Class 8 Maths Prachi Publication Chapter 1 Rational Numbers (New Syllabus)

In this article we will get the solution of all the assignments of Class 8 Maths Prachi Publication Chapter 1 Rational Numbers
, In this chapter, we have been given the solutions of assignments 1.1 and 1.2 in a simple and easy way by Study Circle. Class 8 Maths Prachi Publication Chapter 1 Rational Numbers and Exercises also have solutions for Section A and Section B. Study Circle provided by

Class 8 Maths Prachi Publication Chapter 1

Assignment 1.1 

Question 1.  Multiple Choice Questions ( MCQ) 

(I) The standard form of 28/-70 is

(a) -28/70

(b) -2/5

(c) -4/10

(d) 2/-5

Solution:

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

 

(ii) The rational numbers not equivalent to -16/28 is

(a) -48/84

(b) -12/21

(c) -4/7

(d) -64/116

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

(iii) What should be added to (3/6 + 1/2 – 2/4) to get 1?

(a) 1/12

(b) 1/3

(c) 1/2

(d) 1/8

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

(iv) If  X=7/8 and Y = -5/4, then
a. (x+y)>0
b.(x+y)<0
c.(x+y)=0
d.(x+y)->0

Solution:–  Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

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Question – 2.   Write two rational numbers which are their own reciprocals.

Solution:–

1 and -1 are the rational numbers which are their own reciprocals.

Question -3. Which rational number is the multiplicative identity for rational numbers ?

Solution:-– When we multiply a number by 1, we can say that 1 is a multiplicative identity.

examples — 2/3 x 1 = 2/3

3/5 x 1 = 3/5

Question – 4.  Express 2/-3 as rational number with  denominator :

(i) – 15            (ii) 18

Solution:–

(i)-15

denominator should be -15

2/-3

-3×5=-15

so,multiply 2/-3 with 5/5

2/-3×5/5

=10/-15

(ii)18

denominator should be 18

2/-3=-2/3

3×6=18

so, multiply -2/3 with 6/6

-2/3×6/6=-12/18

ans) -12/18

Question -5.  Express 24 / -30 as rational number with numerator :

(i) -8   and     (ii) -12

Answer:

i) 24/-30 with numerator -8 = -8/10 (Divide both of them by 3 we get 8/-10 = -8/10)

ii)24/-30 with numerator -12 = -12/15 (Divide both of them by 2 we get 12/-15 = -12/15

Question – 6. If x = 7/12 , y = 0/12 and z = -5/12 , write whether x>y , y = z or z>x .

Class 8 Maths Prachi Publication Chapter 1

Question -7 Find the reciprocal of the following rational numbers : 

(i) – 6/7                                        (ii)  3/-5

Solution: (i) Reciprocal of -6/7 is -7/6

(ii) Reciprocal of  3/-5 is -3/5

Question – 8 Subtract the sum of -3/10 and 5/8 from the sum of 4/15 and 2/-5.

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Question – 9 Subtract the sum of -11/5 and -2/3 from the sum of 3/5 and 7/3.

Class 8 Maths Prachi Publication Chapter 1

Question -10 If x = 5/9 and y = 9/11, prove that | x+y| = |x| + |y|.

Solution:

 

Class 8 Maths Prachi Publication Chapter 1

Question 11. Simplify : 

(i) – (3/11x -5/6 ) – ( 9/12÷ 3/4) – (5/13 x -6/15)

Solution:-

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

(ii) (-13/9 ÷2/15) x (7/3 ÷ 5/8) + (3/5 x 1/2)

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

(iii) -2/5 – (-3/10) – (-4/7)

Solution:- 

Class 8 Maths Prachi Publication Chapter 1 Rational Numbers

(iv) ( 1/2×1/4 ) – (1x 1/4 ) + ( -7/18÷ 7/-15)

Class 8 Maths Prachi Publication Chapter 1

Question 12- The product of two rational numbers is 5/18. If one of them is -3/20 , find the other . 

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Question 13.– The product of two rational numbers is -1. If one of the rational numbers is -17/8 find                               the other. 

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Question 14. – Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Question 15 Verify x × ( y+z ) = x × y + x × z by taking x = 3/13 , y = -2/7 and z= -1/2

Solution :–

Class 8 Maths Prachi Publication Chapter 1

Question -16  Verify x × (y+z) = x ×y + x × z for :

(i) x = 3/5 , y = -2/5 ,z =-7/5                             (ii) x = -5/12 , y = 7/8 , -12/3

Solution:– (i)

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1 

Assignment 1.2

Question 1 Multiple choice Questions ( choice the correct option)

(i) In the number line given at right , the point ‘P’ represents :–

(a) 4/5              (b)  3/5         (c) -2/5            (d) -1/5

Solution :–

Class 8 Maths Prachi Publication Chapter 1 

the answer is (c) 3/5

(ii) In the number line of (i) , the point Q represents :–

(a) -5/6        (b)  5/6       (c)   1/6     (d)  -1/6 

Class 8 Maths Prachi Publication Chapter 1

Question-2 Represent the following rational numbers on number line :-

(i)  -7/8     (ii) 3/7     (iii) -4/5    (iv)  2/9  

Solution (i)

Class 8 Maths Prachi Publication Chapter 1

(ii)

Class 8 Maths Prachi Publication Chapter 1

(iii)

Class 8 Maths Prachi Publication Chapter 1

(iv)

Class 8 Maths Prachi Publication Chapter 1

Question-3 Represent the following rational numbers on number line :-

(i)  13/3               (ii)  -7/5        (iii)  15/4      (iv) -23/7

Solution –: 

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Assignment 1.3

Question -1 Multiple choice Questions (MCQ)

(i) Two possible rational numbers between -4/5 and -3/7 are 

(a) 3/35, 4/35     (b)  -1/35, -2/35    (c)  -3/35 , -4/35   (d)  -21/35 , -20/35

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Option d is right answer .

