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Rational Numbers (Exercise 4.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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 Page 1


 
Exercise 4.2 page no: 4.8 
1. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
(iii) (-28/-11)
(iv) (19/-7)
Solution: 
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-15/-28) = (-15/-28) × (-1/-1)
= (15/28)
(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(6/-9) = (6/-9) × (-1/-1)
= (-6/9)
(iii) Given (-28/-11)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-28/-11) = (-28/-11) × (-1/-1)
= (28/11)
(iv) Given (19/-7)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(19/-7) = (19/-7) × (-1/-1)
= (-19/7)
2. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
Page 2


 
Exercise 4.2 page no: 4.8 
1. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
(iii) (-28/-11)
(iv) (19/-7)
Solution: 
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-15/-28) = (-15/-28) × (-1/-1)
= (15/28)
(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(6/-9) = (6/-9) × (-1/-1)
= (-6/9)
(iii) Given (-28/-11)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-28/-11) = (-28/-11) × (-1/-1)
= (28/11)
(iv) Given (19/-7)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(19/-7) = (19/-7) × (-1/-1)
= (-19/7)
2. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
 
 
 
 
 
 
(iii) 21 
(iv) -27 
 
Solution: 
(i) Given (3/5)  
To get numerator 6 we have to multiply both numerator and denominator by 2 
Then we get, (3/5) × (2/2) = (6/10) 
Therefore (3/5) as a rational number with numerator 6 is (6/10) 
 
(ii) Given (3/5) 
To get numerator -15 we have to multiply both numerator and denominator by -5 
Then we get, (3/5) × (-5/-5) 
= (-15/-25) 
Therefore (3/5) as a rational number with numerator -15 is (-15/-25) 
 
(iii) Given (3/5)  
To get numerator 21 we have to multiply both numerator and denominator by 7 
Then we get, (3/5) × (7/7) 
= (21/35) 
Therefore (3/5) as a rational number with numerator 21 is (21/35) 
 
(iv) Given (3/5) 
To get numerator -27 we have to multiply both numerator and denominator by -9 
Then we get, (3/5) × (-9/-9) 
= (-27/-45) 
Therefore (3/5) as a rational number with numerator -27 is (-27/-45) 
 
3. Express (5/7) as a rational number with denominator: 
(i) -14 
(ii) 70 
(iii) -28 
(iv) -84 
 
Solution: 
(i) Given (5/7)  
To get denominator -14 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (-2/-2) 
Page 3


 
Exercise 4.2 page no: 4.8 
1. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
(iii) (-28/-11)
(iv) (19/-7)
Solution: 
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-15/-28) = (-15/-28) × (-1/-1)
= (15/28)
(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(6/-9) = (6/-9) × (-1/-1)
= (-6/9)
(iii) Given (-28/-11)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-28/-11) = (-28/-11) × (-1/-1)
= (28/11)
(iv) Given (19/-7)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(19/-7) = (19/-7) × (-1/-1)
= (-19/7)
2. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
 
 
 
 
 
 
(iii) 21 
(iv) -27 
 
Solution: 
(i) Given (3/5)  
To get numerator 6 we have to multiply both numerator and denominator by 2 
Then we get, (3/5) × (2/2) = (6/10) 
Therefore (3/5) as a rational number with numerator 6 is (6/10) 
 
(ii) Given (3/5) 
To get numerator -15 we have to multiply both numerator and denominator by -5 
Then we get, (3/5) × (-5/-5) 
= (-15/-25) 
Therefore (3/5) as a rational number with numerator -15 is (-15/-25) 
 
(iii) Given (3/5)  
To get numerator 21 we have to multiply both numerator and denominator by 7 
Then we get, (3/5) × (7/7) 
= (21/35) 
Therefore (3/5) as a rational number with numerator 21 is (21/35) 
 
(iv) Given (3/5) 
To get numerator -27 we have to multiply both numerator and denominator by -9 
Then we get, (3/5) × (-9/-9) 
= (-27/-45) 
Therefore (3/5) as a rational number with numerator -27 is (-27/-45) 
 
3. Express (5/7) as a rational number with denominator: 
(i) -14 
(ii) 70 
(iii) -28 
(iv) -84 
 
Solution: 
(i) Given (5/7)  
To get denominator -14 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (-2/-2) 
 
