Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution

Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution . We provide step by step Solutions of lesson-4 Rational Numbers for ICSE Class-7 Foundation RS Aggarwal Mathematics of Goyal Brothers Prakashan . Our Solutions contain all type Questions of Exe-4 A to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.

Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution

Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution

Board ICSE
Publications Goyal brothers Prakashan
Subject Maths
Class 7th
Chapter-4 Rational Numbers
Writer RS Aggrawal
Book Name Foundation
Topics Solution of Exe-4 A
Academic Session 2023 – 2024

Exercise – 4 A

Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution

1. What are rational numbers? Give four examples of each of positive rational and negative rational. Give an example of a rational number which is neither positive nor negative.

Solution: Rational numbers are those numbers which are in the form of (p/q). p and q both are integers and q ≠ 0

Examples of positive rational numbers –

(33/17), (37/18), (43/11), (55/6)

Examples of negative rational numbers –

(-18/5), (37/-19), (-47/5), (-99/7)

(0) is a number which is neither be positive and nor be negative.

2. Which of the following are rational numbers?

(i) (5/15)

Solution:(5/15)

∴ It is an rational number

[In the form of (p/q), q ≠ 0]

(ii) (-6/23)

Solution: (-6/23)

∴ It is an rational number

(iii) 17

Solution: 17

= (17/1)

∴ It is an rational number

(iv) -25

Solution: -25

= (-25/1)

∴ It is an rational number 

(v) 0

Solution: 0

= (0/1)

∴ It is an rational number

(vi) (8/0)

Solution: (8/0)

∴ It is not an rational number

[It is in the form of (p/q), but q = 0]

(vii) (0/0)

Solution: (0/0)

∴ It is not an rational number

[q = 0]

(viii) (0/8)

Solution: (0/8)

∴ It is an rational number

[q ≠ 0]

(ix) (-23/-37)

Solution: (-23/-37)

∴ It is an rational number

(x) (-1/7)

Solution: (-1/7)

∴ It is an rational number

3. Write down the numerator and the denominator of each of the following rational numbers :

(i) (12/17)

Solution: (12/17)

Numerator = 12

Denominator = 17

(ii) (6/-23)

Solution: (6/-23)

Numerator = 6

Denominator = -23

(iii) (-21/5)

Solution: (-21/5)

Numerator = -21

Denominator = 5

(iv) 7

Solution:  7

= (7/1)

Numerator = 7

Denominator = 1

(v) -8

Solution: -8

= (-8/1)

Numerator = -8

Denominator = 1

4. Which of the following are positive rational numbers?

(i) (-7/8)

Solution: (-7/8)

= Not Positive

(ii) (-13/17)

Solution: (-13/17)

= Not Positive

(iii) (-8/-11)

Solution: (-8/-11)

= (-8/-11) ⇒ (8/11)

= Positive

(iv) (0/8)

Solution: (0/8)

= Not Positive

(v) (0/-7)

Solution: (0/-7)

= Not Positive

5. Which of the following are negative rational numbers?

(i) (-16/5)

Solution: (-16/5)

= Negative Rational Number

(ii) (-10/-11)

Solution: (-10/-11)

= Not Negative Rational Number

(iii) -21

Solution:  -21

= Negative Rational Number

(iv) (0/-3)

Solution: (0/-3)

= Not Negative Rational Number

(v) 17

Solution: 17

= Not Negative Rational Number

6. Find four rational numbers equivalent to each of the following :

(i) (3/10)

Solution: (3/10)

(3/10) × (2/2) = (6/20)

(3/10) × (3/3) = (9/30)

(3/10) × (4/4) = (12/40)

(3/10) × (5/5) = (15/50)

∴ The rational numbers will be –

(6/20), (9/30), (12/40), (15/50)

(ii) (-5/9)

Solution: (-5/9)

(-5/9) × (2/2) = (-10/18)

(-5/9) × (3/3) = (-15/27)

(-5/9) × (4/4) = (-20/36)

(-5/9) × (5/5) = (-25/45)

∴ The rational numbers will be –

(-10/18), (-15/27), (-20/36), (-25/45)

(iii) (6/-13)

Solution: (6/-13)

(6/-13) × (2/2) = (12/-26)

(6/-13) × (3/3) = (18/-39)

(6/-13) × (4/4) = (24/-52)

(6/-13) × (5/5) = (30/-65)

∴ The rational numbers will be –

(12/-26), (18/-39), (24/-52), (24/-52)

(iv) 9

Solution:  9

(9/1) × (2/2) = (18/2)

(9/1)  × (3/3) = (27/3)

(9/1)  × (4/4) = (36/4)

(9/1)  × (5/5) = (45/5)

∴ The rational numbers will be –

(18/2), (27/3), (36/4), (45/5)

