Class 8 Maths Chapter 1 Question Answers - Rational Numbers

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Q1: List any five rational numbers between:
(a) -1 and 0
Ans: The five rational numbers present between the numbers -1 and 0 are as follows,
-1< (-2/3) < (-3/4) < (-4/5) < (-5/6) < (-6/7) < 0
(b) -2 and -1
The five rational numbers present between the numbers -2 and -1 are,
-2 < (-8/7) < (less than) (-9/8) < (-10/9) < (-11/10) < (-12/11) < -1
(c) -4/5 and -2/3
The five rational numbers present between the numbers -4/5 and -2/3 are,
-4/5 < (less than) (-13/12) < (-14/13) < (-15/14) < (-16/15) < (-17/16) < -2/3
(d) -1/2 and 2/3
The five rational numbers present between -1/2 and 2/3 are,
-1/2 < (less than) (-1/6) < (0) < (1/3) < (1/2) < (20/36) < 2/3

Q2: Write any four more rational numbers in each of these following patterns:
(a) -3/5, -6/10, -9/15, -12/20, …..
Ans: 
In the above given question, we can easily observe that the numerator and the denominator are the multiples of numbers three and five.
= (-3 × 1)/ (5 × 1) and (-3 × 2)/ (5 × 2), (-3 × 3)/ (5 × 3), (-3 × 4)/ (5 × 4)
Thus, the next four rational numbers present in this same pattern are as follows,
= (-3 × 5)/ (5 × 5) and (-3 × 6)/ (5 × 6), (-3 × 7)/ (5 × 7), (-3 × 8)/ (5 × 8)
= -15/25, -18/30, -21/35, -24/40 ….
(b) -1/4, -2/8, -3/12, …..
In the above given question, we can easily observe that the numerator and the denominator are the multiples of the numbers one and four.
= (-1 × 1)/ (4 × 1) and (-1 × 2)/ (4 × 2), (-1 × 3)/ (1 × 3)
Then we get, the next four rational numbers present in this pattern will be,
= (-1 × 4)/ (4 × 4) and (-1 × 5)/ (4 × 5), (-1 × 6)/ (4 × 6), (-1 × 7)/ (4 × 7)
= -4/16, -5/20, -6/24, -7/28 and so on.

Q3: Give any four rational numbers equivalent to:
(a) -2/7
Ans: The four rational numbers present whic are equivalent to the fraction -2/7 are,
= (-2 × 2)/ (7 × 2) and (-2 × 3)/ (7 × 3), (-2 × 4)/ (7 × 4) and (-2 × 5)/ (7× 5)
= -4/14, -6/21, -8/28 and -10/35
(b) 5/-3
The four rational numbers present which are equivalent to the fraction 5/-3 are,
= (5 × 2)/ (-3 × 2), (5 × 3)/ (-3 × 3), (5 × 4)/ (-3 × 4) and (5 × 5)/ (-3× 5)
= 10/-6, 15/-9, 20/-12 and 25/-15
(c) 4/9
The four rational numbers present which are equivalent to the fraction 5/-3 are,
= (4 × 2)/ (9 × 2), (4 × 3)/ (9 × 3), (4 × 4)/ (9 × 4) and (4 × 5)/ (9× 5)
= 8/18, 12/27, 16/36 and 20/45

Q4: Which of these following pairs represents the same rational number?
(i) (-7/21) and (3/9)
Ans: We have to check whether the given pair represents the same rational number.
Then,
-7/21 = 3/9
-1/3 = 1/3
∵ -1/3 ≠ 1/3
Hence -7/21 ≠ 3/9
So, the given pair do not represent the same rational number.
(ii) (-16/20) and (20/-25)
We have to check whether the given pair represents the same rational number.
Then,
-16/20 = 20/-25
-4/5 = 4/-5
∵ -4/5 = -4/5
Hence -16/20 = 20/-25
So, the given pair represents same rational number.
(iii) (-2/-3) and (2/3)
We have to check whether the given pair represents the same rational number.
Then,
-2/-3 = 2/3
2/3= 2/3
∵ 2/3 = 2/3
Hence, -2/-3 = 2/3
So, the given pair represents same rational number.

Q5: Rewrite the following rational numbers given below in the simplest form:
(i) -8/6
Ans:
The given above rational numbers can be simplified further,
Then,
= -4/3 … [∵ Divide both the numerator and denominator by 2]
(ii) 25/45
The given above rational numbers can be simplified further,
Then,

= 5/9 … [∵ Divide both the numerator and denominator by 5]
(iii) -44/72
The given above rational numbers can be simplified further,
Then,
= -11/18 … [∵ Divide both the numerator and denominator by 4]
(iv) -8/10
The given above rational numbers can be simplified further,
Then,
= -4/5 … [∵ Divide both the numerator and denominator by 2]

Q6: Fill in the below boxes with the correct symbol of >, <, and =.
(a) -5/7 [ ] 2/3
Ans:
The LCM of the denominators of numbers 7 and 3 is the number 21
Therefore, (-5/7) = [(-5 × 3)/ (7 × 3)] is = (-15/21)
And (2/3) = [(2 × 7)/ (3 × 7)] equals to (14/21)
Now,
-15 < 14
So, (-15/21) < (14/21)
 -5/7 [<] 2/3
(b) -4/5 [ ] -5/7
The LCM of the denominators of 5 and 7 is the number 35
Therefore (-4/5) = [(-4 × 7)/ (5 × 7)] is = (-28/35)
And (-5/7) = [(-5 × 5)/ (7 × 5)] equals to (-25/35)

Now,
-28 < -25
So, (-28/35) < (- 25/35)
 -4/5 [<] -5/7
(c) -7/8 [ ] 14/-16
14/-16 can simplified further,
Then,
7/-8 … [∵ Divide both the numerator and denominator by 2]
So, (-7/8) = (-7/8)
Hence, -7/8 [=] 14/-16