 
 
 
 
 
= (-10/-14) 
Therefore (5/7) as a rational number with denominator -14 is (-10/-14) 
 
(ii) Given (5/7) 
To get denominator 70 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (10/10) 
= (50/70) 
Therefore (5/7) as a rational number with denominator 70 is (50/70) 
 
(iii) Given (5/7)  
To get denominator -28 we have to multiply both numerator and denominator by -4 
Then we get, (5/7) × (-4/-4) 
= (-20/-28) 
Therefore (5/7) as a rational number with denominator -28 is (-20/-28) 
 
(iv) Given (5/7) 
To get denominator -84 we have to multiply both numerator and denominator by -12 
Then we get, (5/7) × (-12/-12) 
= (-60/-84) 
Therefore (5/7) as a rational number with denominator -84 is (-60/-84) 
 
4. Express (3/4) as a rational number with denominator: 
(i) 20 
(ii) 36 
(iii) 44 
(iv) -80 
 
Solution: 
(i) Given (3/4)  
To get denominator 20 we have to multiply both numerator and denominator by 5 
Then we get, (3/4) × (5/5) 
= (15/20) 
Therefore (3/4) as a rational number with denominator 20 is (15/20) 
 
(ii) Given (3/4)  
To get denominator 36 we have to multiply both numerator and denominator by 9 
Then we get, (3/4) × (9/9) 
Page 4


 
Exercise 4.2 page no: 4.8 
1. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
(iii) (-28/-11)
(iv) (19/-7)
Solution: 
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-15/-28) = (-15/-28) × (-1/-1)
= (15/28)
(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(6/-9) = (6/-9) × (-1/-1)
= (-6/9)
(iii) Given (-28/-11)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-28/-11) = (-28/-11) × (-1/-1)
= (28/11)
(iv) Given (19/-7)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(19/-7) = (19/-7) × (-1/-1)
= (-19/7)
2. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
 
 
 
 
 
 
(iii) 21 
(iv) -27 
 
Solution: 
(i) Given (3/5)  
To get numerator 6 we have to multiply both numerator and denominator by 2 
Then we get, (3/5) × (2/2) = (6/10) 
Therefore (3/5) as a rational number with numerator 6 is (6/10) 
 
(ii) Given (3/5) 
To get numerator -15 we have to multiply both numerator and denominator by -5 
Then we get, (3/5) × (-5/-5) 
= (-15/-25) 
Therefore (3/5) as a rational number with numerator -15 is (-15/-25) 
 
(iii) Given (3/5)  
To get numerator 21 we have to multiply both numerator and denominator by 7 
Then we get, (3/5) × (7/7) 
= (21/35) 
Therefore (3/5) as a rational number with numerator 21 is (21/35) 
 
(iv) Given (3/5) 
To get numerator -27 we have to multiply both numerator and denominator by -9 
Then we get, (3/5) × (-9/-9) 
= (-27/-45) 
Therefore (3/5) as a rational number with numerator -27 is (-27/-45) 
 
3. Express (5/7) as a rational number with denominator: 
(i) -14 
(ii) 70 
(iii) -28 
(iv) -84 
 
Solution: 
(i) Given (5/7)  
To get denominator -14 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (-2/-2) 
 
 
 
 
 
 
= (-10/-14) 
Therefore (5/7) as a rational number with denominator -14 is (-10/-14) 
 
(ii) Given (5/7) 
To get denominator 70 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (10/10) 
= (50/70) 
Therefore (5/7) as a rational number with denominator 70 is (50/70) 
 
(iii) Given (5/7)  
To get denominator -28 we have to multiply both numerator and denominator by -4 
Then we get, (5/7) × (-4/-4) 
= (-20/-28) 
Therefore (5/7) as a rational number with denominator -28 is (-20/-28) 
 
(iv) Given (5/7) 
To get denominator -84 we have to multiply both numerator and denominator by -12 
Then we get, (5/7) × (-12/-12) 
= (-60/-84) 
Therefore (5/7) as a rational number with denominator -84 is (-60/-84) 
 
