Collins Maths Solutions Class 7 Chapter 2 Rational Numbers
Welcome to NCTB Solution. Here with this post we are going to help 7th class students for the Solutions of Collins Maths Class 7 Mathematics, Chapter 2, Rational Numbers. Here students can easily find Exercise wise solution for chapter 2, Rational Numbers. Students will find proper solutions for Exercise 2.1, 2.2, 2.3, 2.4 and 2.5 Our teacher’s solved every problem with easily understandable methods so that every students can understand easily. Here in this post all the solutions are based on ICSE latest Syllabus.
Rational Numbers Exercise 2.1 Solution :
Question no – (1)
Solution :
(a) Numerator = 1
Denominator = 5
(b) Numerator = -11
Denominator = 13
(c) Numerator = -14
Denominator = -15
(d) Numerator = 7
Denominator = – 8
(e) Numerator = 5
Denominator = 1
Question no – (2)
Solution :
(a) Given statement is False
(b) Given statement is True
(c) Given statement is True
(d) Given statement is False
(e) Given statement is True
Question no – (3)
Solution :
(a) -18
= – 36/2
(b) 29
= 87/3
(c) -101
= -201/2
(d) 315
= 6 30/2
(e) – 1234
= – 2468/2
Question no – (5)
Solution :
(a) 29/-3
= 5/-8
= 35/-56
(b) 35/17
= 5/-8
= 40/-64
(c) -25/20
= 5/-8
= 50/-80
Question no – (7)
Solution :
(a) 4/6 = 40/60
(b) 2/3 = 14/21
(c) 6/8 = 18/24
(d) 6/8 = 42/56
Question no – (8)
Solution :
(a) 4/9 = 8/18, 12/27, 16/36, 20/45
(b) -3/5 = -6/10, -9/15, -12/20, -15/25
(c) 8/-11 = 16/-22, 24/-33, 32/-44, 40/-55
(d) 7/-9 = 14/-18, 21/-27, 28/-36, 35/-45
Question no – (9)
Solution :
(a) 2/-14 = 1/-7
(b) -10/-8 = 5/4
(c) 32/288/7
(d) -16/20 = -4/5
(e) -24/80 = -6/20
= – 3/10
(f) 28/63 = 4/9
Question no – (10)
Solution :
(a) -8/5 and 546/-35
∴ – 8 × (-35) = + 280
and (56 × 5) = 280
So, yes, it is equal.
(b) -12/7 and 32/21
∴ (-12 × 21) = – 252
and, (32 × 7) = 224
So, it is not equal.
(c) -7/3 and 84/-36
∴ (-7 × 36) = + 252
and, (3 × 84) = 252
So, Yes, it is Equal.
Question no – (11)
Solution :
(a) 25/125 = 100/625
(b) 34/84 l = 204/504
Rational Numbers Exercise 2.2 Solution :
Question no – (1)
Solution :
(a) 5/9 and -4/9
= 45 > -36
∴ 5/9 > – 4/3
(b) -4/7 and 5/-7
= + 28 < 35
∴ -4/7 < 5/-7
(c) -3/7 and 0
∴ -3/7 < 0
(d) 5/9 and -4/5
= 25 > – 36
∴ 5/9 > -4/5
(e) -8 and -11/2
= -16 < – 11
∴ -8 < -11/2
Question no – (2)
Solution :
(a) 2/3, 4/5, 3/7
L.C.M of 3, 5, 7 = 105
2/3 = 2 × 35/3 × 35 = 70/105
4/5 = 4 × 21/5 × 21 = 84/105
3/7 = 3 × 15/7 × 15 = 45/105
∴ In ascending order,
= 3/7 < 2/3 < 4/5
(b) 3/5, -7/10, -11/12, -13/-30
∴ L.C.M is = 60
= 3/5 = 3 × 12/5 × 12 = 36/60
= -7/10 = -7 × 6/10 × 6 = -42/60
= -11/12 = -11 × 5/12× 5 = -55/60
= -13/-30 = -13 × (-2)/-30 × (-2) = 26/60
∴ In ascending order,
= -11/12 < -7/10 < -13/-30 < 3/5
(c) 2/3, 4/7, -8/3, 6/9
L.C.M of 3,7,3 -9 is = 63
= 2/3 = 2 × 21/3 × 21 = 42/63
= 4/7 = 4 × 9/7 × 9 = 36/63
= -8/3 = -8 × 21/3× 21 = -42/63
= 6/-9 = 6 × (-7)/-9 × (-7) = -42/63
∴ In ascending order,
= -8/3 < 6/-9 < 4/7 < 2/3
(d) -8/9, 5/-2, 5/-6, -5/3
L.C.M is = 18
= -8/9 = -8 × 2/9× 2 = -16/18
= 5/-2 = 5 × (9)/-2 × (9) = -45/18
= 5/-6 = 5 × (-3)/-6 × (-3) = -15/18
= -5/3 = -5 × 6/3 × 6 = -30/18
∴ In ascending order,
= 5/-2 < -5/3 < -8/9 < 5/-6
(e) -2/3, -7/18, -5/12, -4/9
L.C.M is = 36
= -2/3 = -2 × 12/3 × 12 = -24/36
= -7/18 = -7× 2/18 × 2 = -14/36
= -5/12 = -5 × 3/12 × 3 = -15/36
= -4/9 = -4 × 4/9 × 4 = 16/36
∴ In ascending order,
-2/3 < -4/9 < -5/12 < -7/18
Question no – (3)
Solution :
(a) 4/9, -4/3, -7/-12, -11/24
L.C.M is = 72
= 4/9 = 4 × 8 /9 × 8 = 32/72
= -4/3 = -4 × 24/3 × 24 = -96/72
= -7/-12 = – 7 × (-6) /- 12 × (-6) = 42/72
= -11/24 = -11 × 3/ 24 × 3 = -3372
∴ In descending order,
= -7/12 > 4/9 > -11/24 > -4/3
(b) 3/4, 5/-8, 3/-16, -5/-8
L.C.M is = 169
= 3/4 = 3 × 4/4 × 4 = 12/16
= 5/-8 = 5 × (-2)/-8 × (-21) = -3/16
= 3/-16 = 3 × (-1)/-16 × (-1) = -3/16
= -5/-8
= -5
Rational Numbers Exercise 2.3 Solution :
Question no – (1)
Solution :
Five rational number between -2 and 2
-2 = – 10/5
2 = 10/5
Five rational number are,
= -9/5, -6/5, 1/5, 4/5, 8/5
Question no – (2)
Solution :
Six rational numbers between -3/11 and 8/11.
