = 26

Or 33x = 26+15 = 41

Or x = 41/33

**Question no – (9) **

**Solution : **

Let x should be added

**∴** According to question,

= -5/7 + x -2/3

Or, x = -2/3+5/7

= -14 + 15/21

= 1/21

So, the required number is 1/21.

**Question no – (10) **

**Solution : **

According to question,

= -5/3 – x = 5/6

Or -5-3x/3 = 5/6

Or -30 -18x = 15

Or 30 – 15 = 18x

Or, -45 = 18x

Or x = 45/18

= -5/2

**∴** The required number is -5/2.

**Question no – (11) **

**Solution : **

According to question,

= 3/7 – x = 5/4

Or 3-7x/7 = 5/4

Or, 12-28 = 35

Or, 28x = 35-12 = 23

Or x = -23/28

Thus, -23/28 should be subtracted.

**Question no – (12) **

**Solution : **

According to question,

= (2/3 +3/5) + x = -2/15

Or, (10+9/15) + x = -2/15

Or, 19/15 + x = -2/15

Or, x = -2/15 – 19/15 = -21/15

Or x = -7/5

So, -7/5 should be added to get -2/15.

**Question no – (13) **

**Solution : **

Let, x should be added,

According to question –

= (1/2 + 1/3 +1/5) + x = 3

Or, (15 + 10 + 6/30) + x = 3

Or, 31/30 + x = 3

Or, x = 3 – 31/30

= 90 – 31/30

= 59/30

**Rational Numbers Exercise 1.4 Solution : **

**Question no – (1) **

**Solution : **

**(i) 3/4 + 5/6 + -7/8**

= 9 +10/12 – 7/8

= 19/12 – 7/8

= 38-21/24

= 17/24

**(ii) 2/3 + -5/6 + -7/9**

= 2/3 – 5/6 – 7/9

= 12 – 15 -14/18

= 12 – (15 + 14)/18

= 12 – 29/18

= -17/18

**(iii) -11/2 + 7/6 + -5/8**

= -11/2 + 7/6 + -5/8

= – 11/2 + 7/6 – 5/8

= -132 + 28 – 15 /24

= -132 + 13/24

= -119/24

**(iv) -4/5 + -7/10 + -8/15**

= -24 – 21 – 16/30

= -61/30

**(v) -9/10 + 22/15 + 13/-20**

= -9/10 + 22/15 + 13/-20

= -54+44-39/60

= 44-(54+39)/60

= 44-93/60

= -49/60

**Question no – (2) **

**Solution : **

**(i) -8/3 + -1/4 + -11/6 + 3/8 – 3**

= -128 – 12 -88 + 18 -144/8

= 18 – (128 + 12 + 88 + 144)/48

= 18-372/48

= -354/48

= -59/8

**(ii) 6/7 + 1 + -7/9 + 19/21 + -12/7**

= 54 + 63-49 + 57-108/63

= (54 + 63 + 57) – (49 + 108)/63

= 174 – 157/63

= 17/63

**(iii) 15/2 + 9/8 + -11/3 + 6 + -7/6**

= 180 + 27- 88 + 144 – 28/24

= (108 + 27 + 144) – (88 + 28)/24

= 251 – 116/24

= 235/24

**(iv) -7/4 +0 + -9/5 + 19/10 + 11/1**

= -245 + 0 – 252 + 266 + 100/140

= -497 + 376/140

= -121/140

**(v) -7/4 +5/3 + -1/2 + -5/6 + 2**

= -63 + 60 – 18 – 30 + 72/36

= -111 + 132/36

= 21/36

= 7/12

**Question no – (3) **

**Solution : **

**(i) -3/2 + 5/4 – 7/4**

= – 6 + 5 – 7/4

= – 8/4

= – 2

**(ii) 5/3 – 7/6 + -2/3**

= -10 – 7 – 4/6

= – 1/6

**(iii) 5/4 – 7/6 – -2/3**

= 15 – 14 + 8/12

= 23 -14/12

= 9/12

= 3/4

**(iv) -2/5 – -3/10 – -4/7**

= -28 + 21 + 12/70

= -28 + 33/70

= 5/70

**(v) 5/6 + -2/5 – -2/15**

= 25 -12-16/30

= 25 – 28/30

= -3/30

= -1/10

**(vi) 3/8 – -2/9 + -5/36**

= 27 + 16 – 10/72

= 27+6/72

= 33/72

= 11/24

**Rational Numbers Exercise 1.5 Solution : **

**Question no – (1) **

**Solution:**

**(i)** 7/11 by 5/4

= 35/44

**(ii)** 5/7 by -3/4

= -15/28

**(iii)** -2/9 by 5/11

= -2/11

