# ML Aggarwal Solutions for Class 7 Maths Chapter 3 - Rational Numbers

ML Aggarwal Solutions for Class 7 Maths Chapter 3 – Rational Numbers are provided here to help students prepare for the final exam and score well. The chapter mainly deals with problems based on rational numbers. To make learning easy and fun, the solutions given here are developed in an interesting manner. With ML Aggarwal Solutions, students can effortlessly prepare for their exams and are also advised to practise on a daily basis to score excellent marks. Students can easily download the solutions and can start practising offline in order to grasp the concepts thoroughly.

Chapter 3 – Rational Numbers provides solutions to questions related to each and every topic present in the chapter. Students can refer to and easily download the PDF of ML Aggarwal Class 7 Solutions for free from the link given below.

## ML Aggarwal Solutions for Class 7 Maths Chapter 3 – Rational Numbers

### Access answers to ML Aggarwal Solutions for Class 7 Maths Chapter 3 – Rational Numbers

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, and 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, and 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, and 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.