NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Mathematics (Maths) Class 7

Class 7 : NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

The document NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, five rational numbers between -1 and 0 would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

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

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, Five rational numbers between -2 and -1 would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans: Let us write  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes as rational numbers with the same denominators.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, five rational numbers between NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans: Let us write  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notesas rational numbers with the same denominators.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, five rational numbers between  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes would be  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


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

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, the next four rational numbers of this pattern would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, the next four rational numbers of this pattern would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, the next four rational numbers of this pattern would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, the next four rational numbers of tins pattern would be
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


Q3. Give four rational numbers equivalent to:

(i) -2/7
Ans:
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii) 5/-3

Ans:
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii) 4/9

Ans:
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


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

(i) 3/4
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii) -5/8
Ans:

  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  -7/4
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv) 7/8
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Ans:
Therefore,  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Similarly  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Thus, the rational numbers represented P, Q, R and S are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes respectively.


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

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [Converting into lowest term]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [Converting into lowest terra]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans: Since, (-5/11) = (-5/11)
Hence, 5/-11 [=] -5/11

(vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans: The given fraction is like friction,
So, -¼ < ¼
Hence ¼ is greater,

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans: First we have to convert mixed fraction into improper fraction,
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes= -23/7
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes= -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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes> NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Hence, NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notesis 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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [L.C.M. of 3 and 5 is 15]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes


Q2. Find: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes 
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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Ans:
First we have to convert the mixed fraction into improper fraction,
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes= -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

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