Six rational number are,
= -2/11, -1/11, 2/11, 4/11, 5/11, 6/11
Question no – (3)
Solution :
Three rational numbers 1/3 and 1/74
Three rational numbers are,
= 1/4, 1/5, 1/6
Question no – (4)
Solution :
Ten rational number between 4/5 and 2/7
4/5 and 2/7
= 4/5 = 4 × 7/5 × 7 = 28/35
= 2/7 = 2 × 8/7 × 8 = 10/35
Rational numbers are, 11/35, 12/35, 13/35, 14/35, 15/35, 16/35, 17/35, 18/35, 19/35, 20/35, 21/35
Rational Numbers Exercise 2.4 Solution :
Question no – (1)
Solution :
(a) 5/6 + (- 1/6)
= 5/6 – 1/6
= 5 – 1/6
= 4/6
= 2/3
(b) 9/17 + (-5/17)
= 9/17 – 5/17
= 9 – 5/17
= 4/17
(c) -17/15 + (-1/15)
= 17/15 – 1/15
= – 17 – 1 /15
= -18/15
= -6/5
(d) 5/6 + 7/9
= 45 + 42/54
= 87/54
= 1 11/18
(e) 5/8 + (-7/2)
= 5/8 – 7/2
= 5 – 28/8
= – 23/8
= – 2 7/8
(f) 7/-18 + 8/27
= – 21 + 16/54
= -5/54
Question no – (2)
Solution :
(a) 4/6 – (-7/9)
= 4/6 + 7/9
= 12 + 14/18
= 26/18
= 13/9
= 1 4/9
(b) 5/6 – 3/4
= 10 -9/12
= 1/12
(c) -3/8 – 1/4
= -3 – 2/8
= -5/8
(d) -5/26 – (-4/13)
= – 5/26 + 4/13
= – 5 + 8/26
= 3/26
(e) 13/15 – 12/625
= 65 – 36/75
= 29/7
(f) (-2/7) – (-3/-8)
= -2/7 – 3/8
= -16 – 21/56
= -37/56
Question no – (3)
Solution :
(a) 7/11 × 5/4
= 35/44
(b) -2/9 × 5/11
= -10/99
(c) 25/-9 × 3/-10
= 5/+6
(d) 16/-21 × 14/5
= 32/-15
(e) -12/5 × 10/-3
= 4 × 10/5
= 8
(f) 5/-18 × -9/20
= 5/2 × 20
= 1/8
Question no – (4)
Solution :
(a) 5 ÷ -5/7
= 5 × 7/-5
= -7
(b) -16/35 ÷ -15/14
= 16/35 × 14/-15
= 32/75
(c) -12/7 ÷ 18
= 12/7 × 1/18
= -2/21
(d) 4/9 ÷ -5/12
= 4/9 × 12/-5
= 16/-15
(e) -3/4 ÷ -6
= – 3/4 × 1/6
= – 1/8
(f) 2/3 ÷ -7/12
= 2/3 × 12/-7
= 8/-7
Rational Numbers Exercise 2.5 Solution :
Question no – (1)
Solution :
(a), (c) and (d) are terminating decimal and (b), (e), (f) are non terminating decimal.
Question no – (2)
Solution :
(a) 0.7
= 7/9
(b) 0.89
= 89/99
(c) 0.567
= 567/999
(d) 0.243
= 243/900
Question no – (3)
Solution :
Distance by A,
= 7/9 + 1/3
= 7 + 3/9
= 10/9 km
Distance by B
= 3/4 + 1/5
= 15 + 4/20
= 19/20
Therefore, “A” travel more distance.
Question no – (4)
Solution :
Sugar sold,
= (75 3/4 × 1/4)
= 303/4 × 1/4
= 303/16 kg.
∴ The shop keeper sold 303/16 kg sugar.
Question no – (5)
Solution :
Doses are there in bottle,
= 1 1/2 ÷ 3/14
= 3/2 × 14/3
= 7 dose
∴ There are 7 doses in the bottle.
Question no – (6)
Solution :
Difference in water level,
= |(2/3 – 4/5)|
= |10 – 12/15|
= 2/15
Therefore, the difference between two cups will be 2/15
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