**(iv)** -3/17 by -5/-4

= 15/68

**(v)** 9/-7 by 36/-11

= 324/77

**(vi)** -11/13 by -21/7

= 33/13

**(vii)** – 3/5 by – 4/7

= 12/35

**(viii)** – 15/11 by 7

= -105/11

**Question no – (2) **

**Solution:**

**(i) -5/17 by 51/-60**

= -5/17× 51/-60

= 1/4

**(ii) -6/11 by -55/36**

= -6/11 × -55/36

= 5/9

**(iii) -8/25 by -5/16**

= -8/25 × -5/16

= 1/10

**(iv) 6/7 by -49/36**

= 6/7 × -49/36

= – 7/6

**(v) 8/-9 by -7/-16**

= 8/-9 × -7/-16

= 7/18

**(vi) -8/9 by 3/64**

= -8/9 × 3/64

= – 1/24

**Question no – (3) **

**Solution:**

**(i) (-16/21) × (14/5)**

= -16/21 × 14/5

= – 32/15

**(ii) (7/6) × (-3/28)**

= 7/6 × (-3/28)

= -1/8

**(iii) (-19/36) × 16**

For simplify we have to know factor part.

So that, we can cut the digit placed in numerator and denominator.

Therefore,

-19/36 × 16

= -76/9

**Note :** When crossing is not possible then you to do, upper upper multiplication and lower lower multiplication to write the answer.

**(iv) (-13/9) × (27/-26)**

=-13/9 × 27/-26

= 3/2

**(v) (-9/16) × (-64/-27)**

For simplify we have to know factor part.

So that, we can cut the digit placed in numerator and denominator.

Therefore,

-9/16 × -64/27

=4/3

**Note** **:** When crossing is not possible then you to do, upper upper multiplication and lower lower multiplication to write the answer.

**(vi) (-50/7) × (14/3)**

= -50/7 × 14/3

= -100/3

**(vii) (-11/9) × (-81/-88)**

= -11/9 × (-81/-88)

= 9/8

**(viii) (-5/9) × (72/-25)**

= -5/9 ×72/-25

= 8/5

**Question no – (4) **

**Solution:**

**(i) (25/8) × (2/5)) – (3/5) × (-10/9)**

= 5/4 + 2/3

= 15 + 8/12

= 23/12

**(ii) (1/2) × (1/4) + (1/2) × 6)**

= 1/8 + 3

= 1+24/8

= 25/8

**(iii) (-5 × (2/15) – (-6 × (2/9)**

= -2/3 + 4/3

= -2 + 4/3

= 2/3

**(iv) (-9/4) × (5/3) + (13/2) × (5/6)**

= -5/4 + 65/12

= – 45 + 65/12

= 20/12

= 5/3

**(v) (-4/3) × (12/-5) + (3/7) × (21/15)**

= 16/5 + 3/5

= 16+3/5

= 19/5

**(vi) (13/5) × (8/3) – (-5/2) × (11/3)**

= 104/15 + 55/6

= 208 + 257/30

= 483/30

**(vii) (13/7) × (11/26) – (-4/3) × (5/6)**

= 11/14 + 10/9

= 99 + 140/126

= 239/126

**(viii) (8/5) × (-3/2) + (-3/10) × (11/16)**

= -12/5 – 33/160

= -384-33/160

= -417/160

**Question no – (5) **

**Solution : **

**(i) (3/2) × (1/6) + (5/3) × (7/2) – (13/8) × (4/3)**

= 1/4+ 35/6 – 13/6

= 9 + 210 – 78/36

= 141/36

= 47/12

**(ii) (1/4) × (2/7) – (5/14) × (-2/3) + (3/7) × (9/2)**

= 1/14 + 5/21 + 27/12

= 3+10+81/42

= 94/42

= 47/21

**(iii) (13/9) × (-15/2) + (7/3) × (8/5) + (3/5) × (1/2)**

= 45/6 + 56/15 + 3/10

= 225 + 386 + 9/30

= 620/30

= 62/3

**(iv) (3/11) × (5/6) – (9/12) × (4/3) + (5/13) × (6/15)**

= 1/22 – 1 + 2/13

= 13 – 286 + 44/286

= -177/286

**Rational Numbers Exercise 1.6 Solution : **

**Question no – (1) **

**Solution : **

**(i) x = -1/3, y = 2/7**

x = -1/3, y = 2/7

**L.H.S,** x × y

= – 1/3 × 2/7

= -2/21

**R.H.S,** y × x

= 2/7 × (-1/3)