4. Express (3/4) as a rational number with denominator: 
(i) 20 
(ii) 36 
(iii) 44 
(iv) -80 
 
Solution: 
(i) Given (3/4)  
To get denominator 20 we have to multiply both numerator and denominator by 5 
Then we get, (3/4) × (5/5) 
= (15/20) 
Therefore (3/4) as a rational number with denominator 20 is (15/20) 
 
(ii) Given (3/4)  
To get denominator 36 we have to multiply both numerator and denominator by 9 
Then we get, (3/4) × (9/9) 
 
 
= (27/36) 
Therefore (3/4) as a rational number with denominator 36 is (27/36) 
(iii) Given (3/4)
To get denominator 44 we have to multiply both numerator and denominator by 11
Then we get, (3/4) × (11/11)
= (33/44)
Therefore (3/4) as a rational number with denominator 44 is (33/44)
(iv) Given (3/4)
To get denominator -80 we have to multiply both numerator and denominator by -20
Then we get, (3/4) × (-20/-20)
= (-60/-80)
Therefore (3/4) as a rational number with denominator -80 is (-60/-80)
5. Express (2/5) as a rational number with numerator:
(i) -56
(ii) 154
(iii) -750
(iv) 500
Solution: 
(i) Given (2/5)
To get numerator -56 we have to multiply both numerator and denominator by -28 
Then we get, (2/5) × (-28/-28)
= (-56/-140)
Therefore (2/5) as a rational number with numerator -56 is (-56/-140)
(ii) Given (2/5)
To get numerator 154 we have to multiply both numerator and denominator by 77 
Then we get, (2/5) × (77/77)
= (154/385)
Therefore (2/5) as a rational number with numerator 154 is (154/385)
(iii) Given (2/5)
To get numerator -750 we have to multiply both numerator and denominator by -375 
Then we get, (2/5) × (-375/-375)
Page 5


 
Exercise 4.2 page no: 4.8 
1. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
(iii) (-28/-11)
(iv) (19/-7)
Solution: 
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-15/-28) = (-15/-28) × (-1/-1)
= (15/28)
(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(6/-9) = (6/-9) × (-1/-1)
= (-6/9)
(iii) Given (-28/-11)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(-28/-11) = (-28/-11) × (-1/-1)
= (28/11)
(iv) Given (19/-7)
Multiplying both numerator and denominator we can rational number with positive 
denominator.
(19/-7) = (19/-7) × (-1/-1)
= (-19/7)
2. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
 
 
 
 
 
 
(iii) 21 
(iv) -27 
 
Solution: 
(i) Given (3/5)  
To get numerator 6 we have to multiply both numerator and denominator by 2 
Then we get, (3/5) × (2/2) = (6/10) 
Therefore (3/5) as a rational number with numerator 6 is (6/10) 
 
(ii) Given (3/5) 
To get numerator -15 we have to multiply both numerator and denominator by -5 
Then we get, (3/5) × (-5/-5) 
= (-15/-25) 
Therefore (3/5) as a rational number with numerator -15 is (-15/-25) 
 
(iii) Given (3/5)  
To get numerator 21 we have to multiply both numerator and denominator by 7 
Then we get, (3/5) × (7/7) 
= (21/35) 
Therefore (3/5) as a rational number with numerator 21 is (21/35) 
 
(iv) Given (3/5) 
To get numerator -27 we have to multiply both numerator and denominator by -9 
Then we get, (3/5) × (-9/-9) 
= (-27/-45) 
Therefore (3/5) as a rational number with numerator -27 is (-27/-45) 
 
3. Express (5/7) as a rational number with denominator: 
(i) -14 
(ii) 70 
(iii) -28 
(iv) -84 
 
Solution: 
(i) Given (5/7)  
To get denominator -14 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (-2/-2) 
 
 
 
 
 
 
= (-10/-14) 
Therefore (5/7) as a rational number with denominator -14 is (-10/-14) 
 
(ii) Given (5/7) 
To get denominator 70 we have to multiply both numerator and denominator by -2 
Then we get, (5/7) × (10/10) 
= (50/70) 
Therefore (5/7) as a rational number with denominator 70 is (50/70) 
 
(iii) Given (5/7)  
To get denominator -28 we have to multiply both numerator and denominator by -4 
Then we get, (5/7) × (-4/-4) 
= (-20/-28) 
Therefore (5/7) as a rational number with denominator -28 is (-20/-28) 
 
