Class 7: Maths Chapter 3 solutions. Complete Class 7 Maths Chapter 3 Notes.
ML Aggarwal Solutions for Class 7 Maths Chapter 3- Rational Numbers
ML Aggarwal 7th Maths Chapter 3, Class 7 Maths Chapter 3 solutions
1. Which of the following are positive rational numbers?
5/8, -3/11, 0/5, 7, -4, -3/-13, -17/-6, 9/-20.
Solution:
The positive rational numbers are:
5/8, 0/5, 7, -3/-13, -17/-6.
2. Which of the following are negative rational numbers?
-5/7, 4/-3, -3/-11, -6, 9, 0, -28/5, 31/7.
Solution:
The negative rational numbers are:
-5/7, 4/-3, -6, -28/5.
3. Find four rational numbers equivalent to each of the following rational numbers:
(i) 3/-7
(ii) -5/-9
Solution:
(i) 3/-7
Let us find the equivalent numbers:
Firstly multiply and divide by 2,
(3/-7) × (2/2) = 6/-14
Similarly, multiply and divide by 3,
(3/-7) × (3/3) = 9/-21
Multiply and divide by 4,
(3/-7) × (4/4) = 12/-28
Multiply and divide by 5,
(3/-7) × (5/5) = 15/-35
Hence, four equivalent rational numbers are:
6/-14, 9/-21, 12/-28, 15/-35
(ii) -5/-9
Let us find the equivalent numbers:
Firstly multiply and divide by 2,
(-5/-9) × (2/2) = -10/-18 = 10/18
Similarly, multiply and divide by 3,
(-5/-9) × (3/3) = -15/-27 = 15/27
Multiply and divide by 4,
(-5/-9) × (4/4) = -20/-36 = 20/36
Multiply and divide by 5,
(-5/-9) × (5/5) = -25/-45 = 25/45
Hence, four equivalent rational numbers are:
10/18, 15/27, 20/36, 25/45
4. Write each of the following rational numbers with positive denominators:
(i) 4/-9
(ii) 17/-33
(iii) -15/-38
Solution:
(i) 4/-9 = -4/9
(ii) 17/-33 = -17/33
(iii) -15/-38 = 15/38
5. Write next four rational numbers in each of the following patterns:
(i) -1/4, -2/8, -3/12, -4/16, ….
(ii) 2/-3, -4/6, -6/9, -8/12, …..
Solution:
(i) -1/4, -2/8, -3/12, -4/16, ….
The next four rational numbers in the same patterns are:
-1/4, -2/8, -3/12, -4/16, -5/20, -6/24, -7/28, -8/32
(ii) 2/-3, -4/6, -6/9, -8/12, …..
The next four rational numbers in the same patterns are:
2/-3, -4/6, -6/9, -8/12, -10/15, -12/18, -14/21, -16/24
6. Which of the following pairs of rational numbers are equal?
(i) -3/-7 and 15/35
(ii) -6/8 and 10/-15
(iii) 6/-10 and -12/20
Solution:
(i) -3/-7 and 15/35
Let us simplify, we get
-3/-7 and 15/35
(-3/-7) = (15/35)
Let us cross multiply, we get
(-3×35) = (15×-7)
-105 = -105
∴ -3/-7 and 15/35 are equal pairs.
(ii) -6/8 and 10/-15
Let us simplify, we get
-6/8 and 10/-15
(-6/8) = (10/-15)
Let us cross multiply, we get
(-6×-15) = (10×8)
90 = 80
∴ -6/8 and 10/-15 are not equal pairs.
(iii) 6/-10 and -12/20
Let us simplify, we get
6/-10 and -12/20
(6/-10) = (-12/20)
Let us cross multiply, we get
(6×20) = (-12×-10)
120 = 120
∴ 6/-10 and -12/20 are equal pairs.
7. Which of the following pairs represent the same rational number?
(i) -7/21, 3/9
(ii) -16/20, 20/-25
(iii) -3/5, -12/20
(iv) 8/-5, -24/15
Solution:
(i) -7/21, 3/9
Let us simplify, we get
(-7/21) = (3/9)
(-1/3) = (1/3)
(-1/3) ≠ (1/3)
∴ -7/21, 3/9 are not same rational numbers.
(ii) -16/20, 20/-25
Let us simplify, we get
(-16/20) = (20/-25)
(-4/5) = (4/-5)
(-4/5) = (-4/5)
∴ -16/20, 20/-25 are same rational numbers.
(iii) -3/5, -12/20
Let us simplify, we get
(-3/5) = (-12/20)
(-3/5) = (-3/5)
∴ -3/5, -12/20 are same rational numbers.
(iv) 8/-5, -24/15
Let us simplify, we get
8/-5, -24/15
(8/-5) = (-24/15)
(8/-5) = (-8/5)
(-8/5) = (-8/5)
∴ 8/-5, -24/15 are same rational numbers.
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ML Aggarwal Solutions for Class 7 Maths Chapter 3- Rational Numbers
Download PDF: ML Aggarwal Solutions for Class 7 Maths Chapter 3- Rational Numbers PDF
Chapterwise ML Aggarwal Solutions for Class 7 Maths :
- Chapter 1- Integers
- Chapter 2- Fractions and Decimals
- Chapter 3- Rational Numbers
- Chapter 4- Exponents and Powers
- Chapter 5- Sets
- Chapter 6- Ratio and Proportion
- Chapter 7- Percentage and Its Applications
- Chapter 8- Algebraic Expressions
- Chapter 9- Linear Equations and Inequalitie
- Chapter 10- Lines and Angles
- Chapter 11- Triangles and its Properties
- Chapter 12- Congruence of Triangles
- Chapter 13- Practical Geometry
- Chapter 14- Symmetry
- Chapter 15- Visualising Solid Shapes
- Chapter 16- Perimeter and Area
- Chapter 17- Data Handling
About ML Aggarwal
M. L. Aggarwal, is an Indian mechanical engineer, educator. His achievements include research in solutions of industrial problems related to fatigue design. Recipient Best Paper award, Manipal Institute of Technology, 2004. Member of TSTE.