= -2/21 (answer)

**∴** L.H.S = R.H.S (verified)

(iii) x = 2, y = 7/-8

**L.H.S,** x × y

= 2 × 7/-8

= 7/4

**R.H.S,** 7/-8 × 2

= -7/4

**∴** L.H.S = R.H.S [verified]

**(iv) x = 0, y = -15/8**

**L.H.S,** x × y

= 0 × -15/8

= 0

**R.H.S,** y × x

= -15/8 × 0

= 0

**∴** L.H.S = R.H.S [verified]

**Question no – (2) **

**Solution : **

**(i) x = -7/3, y = 12/5, z = 4/9**

**L.H.S,** x × (y × z)

= – 7/3 ×(12/5 ×4/9)

= – 7 × 4×4/3×5×3

= – 112/45

**R.H.S,** (x × y) × z

= (-7/3 × 12/5) × 4/9

= -7×4×4/3×5×3

= – 112/45

**∴** L.H.S = R.H.S [verified]

**(ii) x = 0, y = -3/5, z = -9/4**

**L.H.S,** x × (y × z)

= 0 × -3/5 × -9/4

= 0

**R.H.S,** (x × y) × z

= 0 × -3/5 × -9/4

= 0

**∴** L.H.S = R.H.S [verified]

**(iii) x = 1/2, y = 5/-4, z = -7/5**

**L.H.S,** x × (y × z)

= 1/2 × (5/4 × -7/5)

= 1 × 5 × (-7)/2 × (-4) × 5

= 7/8

**R.H.S,** (x × y) × z

= (1/2 × 5/-4) × -7/5

= 1 × 5 × (-7)/2 × (-4) × 5

= 7/8

**∴** L.H.S = R.H.S [verified]

**Question no – (3) **

**Solution : **

**(i) x = -3/7, y = 12/13, z = -5/6**

L.H.S, [x × (y + z)]

= -3/7 × (12/13 + -5/6)

= -3/7 × (24-5/6)

= -3/7 × 19/6

= -19/14

R.H.S, x × y + x × z

= (-3/7 × 12/3) + (-3/7 × 5/6)

= -12/7 + 5/14

= -24 + 5/14

= -19/14

**∴** L.H.S = R.H.S [verified]

**(ii) x = -12/5, y = -15/4, z = 8/3**

L.H.S, x × (y + z )

= – 12/5 ×(-15/4 +8/3)

= -12/5 × (-45+32/12)

= -12/5× -13/12

= 13/5

R.H.S, (x × y + x × z )

= (-12/5 × -15/4) + (-12/5 × 8/3)

= 9 – 32/5

= 45-32/5

= 13/5

**∴ **L.H.S = R.H.S [verified]

**(iii) x = -8/3, y = 5/6, z = -13/12**

L.H.S, x × (y + z )

= -8/3 × (5/6 + -13/12)

= -8/3 × (10 – 13/12)

= – 8/3 × -3/12

= 2/3

R.H.S, x × y + x × z

= (-8/3 × 5/6) + (-8/3 × -13/12)

= -20/9 + 26/9

= 6/9

= 2/3

**∴** L.H.S = R.H.S [verified]

**(iv) x = -3/4, y = -5/2, z = 7/6**

L.H.S, x × (y + z )

= – 3/4 × (- 5/2 + 7/6)

= – 3/4 × ( -15+7/6)

= – 3/4 × (-22/6)

= 11/4

R.H.S, (x × y) + (x × z)

= (-3/4 ×-5/2) + (-5/4 × 7/6)

= 15/8 – 21/8

= 15-7/8

= 1

**∴** L.H.S ≠ R.H.S [Not verified]

**Question no – (4) **

**Solution : **

**(i) 3/5 × (35/24) + (10/1)**

= – 3/ × (35+240/24)

= 3/5 × 275/24

= 55/8

**(ii) -5/4 × (8/5) + (16/5)**

= -5/4 × (8 + 16/5)

= -5/4 × 24/5

= -6

**(iii) 2/7 × (7/16) – (21/4)**

= 2/7 × (7-84/16)

= 2/7 × -77/16

= – 11/8

**(iv) 3/4 × (8/9) – 40)**

= 3/4 × (8-360/9)

= 3/4 × -35/9

= -88/3

**Question no – (5) **

**Solution : **

**(i)** 9

= 1/9

So, Multiplicative inverse of 9 is 1/9.

