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NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

Document Description: NCERT Solutions: Rational Numbers for Class 7 2022 is part of Class 7 Mathematics for Mathematics (Maths) Class 7 preparation. The notes and questions for NCERT Solutions: Rational Numbers have been prepared according to the Class 7 exam syllabus. Information about NCERT Solutions: Rational Numbers covers topics like Exercise 9.1, Exercise 9.2  and NCERT Solutions: Rational Numbers Example, for Class 7 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions: Rational Numbers.

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Table of contents
Exercise 9.1
Exercise 9.2 
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Exercise 9.1

Q1. List five rational numbers between:

(i) -1 and 0
Ans: Let us write -1 and 0 as rational numbers with denominator 6.

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, five rational numbers between -1 and 0 would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(ii) -2 and -1
Ans: Let us write -2 and -1 as rational numbers with denominator 6.

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, Five rational numbers between -2 and -1 would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Let us write  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 as rational numbers with the same denominators.

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, five rational numbers between NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Let us write  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7as rational numbers with the same denominators.

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, five rational numbers between  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 would be  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7


Q2. Write four more rational numbers in each of the following patterns: 

(i) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, the next four rational numbers of this pattern would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(ii)   NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, the next four rational numbers of this pattern would be

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, the next four rational numbers of this pattern would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Therefore, the next four rational numbers of tins pattern would be
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7


Q3. Give four rational numbers equivalent to:

(i) -2/7
Ans: The four rational numbers equivalent to -2/7 are,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

Therefore, four equivalent rational numbers are NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(ii) 5/-3

Ans: The four rational numbers equivalent to 5/-3 are,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

Therefore, four equivalent rational numbers are  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iii) 4/9

Ans: The four rational numbers equivalent to 5/-3 are,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

Therefore, four equivalent rational numbers are  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7


Q4. Draw the number line and represent the following rational numbers on it: 

(i) 3/4
Ans: 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: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(ii) -5/8
Ans: 
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: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iii)  -7/4
Ans: 
Now above question can be written as,
= (-7/4) = NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
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,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

(iv) 7/8
Ans: 
We know that 7/8 is greater than 0 and less than 1.
∴ it lies between 0 and 1. It can be represented on number line as,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7


Q5. 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: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

Ans:
Therefore,  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Similarly  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Thus, the rational numbers represented P, Q, R and S are  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 respectively.


Q6. Which of the following pairs represent the same rational numbers: 

(i) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7    [Converting into lowest term]
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is not represents the same rational number.

(ii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 [Converting into lowest term]

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is represents the same rational number.

(iii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 [Converting into lowest term]

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is represents the same rational number.

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7  [Converting into lowest term]

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is represents the same rational number.

(v)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7   [Converting into lowest term]

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is represents the same rational number.

(vi)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7   [Converting into lowest term]

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is not represents the same rational number.

(vii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 
We have to check the given pair represents the same rational number.
Then,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7  [Converting into lowest terra]
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
So, the given pair is not represents the same rational number.


Q7. Rewrite the following rational numbers in the simplest form:

(i) -8/6
Ans: 
The given rational numbers can be simplified further,
Then,
= -4/3 … [∵ Divide both numerator and denominator by 2]

(ii) 25/45
Ans: 
The given rational numbers can be simplified further,
Then,
= 5/9 … [∵ Divide both numerator and denominator by 5]

(iii) -44/72
Ans: 
The given rational numbers can be simplified further,
Then,
= -11/18 … [∵ Divide both numerator and denominator by 4]

(iv) -8/10
Ans: 
The given rational numbers can be simplified further,
Then,
= -4/5 … [∵ Divide both numerator and denominator by 2]


Q8. Fill in the boxes with the correct symbol out of <, > and =:

(i) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 7 and 3 is 21
∴ (-5/7) = [(-5 × 3)/ (7 × 3)] = (-15/21)
And (2/3) = [(2 × 7)/ (3 × 7)] = (14/21)
Now, -15 < 14
So,
(-15/21) < (14/21)
Hence, -5/7 [<] 2/3