(ii) If -1/3 is between 0 and -1 , then -1/6 may be between 

(a) -1 and -2     (b)  0 and -2/6     (c)  0 and -1/6    (d)  -2/6 and -3/6  

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Option B is the right answer.

(iii) The no. of rational numbers between -5/9 and 5/6 is 

(a) 9      (b)    90     (c) 11    (d)  infinity

Solution :– Option D is the right answer.

Question 2 Insert 5 rational numbers between :–

(i)  -3/11 and -1/13       (ii)  3/8 and -1/2      (iii)  2/3 and 3/13 

Solution:– (i)

Class 8 Maths Prachi Publication Chapter 1

(ii) 

Class 8 Maths Prachi Publication Chapter 1

(iii) 

Class 8 Maths Prachi Publication Chapter 1

Question 3 Insert 6 rational numbers between :– 

(i) 7/13 and -4/13    (ii)  7/11 and 8/11    (iii) -10/17 and -11/17 

Solution:–(i)

Class 8 Maths Prachi Publication Chapter 1

(ii)

Class 8 Maths Prachi Publication Chapter 1

(iii) 

Class 8 Maths Prachi Publication Chapter 1

Question- 4 Insert 10 rational numbers between :–

(i) -3/11 and -2/11    (ii)  10/13 and 12/13  

Solution :–(i)

Class 8 Maths Prachi Publication Chapter 1

(ii)

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Assignment 1.4

 

Question -1 (i) The price of 100 pens is rupees 500 3/5 and the price of 50 pencil is rupees 100 1/5 . Find the price of 3 pens and 5 pencils.​

(a) 2504            (b) ₹ 25.04      (c)  ₹ 25.4            (d)  ₹ 25

Solution :–(i)

Class 8 Maths Prachi Publication Chapter 1 

= 25.038 or 25.04  option B, is right answer

(ii) If the price of 12 shirts is rupees 3600 2/5 and of 6 pants is rupees 3000 3/4 . Find the price of 4 shirts and 4 pants ​is 

(a) ₹ 320         (b) ₹ 3200        (c) ₹ 32000           (d)  ₹ 3200.63

Solution —

Class 8 Maths Prachi Publication Chapter 1

(iii) The speed of a bus is 40 1/4 km/h. The time (in minutes) to travel 1000/3 km by the bus is 

(a)  496 min.      (b)  497 min.           (c)    496.6 min.    (d)    498 min.

Solution: –Option ‘c’ is right answer.

Class 8 Maths Prachi Publication Chapter 1

(iv)  The speed of a train is 60 1/2 km/h . How much distance the train will travel in 10 1/2 hours 45/2 minutes ? 

(a) 657.94 km       (b)  657 km     (c)  65.79 km    (d)  657.98 km

Solution:– Option ‘a’ is a right answer.

Class 8 Maths Prachi Publication Chapter 1

Question -2   A  train travels a distance of 1000 km 400 m in 15 1/2 hours 30 minutes. What is the average speed of the train ?

Solution:–

Class 8 Maths Prachi Publication Chapter 1

Question -3   A Car is travelling with a speed of 50 2/5 km/h. How much time will it take to travel the distance of 200 km 100 m ? 

Solution :– 

 

Class 8 Maths Prachi Publication Chapter 1

Question- 4  A boy has a cardboard of length 10/7 m and breadth 5/4 m. He wants to make 5 pieces from to cardboard by cutting and pasting. Find the area of 3 such pieces.

Solution :–

Class 8 Maths Prachi Publication Chapter 1

Question- 5  One seller quoted the price of 5 pens and 7 pencils as Rs. 55 1/3 and Rs. 14 2/3 respectively. Second seller quoted the price of 7 pens and 5 pencils as Rs. 78 2/5 and Rs. 10 3/4 respectively. From where we should buy?

Solution :–

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Question- 6   The length and breadth of a cardboard 2 1/5 m and 1 1/5 m respectively. The length and breadth of the second cardboard 3 1/5 m and 2 2/5 m  respectively. Both cardboards are divided into 10 equal small pieces. What is the total area of the cardboard , if it is made using 5 small pieces from the first cardboard and 3 small pieces from the second cardboard. 

Solution :– 

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Class 8 Maths Prachi Publication Chapter 1

Chapter End Exercise : Section A

Multiple Choice Question (MCQ)

Question -1  If x = 1/2 and y = -1/2 then 

(a) x +y > 0    (b)  x – y < 0   (c)   x – y = 1       (d)  x + y = 1

Solution:– Option C is right answer.

Class 8 Maths Prachi Publication Chapter 1

Question-2 Which of the following rational numbers is in the standard form ?

(a)  -9/16     (b)  – 49/ 91      (c) -12/26     (d)  28/-105

Answer :–

Class 8 Maths Prachi Publication Chapter 1

Option  (a) -9/16

Question 3 — The reciprocal of a rational number 

(a) is a positive rational number.

(b) is a negative rational number.

(c) does not exist.

(d) can be either a positive or a negative rational number.

Solution :– (b) is a negative rational number.

Question 4 — The value of (-9/16 X 24/27)

Class 8 Maths Prachi Publication Chapter 1

Option D is right answer.

Question 5 —

Class 8 Maths Prachi Publication Chapter 1

Solution :–

Class 8 Maths Prachi Publication Chapter 1

Question 6 :–

Class 8 Maths Prachi Publication Chapter 1

Solution :–

Class 8 Maths Prachi Publication Chapter 1

 

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