**(ii) -7**

We know,

Additive inverse of 7 is = -7

Multiplicative inverse of 7 is = 1/7

**∴** Sum, -7 + 1/7

= -49 + 1/7

= – 48/7

**(iii) 12/5**

= 5/12

**∴** Multiplicative inverse of 12/5 is 5/12.

**(iv) -7/9**

= 9/-7

So, Multiplicative inverse of -7/9 is 9/-7.

**(v) -3/-5**

The multiplicative inverse of -3/-5

= 5/3

**(vi) 2/3 × 9/4**

= 2/3

So, Multiplicative inverse of 2/3 × 9/4 is 2/3.

**(vii) -5/8 × 16/15**

= -3/2

So, Multiplicative inverse of -5/8 ×16/15 is -3/2.

**(viii) -2 × -3/5**

= 6/5

= 5/6

**∴** Multiplicative inverse of -2 × -3/5 is 5/6.

**(ix) -1**

The multiplicative inverse of -1

= -1

**(x) 0/3**

For the given number multiplicative inverse Does’t exist.

**(xi) 1**

= 1

So, the Multiplicative inverse of 1 is 1.

**Question no – (6) **

**Solution : **

**(i)** -5/16 × 8/15 = 8/15×-5/16

= Commutativity

**(ii)** -17/5×9=9×-17/5

= Commutativity

**(iii)** 7/4 ×(-8/3+ -13/12) = 7/4×-8/3+7/4×-13/12

= Distributitivity of multiplication over addition

**(iv)** -5/9 ×(4/15v -9/8) = (-5/9 ×4/15) × -9/8

= Associatively of multiplication

**(v)** 13/-17 × 1= 13/-17 = 1 ×13/-17

= Existence of identify for multiplication

**(vi)** -11/16 × 16/11 = 1

= Existence of multiplication for inverse

**(vii)** 2/13 × 0 = 0 × 2/13

= Multiplication

**(viii)** -3/2 × 5/4 + -3/2× -7/6 = -3/2 × (5/4+ -7/6)

= Distributitivity.

