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**Mathsight Class 7 Solutions Chapter 3 Rational Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students to solve MathSight Class 7 Mathematics Book, Chapter 3, Rational Numbers. Here students can easily get all the exercise questions solution for Chapter 3, Rational Numbers Exercise 3.1, 3.2 and 3.3

**Rational Numbers Exercise 3.1 Solution : **

**Question no – (1)**

**Solution :**

**(a)** 0 = 5/0

**(b)** -67 = -335/5

**(c)** 14 = 112/8

**(d)** 3^{2} (-5) = 3/-5

**Question no – (2)**

**Solution :**

**(a)** 121/-110 = 11/-10

**(b)** -84/-27 = 28/9

**(c)** -95/-19 = 5

**(d)** 108/-21 = 36/-7

**Question no – (3)**

**Solution :**

**(a)** -4/7 = -16/28

**(b)** 2/-11 = 22/-121

**(c)** -7/-8 =-14/-16

**(d)** 5/9 = 30/54

**Question no – (4)**

**Solution :**

**(a)** 4/5 = positive

**(b)** -7/8 = negative

**(c)** -4/13 = negative

**(d)** 4/11 = negative

**(e)** -6/-14 = 6/14 = positive

**(f)** -15/6 = negative

**Question no – (5)**

**Solution :**

**Question no – (6)**

**Solution :**

**(a)** 4/7 = 4 × 9/7 × 9 = 36/63

5/9 = 5 × 7/9 × 7 = 35/63

∴ 4/7 > 5/9

**(b)** 6/-11 = 6 × 7 / -11 × 7 = -42/77

-5/7 = -5 × 11 / 7 × 11 = -55/77

∴ 6/-11 < -5/7

**(c)** 10/3 – 4/-3 = 4/3

∴ 10/3 > 4/3

**(d)** -4/11 = -4 × 6/11 × 6 = -24/66

-5/6 = -5 × 11/6 × 11 = -55/66

∴ -4/11 > -5/6

**Question no – (7)**

**Solution :**

**(a)** -3/7, 4/5, 6/7

**(b)** -14/48, -2/3, -1/4

**(c)** 0/5, -5/3, -2/3

**(d)** -7/8, 1/2, 6/8

**Question no – (8)**

**Solution :**

**(a)** 8/7, 3/7, 4/14, 1/2

**(b)** 1/2, 0/3, -4/8, 5/-3

**(c)** 6/12, -5/8, -3/4, 5/-6

**(d)** 9/10, 9/2, 4/3, 2/5

**Question no – (9)**

**Solution :**

**(a)** >

**(b)** =

**(c)** >

**(d)** <

**Question no – (10)**

**Solution :**

**(a)** |3/13|

**(b)** |5/16|

**(c)** |2/11|

**(d)** |7/15|

**(e)** |19/23|

**Question no – (11)**

**Solution :**

Riya distance,

= 4/5 = 4 × 4 / 5 × 4

= 16/20 km

Anam distance,

= 3/4 = 3 × 5 / 4 × 5

= 15/20 km .

∴ 4/5 > 3/4

∴ Riya lives farther from school.

**Question no – (12)**

**Solution :**

= |-2/3| = 2/3 ….[absolute value]