(iv) Given (5/7) 
To get denominator -84 we have to multiply both numerator and denominator by -12 
Then we get, (5/7) × (-12/-12) 
= (-60/-84) 
Therefore (5/7) as a rational number with denominator -84 is (-60/-84) 
 
4. Express (3/4) as a rational number with denominator: 
(i) 20 
(ii) 36 
(iii) 44 
(iv) -80 
 
Solution: 
(i) Given (3/4)  
To get denominator 20 we have to multiply both numerator and denominator by 5 
Then we get, (3/4) × (5/5) 
= (15/20) 
Therefore (3/4) as a rational number with denominator 20 is (15/20) 
 
(ii) Given (3/4)  
To get denominator 36 we have to multiply both numerator and denominator by 9 
Then we get, (3/4) × (9/9) 
 
 
= (27/36) 
Therefore (3/4) as a rational number with denominator 36 is (27/36) 
(iii) Given (3/4)
To get denominator 44 we have to multiply both numerator and denominator by 11
Then we get, (3/4) × (11/11)
= (33/44)
Therefore (3/4) as a rational number with denominator 44 is (33/44)
(iv) Given (3/4)
To get denominator -80 we have to multiply both numerator and denominator by -20
Then we get, (3/4) × (-20/-20)
= (-60/-80)
Therefore (3/4) as a rational number with denominator -80 is (-60/-80)
5. Express (2/5) as a rational number with numerator:
(i) -56
(ii) 154
(iii) -750
(iv) 500
Solution: 
(i) Given (2/5)
To get numerator -56 we have to multiply both numerator and denominator by -28 
Then we get, (2/5) × (-28/-28)
= (-56/-140)
Therefore (2/5) as a rational number with numerator -56 is (-56/-140)
(ii) Given (2/5)
To get numerator 154 we have to multiply both numerator and denominator by 77 
Then we get, (2/5) × (77/77)
= (154/385)
Therefore (2/5) as a rational number with numerator 154 is (154/385)
(iii) Given (2/5)
To get numerator -750 we have to multiply both numerator and denominator by -375 
Then we get, (2/5) × (-375/-375)
 
 
 
 
 
 
= (-750/-1875) 
Therefore (2/5) as a rational number with numerator -750 is (-750/-1875) 
 
(iv) Given (2/5) 
To get numerator 500 we have to multiply both numerator and denominator by 250 
Then we get, (2/5) × (250/250) 
= (500/1250) 
Therefore (2/5) as a rational number with numerator 500 is (500/1250) 
 
6. Express (-192/108) as a rational number with numerator: 
(i) 64 
(ii) -16 
(iii) 32 
(iv) -48 
 
Solution: 
(i) Given (-192/108) 
To get numerator 64 we have to divide both numerator and denominator by -3 
Then we get, (-192/108) ÷ (-3/-3) 
= (64/-36) 
Therefore (-192/108) as a rational number with numerator 64 is (64/-36) 
 
(ii) Given (-192/108) 
To get numerator -16 we have to divide both numerator and denominator by 12 
Then we get, (-192/108) ÷ (12/12) 
= (-16/9) 
Therefore (-192/108) as a rational number with numerator -16 is (-16/9) 
 
(iii) ) Given (-192/108) 
To get numerator 32 we have to divide both numerator and denominator by -6 
Then we get, (-192/108) ÷ (-6/-6) 
= (32/-18) 
Therefore (-192/108) as a rational number with numerator 32 is (32/-18) 
 
(iv) Given (-192/108) 
To get numerator -48 we have to divide both numerator and denominator by 4 
Then we get, (-192/108) ÷ (4/4)
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Document Description: RD Sharma Solutions: Rational Numbers (Exercise 4.2) for Class 7 2024 is part of Mathematics (Maths) Class 7 preparation. The notes and questions for RD Sharma Solutions: Rational Numbers (Exercise 4.2) have been prepared according to the Class 7 exam syllabus. Information about RD Sharma Solutions: Rational Numbers (Exercise 4.2) covers topics like and RD Sharma Solutions: Rational Numbers (Exercise 4.2) Example, for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Rational Numbers (Exercise 4.2).
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