class 7 maths chapter 9
Answers
Class 7 Chapter 9 – Rational Numbers
Exercise 9.1 Page: 182
1. List five rational numbers between:
(i) -1 and 0
Solution:-
The five rational numbers between -1 and 0 are,
-1< (-2/3) < (-3/4) < (-4/5) < (-5/6) < (-6/7) < 0
(ii) -2 and -1
Solution:-
The five rational numbers between -2 and -1 are,
-2 < (-8/7) < (-9/8) < (-10/9) < (-11/10) < (-12/11) < -1
(iii) -4/5 and -2/3
Solution:-
The five rational numbers between -4/5 and -2/3 are,
-4/5 < (-13/12) < (-14/13) < (-15/14) < (-16/15) < (-17/16) < -2/3
(iv) -1/2 and 2/3
Solution:-
The five rational numbers between -1/2 and 2/3 are,
-1/2 < (-1/6) < (0) < (1/3) < (1/2) < (20/36) < 2/3
2. Write four more rational numbers in each of the following patterns:
(i) -3/5, -6/10, -9/15, -12/20, …..
Solution:-
In the above question, we can observe that the numerator and denominator are the multiples of 3 and 5.
= (-3 × 1)/ (5 × 1), (-3 × 2)/ (5 × 2), (-3 × 3)/ (5 × 3), (-3 × 4)/ (5 × 4)
Then, next four rational numbers in this pattern are,
= (-3 × 5)/ (5 × 5), (-3 × 6)/ (5 × 6), (-3 × 7)/ (5 × 7), (-3 × 8)/ (5 × 8)
= -15/25, -18/30, -21/35, -24/40 ….
(ii) -1/4, -2/8, -3/12, …..
Solution:-
In the above question, we can observe that the numerator and denominator are the multiples of 1 and 4.
= (-1 × 1)/ (4 × 1), (-1 × 2)/ (4 × 2), (-1 × 3)/ (1 × 3)
Then, next four rational numbers in this pattern are,
= (-1 × 4)/ (4 × 4), (-1 × 5)/ (4 × 5), (-1 × 6)/ (4 × 6), (-1 × 7)/ (4 × 7)
= -4/16, -5/20, -6/24, -7/28 ….
(iii) -1/6, 2/-12, 3/-18, 4/-24 …..
Solution:-
In the above question, we can observe that the numerator and denominator are the multiples of 1 and 6.
= (-1 × 1)/ (6 × 1), (1 × 2)/ (-6 × 2), (1 × 3)/ (-6 × 3), (1 × 4)/ (-6 × 4)
Then, next four rational numbers in this pattern are,
= (1 × 5)/ (-6 × 5), (1 × 6)/ (-6 × 6), (1 × 7)/ (-6 × 7), (1 × 8)/ (-6 × 8)
= 5/-30, 6/-36, 7/-42, 8/-48 ….
(iv) -2/3, 2/-3, 4/-6, 6/-9 …..
Solution:-
In the above question, we can observe that the numerator and denominator are the multiples of 2 and 3.
= (-2 × 1)/ (3 × 1), (2 × 1)/ (-3 × 1), (2 × 2)/ (-3 × 2), (2 × 3)/ (-3 × 3)
Then, next four rational numbers in this pattern are,
= (2 × 4)/ (-3 × 4), (2 × 5)/ (-3 × 5), (2 × 6)/ (-3 × 6), (2 × 7)/ (-3 × 7)
= 8/-12, 10/-15, 12/-18, 14/-21 ….
3. Give four rational numbers equivalent to:
(i) -2/7
Solution:-
The four rational numbers equivalent to -2/7 are,
= (-2 × 2)/ (7 × 2), (-2 × 3)/ (7 × 3), (-2 × 4)/ (7 × 4), (-2 × 5)/ (7× 5)
= -4/14, -6/21, -8/28, -10/35
(ii) 5/-3
Solution:-
The four rational numbers equivalent to 5/-3 are,
= (5 × 2)/ (-3 × 2), (5 × 3)/ (-3 × 3), (5 × 4)/ (-3 × 4), (5 × 5)/ (-3× 5)
= 10/-6, 15/-9, 20/-12, 25/-15
(iii) 4/9
Solution:-
The four rational numbers equivalent to 5/-3 are,
= (4 × 2)/ (9 × 2), (4 × 3)/ (9 × 3), (4 × 4)/ (9 × 4), (4 × 5)/ (9× 5)
= 8/18, 12/27, 16/36, 20/45
4. Draw the number line and represent the following rational numbers on it:
(i) ¾
Solution:-
We know that 3/4 is greater than 0 and less than 1.
∴it lies between 0 and 1. It can be represented on number line as,
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 1
(ii) -5/8
Solution:-
We know that -5/8 is less than 0 and greater than -1.
∴it lies between 0 and -1. It can be represented on number line as,
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 2
(iii) -7/4
Solution:-
Now above question can be written as,
= (-7/4) =
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 3
We know that (-7/4) is Less than -1 and greater than -2.
∴it lies between -1 and -2. It can be represented on number line as,
5. The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 6
Solution:-
By observing the figure, we can say that,
The distance between A and B = 1 unit
And it is divided into 3 equal parts = AP = PQ = QB = 1/3
P = 2 + (1/3)
= (6 + 1)/ 3
= 7/3
Q = 2 + (2/3)
= (6 + 2)/ 3
= 8/3
Similarly,
The distance between U and T = 1 unit
And it is divided into 3 equal parts = TR = RS = SU = 1/3
R = – 1 – (1/3)
= (- 3 – 1)/ 3
= – 4/3
S = – 1 – (2/3)
= – 3 – 2)/ 3
= – 5/3
6. Which of the following pairs represent the same rational number?
(i) (-7/21) and (3/9)
Solution:-
We have to check the given pair represents the same rational number.
Then,
-7/21 = 3/9
-1/3 = 1/3
∵ -1/3 ≠ 1/3
∴ -7/21 ≠ 3/9
So, the given pair is not represents the same rational number.
(ii) (-16/20) and (20/-25)
Solution:-
We have to check the given pair represents the same rational number.
Then,
-16/20 = 20/-25
-4/5 = 4/-5
∵ -4/5 = -4/5
∴ -16/20 = 20/-25
So, the given pair is represents the same rational number.
(iii) (-2/-3) and (2/3)
Solution:-
We have to check the given pair represents the same rational number.
Then,
-2/-3 = 2/3
2/3= 2/3
∵ 2/3 = 2/3
∴ -2/-3 = 2/3
So, the given pair is represents the same rational number.