**Rational Numbers Exercise 3.2 Solution : **

**Question no – (1)**

**Solution :**

**(a)** -7/9 + (-2/5)

= -7/9 – 2/5

= – 35 -18/45

= -53/45

**(b)** -7/9 + 2/9

= -7+2/9

= -5/9

**(c)** -7/9 + (-2/5)

=-7/9 – 2/5

= -35 -18/45

= -53/45

**(d)** -2/5 + (-7/9)

= -18-35/45

= -53/45

**Question no – (2)**

**Solution :**

**(a)** 4/9 + (-7/9)

= 4-7/9

= -3/9

= -1/3

**(b)** -3/4 + (-5/4)

= -3-5/4

= -8/4

= -2

**(c)** -7/11 + 9/11

= -7 + 9/11

= 2/11

**(d)** -1/5 + 3/5

= -1 + 3/7

= 2/5

**Question no – (3)**

**Solution :**

**(a)** 4/7 + 3/4

= 16+21/28

= 37/28

**(b)** -7/8 + -4/3

= -21-32/24

= -53/24

**(c)** -14/15 + 7/5

= -14+21/15

= 7/15

**(d)** 4/9 + (-7/11)

= 44-63/99

= -19/99

**Question no – (4)**

**Solution :**

**(a)** 1/2 – (-3/4)

= 2 + 3/4

= 5/4

**(b)** -2/9 – (-7/18)

= -4 + 7/18

= 3/18

= 1/6

**(c)** -8/34 – 4/17

= -8-8/34

= -16/34

= -8/77

**(d)** -6/7 – (-4/11)

= -66 + 28/77

= -38/77

**Question no – (5)**

**Solution :**

**(a)** 4/7 – (-3/8)

= 32 + 21/56

= 53/56

**(b)** -9/10 + 4/-7

= -63 – 40/70

= -103/70

**(c)** 15/16 + -7/8

= 15-14/16

= 1/16

**(d)** -4/5 – (-3/-7)

= -28 – 15/35

= -43/35

**Question no – (6)**

**Solution :**

**(a)** 3/4 + -4/9 – 7/4

= 27-16 – 63/36

= -52/36

= -26/18

= -13/9

**(b)** -3/18 + -2/9 – 2/3

= -3-4-12/18

= -19/18

**(c)** -1/8 + 5/12 + -1/12

= -9+30-30/72

= -9/72

= -1/8

**(d)** -3 1/4 + 7/12 – 5/6

= -13/4 + 7/12 – 5/6

= -39 + 7 – 10/12

**(e)** 4 1/3 × (6/3 + 4/7)

= 12/3 × (42+12/21)

= 12/3 × 54/21

= 72/7

**(f)** -22/16 × (16/22 – 3/11)

= -22/16 × (16-6/22)

= -22/16 × 10/22

= -5/8

**(g)** -7/8 × (4/5 × 8/20)

= -(7/8 × 4/5 × 8/20)

= -7/25

**(h)** -7/12 × (6/7 / 5/6)

= -7/12 × 6/7 × 6/5

= -3/5

**Question no – (7)**

**Solution : **

**(a)** -14/15 × 5/24

= -7/36

**(b)** 3/7 × -4/9 × 1/2

= -2/21

**(c)** 19/27 × -63/95

= -7/15

**(d)** 17/68 × 7/28 × 15/10

= 357/3808

**Question no – (8)**

**Solution :**

**(a)** 9/10/1/5

= 9/10 × 5

= 9/2

**(b)** -6/7/4/14

= -6/7 × 14/4

= -3

**(c)** -11 1/2 / 23

= -23/2 × 1/23

= -1/2

**(d)** -18/20 / 75/15

= -18/20 × 15/75

= -9/50

**Question no – (9)**

**Solution :**

1/2 = 1 × 3/2 × 3 = 3/6

4/3 = 4 × 2/3 × 2 = 6/6

∴ 4/6, 5/6

**Question no – (10)**

**Solution :**

**(a)** 1/3 + a

= 1/3 + (-2/3)

= 1 – 2/3

= 1/3

**(b)** b – 6/13

= 4/5 – 6/13

= 52 – 30/65

= 22/65

**(c)** b – a

= 4/5 – (-2/3)

= 4/5 + 2/3

= 12 + 10/15

= 22/15

**(d)** a + 2b

= -2/3 + (2 × 4/5)

= -2/3 + 8/5

= -10 + 24/15

**Question no – (11)**

**Solution :**

= 14/16 -10/16

= 14 – 10/16

= 4/16

= 1/4

Hence, 1/4 longer.

**Question no – (12)**

**Solution :**

Flour need = 1 1/3 – 1 3/4

= -1 3/4 – 1 1/3

= 21 – 16/12

= 5/12

Therefore, more 5/12 cups flour will be needed.

**Rational Numbers Exercise 3.3 Solution : **

**Question no – (1)**

**Solution :**

**(a)** 5/12 = non terminating

**(b)** -17/16 = terminating

**(c)** 49/50 = terminating

**(d)** -64/100 = terminating

**(e)** 7/10 = terminating

**(f)** 9/14 = terminating

**(g)** -26/25 = terminating

**(h)** 83/12 = non terminating

**Question no – (2)**

**Solution :**

**(a)** Given, 5/11

= 0.45

∴ Non reciprocal.

**(b)** Given, 8/24

= 0.3

∴ Non reciprocal.

**(c)** Given, -18/256

= -0.0703125

∴ Reciprocal

**(d)** Given, 33/24

= 1.375

∴ Reciprocal

**(e)** Given, 201/125

= 1.608

∴ Reciprocal

**(f)** Given, 19/32

= 0.59375

∴ Reciprocal

**(g)** Given, 45/-230

= 0.195652174

∴ Reciprocal

**(h)** Given, 34/190

= 0.1789

∴ Reciprocal

**Question no – (3)**

**Solution :**

**(a)** Given, 0.25

= 25/100

= 1/4

**(b)** Given, 0.013

= 13/1000

**(c)** Given, -0.168

= -168/1000

= -21/125

**(d)** Given, 0.0021

= 21/10000

**(e)** Given, 0.145

= 145/1000

= 29/200

**Question no – (4)**

**Solution :**

**(a)** 0.016 = 16/100

**(b)** 0.3 = 33/10

**(c)** 1.16 = 1166/100

**(d)** 2.3 = 233/10

**Question no – (5)**

**Solution :**

= 8-(1/4 + 1/5 + 1/6)

= 8- (15+12+10/60)

= 8 – 37/60

= 480 – 37/60

= 443/60

**Question no – (6)**

**Solution :**

**(a)** Given, 2.8 + 3.5

= 6.3

**(b)** Given, 1.5 + 2.6 + 3.7

= 7.8

**Previous Chapter Solution : **