**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

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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