(v) -1

Solution:  -1

(-1/1) × (2/2) = (-2/2)

(-1/1) × (3/3) = (-3/3)

(-1/1) × (4/4) = (-4/4)

(-1/1) × (5/5) = (-5/5)

∴ The rational numbers will be –

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

7. Write each of the following rational numbers with positive denominator :

(i) (16/-21)

Solution: (16/-21)

= (-16/21)

(ii) (1/-5)

Solution: (1/-5)

= (-1/5)

(iii) (-7/-12)

Solution:  (-7/-12)

= (7/12)

(iv) (5/-1)

Solution: (5/-1)

= (-5/1)

(v) (-6/-1)

Solution: (-6/-1)

= (6/1)

8. Express (4/9) as a rational number with numerator (i) 24 (ii) -20

(i) 24

Solution: 24

(4/9) × (6/6)               [We know 4 × 6 = 24]

= (24/54)

(ii) -20

Solution: -20

(4/9) × (-5/-5)            [We know 4 × -5 = -20]

= (-20/-45)

9. Express (3/8) as a rational number with denominator (i) 48 (ii) -32

(i) 48

Solution: 48

(3/8) × (6/6)            [We know 8 × 6 = 48]

= (18/48)

(ii) -32

Solution: -32

(3/8) × (-4/-4)            [We know 8 × -4 = -32]

= (-12/-32)

10. Express (-6/11) as a rational number with numerator (i) -36 (ii) 42

(i) -36

Solution: -36

(-6/11) × (6/6)              [We know -6 × 6 = -36]

= (-36/66)

(ii) 42

Solution: 42

(-6/11) × (-7/-7)              [We know -6 × -7 = 42]

= (42/-77)

11. Express (2/-7) as a rational number with denominator (i) 42 (ii) -28

(i) 42

Solution: 42

(2/-7) × (-6/-6)              [We know -6 × -7 = 42]

= (-12/42)

(ii) -28

Solution: -28

(2/-7) × (4/4)              [We know -7 × 4 = -28]

= (8/-28)

12. Express (-48/36) as a rational number with numerator (i) -4 (ii) 8

(i) -4

Solution: -4

(-48/36) ÷ (12/12)                   [We know -48 ÷ 12 = -4]

= (-4/3)

(ii) 8

Solution: 8

(-48/36) ÷ (-6/-6)                   [We know -48 ÷ (-6) = 8]

= (8/-6)

13. Express (78/-117) as a rational number with numerator (i) -6 (ii) 2

(i) -6

Solution: -6

(78/-117) ÷ (-13/-13)               [We know 78 ÷ (-13) = -6]

= (-6/9)

(ii) 2

Solution: 2

(78/-117) ÷ (39/39)               [We know 78 ÷ (-13) = 2]

= (2/-3)

14. Write each of the following rational numbers in standard form :

(i) (56/32)

Solution: (56/32)

= (7/4)

(ii) (16/-40)

Solution: (16/-40)

= (2/-4)

(iii) (-36/54)

Solution: (-36/54)

= (-2/3)

(iv) (-22/-77)

Solution: (-22/-77)

= (2/7)

(v) (78/-65)

Solution: (78/-65)

= (6/-5)

(vi) (-95/114)

Solution: (-95/114)

= (-5/6)

(vii) (-69/115)

Solution: (-69/115)

= (-3/5)

(viii) (155/-217)

Solution: (155/-217)

= (5/-7)

15. Find the value of x such that :

(i) (-2/3) = (14/x)

Solution: (-2/3) = (14/x)

-2x = 42

x = (42/2)                     [Gross multiply]

x = -21

(ii) (8/-3) = (x/6)

Solution: (8/-3) = (x/6)

-3x = 48

x = (48/-3)

x = -16

(iii) (5/9) = (x/-27)

Solution: (5/9) = (x/-27)

9x = -135

x = (-135/9)

x = -15

(iv) (11/6) = (-55/x)

Solution: (11/6) = (-55/x)

11x = -330

x = (-330/11)

x = -30

(v) (15/x) = -3

Solution: (15/x) = -3

(15/x) = (-3/1)

-3x = 15

x = (15/-3)

x = -5

(vi) (-36/x) = 2

Solution: (-36/x) = 2

(-36/x) = (2/1)

2x = -36

x = (-36/2)

x = -18

16. State whether the given statement is true (T) or false (F) :

Statement True/False
(i) The quotient of two integers is always a rational number. F
(ii) Every rational number is a fraction. F
(iii) Zero is the smallest rational number. F
(iv) Every fraction is a rational number. T

— : end of Rational Numbers Class- 7th RS Aggarwal Exe-4 A Goyal Brothers ICSE Math Solution:–

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