Dinah Convent Tarana CBSE Class 7th Chapter 9
Answers
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maths MCQ ok
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:-
= (-27/30) + (44/30) … [∵ denominator is same in both the rational numbers]
= (-27 + 44)/30
= (17/30)
(iv) (-3/-11) + (5/9)
Solution:-
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) (-8/19) + (-2/57)
Solution:-
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) -2/3 + 0
Solution:-
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
(vii) NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 14 + NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 15
Solution:-
First we have to convert mixed fraction into improper fraction.
=
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 16= -7/3
=
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Image 17= 23/5
We have, -7/3 + 23/5
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,
(-7/3)= [(-7×5)/ (3×5)] = (-35/15)
(23/5)= [(23×3)/ (15×3)] = (69/15)
Then,
= (-35/15) + (69/15) … [∵ denominator is same in both the rational numbers]
= (-35 + 69)/15
= (34/15)
2. Find
(i) 7/24 – 17/36
Solution:-
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) 5/63 – (-6/21)
Solution:-
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