# Mathsight Class 7 Solutions Chapter 3

## 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) 32 (-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 :

Updated: May 27, 2023 — 5:39 am