**Question no – (7) **

**Solution : **

**(i)** The product to two positive rational numbers is always Positive.

**(ii)** The product of a positive rational number and a negative rational numbers is always Negative.

**(iii) Answer** : The product of two negative rational numbers is always Positive.

**(iv) Answer** : The reciprocal of a positive rational numbers is Positive.

**(vi)** Zero has “No” reciprocal.

**(vii)** The product of a rational number and its reciprocal is 1.

**(viii)** The numbers 1 and -1 are their own reciprocals

**(ix)** If a reciprocal of b, then the reciprocal of b is a.

**(x)** The number 0 is Not the reciprocal of any number.

**(xi)** Reciprocal of 1/a, a ≠ 0 is a.

**(xii)** (17 × 12)^-1 = 17^- 1 × (12)^-1

**Question no – (8) **

**Solution : **

**(i)** 5/11× -3/8 = -3/8 × 5/11.

**(ii)** 1/2 × (3/4 + -5/12) = 1/2 × 3/4 + 1/2× -5/12

**(iii)** -4/5 × (5/7 + -8/9) + = (-4/5 × 5/7) + -4/5 × -8/9

**Rational Numbers Exercise 1.7 Solution : **

**Question no – (1) **

**Solution : **

**(i) 1 by 1/2**

= 1 ÷ 1/2

= 1 × 2/1

= 2

**(ii) 5 by -5/7**

= 5 ÷ -5/7

= 5 × -7/5

= -7

**(iii) -3/4 by 9/-16**

**∴** -3/4 ÷ -9/16

= -3/4 × 16/-9

= 4/3

= 1 1/3

**(iv) -7/8 by -21/16**

= -7/8 ÷ -21/16

= -7/8 × 16/-21

= 2/3

**(v) 7/-4 by 63/64**

= 7/-4 ÷ 63/64

= 7/-4 × 64/63

= -16/9

**(vi) 0 by -7/5**

= 0 ÷ -7/5

= 0

**(vii) -3/4 by -6**

= -3/4 ÷ -6

= -3/4 ×1/-6

= 1/8

**(viii) 2/3 by -7/12**

= 2/3 ÷ -7/12

= 2/3 × -12/7

= -8/7

**(ix) -4 by -3/5**

= -4 ÷ -3/5

= -4 × 5/-3

= 20/3

**(x) -3/13 by -4/65**

= -3/13 ÷ -4/65

= -3/13 × 65/4

= -15/4

**Question no – (2) **

**Solution : **

**(i) 2/5 ÷ 26/15**

= 2/9 × 15/26

= 3/13

**(ii) 10/3 ÷ -35/12**

= 10/3 × 12/-35

= -8/7

**(iii) -6 ÷ -8/17**

= -6 × -17/8

= 51/4

**(iv) -40/99 ÷ -20**

= – 40/99 × 1/-20

= -2/99

**(v) -22/27 ÷ -110/18**

= -22/27 × 18/110

= 2/15

**(vi) -36/125 ÷ -3/75**

= -36/125 × 75/-3

= 36/5

**Question no – (3) **

**Solution : **

Let, the others number is x

According to question,

x × -(10) = 15

= or x = 15/-10

= -3/2

So, the other number is -3/2.

**Question no – (4) **

**Solution : **

Let, the other number is x

According to question,

x × -4/15 = -8/9

or x = -8 ×15/9×-4

= 10/3

∴ The other number is 10/3.

**Question no – (5) **

**Solution : **

Let, x should be multiplied

According to question,

x × -1/6 = -23/9

or x = -23/9 × -6/1

= 46/3

Thus, the required number is 46/3.

**Question no – (6) **

**Solution : **

Let, x should be multiplied

According to question,

x × -15/28 = -5/7

or, x = -5/7 × 28/-15

= 4/3

So, the required number is 4/3

**Question no – (7) **

**Solution : **

Let, x should be multiplied

According to question

x × -8/13 = 24

or , x = 24× -13/8

= – 39

Thus, the required number is -39.

**Question no – (8) **

**Solution : **

Let, x should be multiplied

According to question

x × -8/13 = 24

or , x = 24× -13/8

= – 39

Thus, the required number is -39.

**Question no – (12) **

**Solution : **

we find required number as follows :

Required number,

= -33/16 ÷ -11/4

= -33/16 × -4/11

= 3/4

So, 3/4 should be divided.

**Question no – (13) **

**Solution : **

= – 13/5 + 12/7

= – 91 + 60/35

= – 31/35

And, -31/7 × – 1/2

= 31/14

Then, -31/35 ÷ 31/14

= – 31/35 × 14/31

= – 14/31

**Rational Numbers Exercise 1.8 Solution : **

**Question no – (1) **

**Solution : **

x = 3, y= 1

We know that,

= x < x + y/2 < y

**∴** x + y/2

= 3/1/2 = -2/2 = -1

**∴** -3 < -1 < 1

**Question no – (2) **

**Solution : **

We take

X = 2, y = 0

Now, 2/1 = 2×5/1×5 = 10/5

Again, 0 = 0/5 = 0

**∴** Integers between 2 and 0 are –

0 <1/5, 2/5, 3/5, 4/5, 5/5 < 2

**Question no – (4) **

**Solution : **

We take, x = 1/5

= 1×2/5×2

= 2/10

y = 1/2

= 1×5/2×5

= 5/10

Now, integers between 2 and 5 are 3, 4,

**∴** 1/5 < 3/5, 4/5 < 5/10

**Question no – (6) **

**Solution : **

We Take,

x = -2/5

= -2×2/5×2

= -4/10

= 4×2/10×2

= -8/20

y = 1/2

= 1×5/2×5

= 5/10

= 5×2/10×2

= 10/20

**∴** Ten integers between -8 and 10 are -7, -6 , -5 …-9

**∴** -2/5 < -7/20, -6/20, -5/20, -4/20….-9/20 < 20/20

**Question no – (7) **

**Solution : **

Given numbers are 3/5 and 3/4.

Now, to convert 3/5 and 3/4 to rational numbers with the same denominators.

3*4/5*4 = 12/20 and 3*5/4*5 = 15/20

Also, 12/20 *5/5 = 60/100

15/20 * 5/5 = 75/100

Thus, we have 61/100, 62/100 , 63/100,…, 74 /100as the rational numbers between 3/5 and 3/4

You can take any ten of these.

**Next Chapter Solution : **

👉 Chapter 3 👈