(ii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 5 and 7 is 35
∴ (-4/5) = [(-4 × 7)/ (5 × 7)] = (-28/35)
And (-5/7) = [(-5 × 5)/ (7 × 5)] = (-25/35)
Now, -28 < -25
So,
(-28/35) < (- 25/35)
Hence, -4/5 [<] -5/7

(iii) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: 14/-16 can be simplified further,
Then,
7/-8 … [∵ Divide both numerator and denominator by 2]
So,
(-7/8) = (-7/8)
Hence, -7/8 [=] 14/-16

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 5 and 4 is 20
∴ (-8/5) = [(-8 × 4)/ (5 × 4)] = (-32/20)
And (-7/4) = [(-7 × 5)/ (4 × 5)] = (-35/20)
Now, -32 > – 35
So,
(-32/20) > (- 35/20)
Hence, -8/5 [>] -7/4

(v) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 3 and 4 is 12
∴ (-1/3) = [(-1 × 4)/ (3 × 4)] = (-4/12)
And (-1/4) = [(-1 × 3)/ (4 × 3)] = (-3/12)
Now, -4 < – 3
So,
(-4/12) < (- 3/12)
Hence, 1/-3 [<] -1/4

(vi)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Since, (-5/11) = (-5/11)
Hence, 5/-11 [=] -5/11

(vii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Since every negative rational number is less than 0.
We have:
= 0 [>] -7/6

Q9. Which is greater in each of the following: 

(i) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 3 and 2 is 6
(2/3) = [(2 × 2)/ (3 × 2)] = (4/6)
And (5/2) = [(5 × 3)/ (2 × 3)] = (15/6)
Now, 4 < 15
So, (4/6) < (15/6)
∴ 2/3 < 5/2
Hence, 5/2 is greater.

(ii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 6 and 3 is 6
∴ (-5/6) = [(-5 × 1)/ (6 × 1)] = (-5/6)
And (-4/3) = [(-4 × 2)/ (3 × 2)] = (-12/6)
Now, -5 > -12
So, (-5/6) > (- 12/6)
∴ -5/6 > -12/6
Hence, – 5/6 is greater.

(iii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The LCM of the denominators 4 and 3 is 12
∴ (-3/4) = [(-3 × 3)/ (4 × 3)] = (-9/12)
And (-2/3) = [(-2 × 4)/ (3 × 4)] = (-8/12)
Now, -9 < -8 So, (-9/12) < (- 8/12)
∴ -3/4 < 2/-3
Hence, 2/-3 is greater.

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: The given fraction is like friction,
So, -¼ < ¼
Hence ¼ is greater,

(v)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: First we have to convert mixed fraction into improper fraction,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7= -23/7
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7= -19/5
Then, The LCM of the denominators 7 and 5 is 35
∴ (-23/7) = [(-23 × 5)/ (7 × 5)] = (-115/35)
And (-19/5) = [(-19 × 7)/ (5 × 7)] = (-133/35)
Now, -115 > -133 So, (-115/35) > (- 133/35)

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7> NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Hence, NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7is greater.

Q10. Write the following rational numbers in ascending order: 

(i)  -3/5, -2/5, -1/5
Ans: 
The given rational numbers are in form of like fraction,
Hence, (-3/5)< (-2/5) < (-1/5)

(ii) -1/3, -2/9, -4/3
Ans:
To convert the given rational numbers into like fraction we have to find LCM,
LCM of 3, 9, and 3 is 9
Now,
(-1/3)= [(-1 × 3)/ (3 × 9)] = (-3/9)
(-2/9)= [(-2 × 1)/ (9 × 1)] = (-2/9)
(-4/3)= [(-4 × 3)/ (3 × 3)] = (-12/9)
Clearly, (-12/9) < (-3/9) < (-2/9)
Hence, (-4/3) < (-1/3) < (-2/9)

