CBSE Class 7 Mathematics Rational Numbers Assignment Set 01

Rational Numbers Assignment 12. Students are advised to refer to the attached assignments and practice them regularly. This will help them to identify their weak areas and will help them to score better in examination. Parents should download and give the assignments to their children for practice.

Question. Express each of the following as a rational number with positive denominator.
(i) (-15/-28)
(ii) (6/-9)
Solution:
(i) Given (-15/-28)
Multiplying both numerator and denominator we can rational number with positive denominator.
(-15/-28) = (-15/-28) × -1
= (15/28)

(ii) Given (6/-9)
Multiplying both numerator and denominator we can rational number with positive denominator.
(6/-9) = (6/-9) × -1
= (-6/9)

Question. Express (3/5) as a rational number with numerator:
(i) 6
(ii) -15
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)

Question. Express (5/7) as a rational number with denominator:
(i) -14
(ii) 70
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)

Question. Express (3/4) as a rational number with denominator:
(i) 20
(ii) 36
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)

Question. Express (2/5) as a rational number with numerator:
(i) -56
(ii) 154
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/-150)

(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)

Question. Express (-192/108) as a rational number with numerator:
(i) 64
(ii) -16
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)

Question. Express (169/-294) as a rational number with denominator:
(i) 14
(ii) -7
Solution:
(i) Given (169/-294)
To get denominator 14 we have to divide both numerator and denominator by -21
Then we get, (169/-294) ÷ (-21/-21)
= (-8/14)
Therefore (169/-294) as a rational number with denominator 14 is (-8/14)

(ii) Given (169/-294)
To get denominator -7 we have to divide both numerator and denominator by 42
Then we get, (169/-294) ÷ (42/42)
= (4/-7)
Therefore (169/-294) as a rational number with denominator -7 is (4/-7)

Question. Write (-14/42) in a form so that the numerator is equal to:
(i) -2
(ii) 7
Solution:
(i) Given (-14/42)
To get numerator -2 we have to divide both numerator and denominator by 7
Then we get, (-14/42) ÷ (7/7)
= (-2/6)
Therefore (-14/42) as a rational number with numerator -2 is (-2/6)

(ii) Given (-14/42)
To get numerator 7 we have to divide both numerator and denominator by -2
Then we get, (-14/42) ÷ (-2/-2)
= (7/-21)
Therefore (-14/42) as a rational number with numerator -14 is (-14/21)

Question. Select those rational numbers which can be written as a rational number with numerator 6:
(1/22), (2/3), (3/4), (4/-5), (5/6), (-6/7), (-7/8)
Solution:
Given rational numbers that can be written as a rational number with numerator 6 are:
Consider (1/22)
On multiplying by 6, (1/22) can be written as
(1/22) = (6/132)
Consider (2/3)
On multiplying by 3, (2/3) can be written as
(2/3) = (6/9)
Consider (3/4)
On multiplying by 2, (3/4) can be written as
(3/4) = (6/8)
Consider (-6/7)
On multiplying by -1, (-6/7) can be written as
(-6/7) = (6/-7)
Therefore rational numbers that can be written as a rational number with numerator 6 are (1/22), (2/3), (3/4) and (-6/7)

Question. Select those rational numbers which can be written as rational number with denominator 4:
(7/8), (64/16), (36/-12), (-16/17), (5/-4), (140/28)
Solution:
Given rational numbers that can be written as a rational number with denominator 4 are:
(7/8) = (3.5/4) (On dividing both denominator and denominator by 2)
(64/16) = (16/4) (On dividing both denominator and numerator by 4)
(36/-12) = (-12/4) (On dividing both denominator and numerator by -3)
(5/- 4) = (- 5/4) (On multiplying both denominator and numerator by -1)
(140/28) = (20/4) (On dividing both numerator and denominator by 7)

Question.In each of the following, find an equivalent form of the rational number having a common denominator:
(i) (3/4) and (5/12)
(ii) (2/3), (7/6) and (11/12)
Solution:
(i) Given (3/4) and (5/12)
On multiplying both numerator and denominator by 3
(3/4) = (3 × 3)/ (4 × 3) = (9/12)
Equivalent forms with same denominators are (9/12) and (5/12)
(ii) Given (2/3), (7/6) and (11/12)
On multiplying both numerator and denominator by 4
(2/3) = (2 × 4)/ (3 × 4) = (8/12)
And (7/6) = (7 × 2)/ (6 × 2) = (14/12)
Equivalent forms are (8/12), (14/12) and (11/12) having same denominators

Please click the link below to download CBSE Class 7 Mathematics Rational Numbers Assignment Set A