(iii) -3/7, -3/2, -3/4
Ans: 
To convert the given rational numbers into like fraction we have to find LCM,
LCM of 7, 2, and 4 is 28
Now, (-3/7)= [(-3 × 4)/ (7 × 4)] = (-12/28)
(-3/2)= [(-3 × 14)/ (2 × 14)] = (-42/28)
(-3/4)= [(-3 × 7)/ (4 × 7)] = (-21/28)
Clearly, (-42/28) < (-21/28) < (-12/28)
Hence, (-3/2) < (-3/4) < (-3/7)


Exercise 9.2 

Q1. Find the sum: 

(i) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We have:
= (5/4) – (11/4) = [(5 – 11)/4] … [∵ denominator is same in both the rational numbers]
= (-6/4)
= -3/2 … [∵ Divide both numerator and denominator by 3]

(ii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Take the LCM of the denominators of the given rational numbers.
LCM of 3 and 5 is 15 Express each of the given rational numbers with the above LCM as the common denominator.
Now, (5/3) = [(5 × 5)/ (3 × 5)] = (25/15)
(3/5) = [(3 × 3)/ (5 × 3)] = (9/15)
Then,
= (25/15) + (9/15) … [∵ denominator is same in both the rational numbers]
= (25 + 9)/15 = 34/15

(iii)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Take the LCM of the denominators of the given rational numbers.
LCM of 10 and 15 is 30 Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(-9/10)= [(-9 × 3)/ (10 × 3)] = (-27/30)
(22/15)= [(22 × 2) / (15 × 2)] = (44/30)
Then, = (-27/30) + (44/30) … [∵ denominator is same in both the rational numbers]
= (-27 + 44)/30
= (17/30)

(iv)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We have, = 3/11 + 5/9
Take the LCM of the denominators of the given rational numbers.
LCM of 11 and 9 is 99
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(3/11) = [(3 × 9)/ (11 × 9)] = (27/99)
(5/9) = [(5 × 11)/ (9 × 11)] = (55/99)
Then,
= (27/99) + (55/99) … [∵ denominator is same in both the rational numbers]
= (27 + 55)/99
= (82/99)

(v)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We have = -8/19 – 2/57
Take the LCM of the denominators of the given rational numbers.
LCM of 19 and 57 is 57
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(-8/19)= [(-8 × 3)/ (19 × 3)] = (-24/57) (-2/57)= [(-2 × 1)/ (57 × 1)] = (-2/57)
Then,
= (-24/57) – (2/57) … [∵ denominator is same in both the rational numbers]
= (-24 – 2)/57 = (-26/57)

(vi) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We know that any number or fraction is added to zero the answer will be the same number or fraction.
Hence,
= -2/3 + 0
= -2/3

(vi)NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:

NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7    [L.C.M. of 3 and 5 is 15]
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7


Q2. Find: 

(i)  NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: Take the LCM of the denominators of the given rational numbers.
LCM of 24 and 36 is 72
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(7/24)= [(7 × 3)/ (24 × 3)] = (21/72)
(17/36)= [(17 × 2)/ (36 × 2)] = (34/72)
Then,
= (21/72) – (34/72) … [∵ denominator is same in both the rational numbers]
= (21 – 34)/72 = (-13/72)

(ii)NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We can also write -6/21 = -2/7
= 5/63 – (-2/7)
We have, = 5/63 + 2/7
Take the LCM of the denominators of the given rational numbers.
LCM of 63 and 7 is 63
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(5/63)= [(5 × 1)/ (63 × 1)] = (5/63)
(2/7)= [(2 × 9)/ (7 × 9)] = (18/63)
Then, = (5/63) + (18/63) … [∵ denominator is same in both the rational numbers]
= (5 + 18)/63 = 23/63

(iii)NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans: We have, = -6/13 + 7/15
LCM of 13 and 15 is 195
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(-6/13)= [(-6 × 15)/ (13 × 15)] = (-90/195)
(7/15)= [(7 × 13)/ (15 × 13)] = (91/195)
Then, = (-90/195) + (91/195) … [∵ denominator is same in both the rational numbers]
= (-90 + 91)/195
= (1/195)

(iv) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 
Ans: Take the LCM of the denominators of the given rational numbers.
LCM of 8 and 11 is 88
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(-3/8)= [(-3 × 11)/ (8 × 11)] = (-33/88)
(7/11)= [(7 × 8)/ (11 × 8)] = (56/88)
Then, = (-33/88) – (56/88) … [∵ denominator is same in both the rational numbers]
= (-33 – 56)/88
= (-89/88)
(v) NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7
Ans:
First we have to convert the mixed fraction into improper fraction,
NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7= -19/9
We have, -19/9 – 6
Take the LCM of the denominators of the given rational numbers.
LCM of 9 and 1 is 9
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(-19/9)= [(-19 × 1)/ (9 × 1)] = (-19/9)
(6/1)= [(6 × 9)/ (1 × 9)] = (54/9)
Then, = (-19/9) – (54/9) … [∵ denominator is same in both the rational numbers]
= (-19 – 54)/9
= (-73/9)

Q3. Find the product: 

(i) (9/2) × (-7/4)
Ans: 
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
The above question can be written as
(9/2) × (-7/4)
We have,
= (9 × -7) / (2 × 4)
= -63/8 

(ii) (3/10) × (-9)
Ans:
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
The above question can be written as
(3/10) × (-9/1)
We have,
= (3 × -9)/ (10×1)
= -27/10

(iii) (-6/5) × (9/11)
Ans: 
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
We have,
= (-6 × 9) / (5 × 11)
= -54/55

(iv) (3/7) × (-2/5)
Ans:
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
We have,
= (3 × -2) / (7 × 5)
= -6/35

(v) (3/11) × (2/5)
Ans: 
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
We have,
= (3 × 2) / (11 × 5)
= 6/55

(vi) (3/-5) × (-5/3)
Ans:
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
We have,
= (3 × -5) / (-5 × 3)
On simplifying, = (1 × -1)/ (-1 × 1)
= -1/-1 = 1

Q4. Find the value of: 

(i) (-4) ÷ (2/3)
Ans:
We have,
= (-4/1) × (3/2) … [∵ reciprocal of (2/3) is (3/2)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-4 × 3) / (1 × 2) = (-2 × 3) / (1 × 1) = -6

(ii) (-3/5) ÷ 2
Ans: 
We have,
= (-3/5) × (1/2) … [∵ reciprocal of (2/1) is (1/2)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-3 × 1) / (5 × 2)
= -3/10

(iii) (-4/5) ÷ (-3)
Ans:
We have,
= (-4/5) × (1/-3) … [∵ reciprocal of (-3) is (1/-3)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-4× (1)) / (5× (-3))
= -4/-15 = 4/15

(iv) (-1/8) ÷ 3/4
Ans: 
We have,
= (-1/8) × (4/3) … [∵ reciprocal of (3/4) is (4/3)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-1 × 4) / (8 × 3)
= (-1 × 1) / (2 × 3) = -1/6

(v) (-2/13) ÷ 1/7
Ans: 
We have,
= (-2/13) × (7/1) … [∵ reciprocal of (1/7) is (7/1)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-2 × 7) / (13 × 1)
= -14/13

(vi) (-7/12) ÷ (-2/13)
Ans:
We have, = (-7/12) × (13/-2) … [∵ reciprocal of (-2/13) is (13/-2)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (-7× 13) / (12× (-2))
= -91/-24 = 91/24

(vii) (3/13) ÷ (-4/65)
Ans:
We have, = (3/13) × (65/-4) … [∵ reciprocal of (-4/65) is (65/-4)]
The product of two rational numbers = (product of their numerator)/ (product of their denominator)
= (3 × 65) / (13 × (-4))
= 195/-52 = -15/4

The document NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7 is a part of the Class 7 Course Mathematics (Maths) Class 7.
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NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

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NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

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NCERT Solutions: Rational Numbers Notes | Study Mathematics (Maths) Class 7 - Class 7

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