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Number Line Prime Class 7 Solutions Chapter 3 Fractions
Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Number Line Prime Class 7 Math Book, Chapter 3, Fractions. Here students can easily find step by step solutions of all the problems for Fractions, Exercise 3A, 3B and 3C Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 3 solutions. Here in this post all the solutions are based on latest Syllabus.
Fractions Exercise 3A all Question Solutions :
Question no – (1)
Solution :
(a) 5/8
= Proper fractions
(b) 7/10
= decimal fraction
(c) 23/7
= Mixed fraction
(d) 3/12
= 1/4 – proper
(e) 21/2
= improper
(f) 58/100
= decimal
(g) 8/12
= 2/3 – proper
(h) 4/9
= 2/3 – proper
(i) 5 2/3
= mixed
Question no – (2)
Solution :
(a) 2 3/4
= 11/4
(b) 1 4/7
= 11/7
(c) 3 3/5
= 18/5
(d) 4 2/3
= 14/3
Question no – (3)
Solution :
(a) 18/36
= 1/2 (irreducible)
(B) 3/7
= not irreducible
(c) 7/42
= 1/6 (irreducible)
(d) 4/12
= 1/3 (irreducible)
Question no – (4)
Solution :
(a) 39/27
(b) 2 12/38
= 2 6/19
(c) 34/289
= 2/17
(d) 13/169
= 1/13
Question no – (5)
Solution :
(a) 8/11, 16/23
= not equivalent
(b) 3/7, 75/175
= equivalent
(c) 1/3, 18/54
= equivalent
(d) 2/3, 26/51
= not equivalent
Question no – (6)
Solution :
(a) 2/3, 5/7
2/3
= 2 × 7/3 × 9
= 14/21,
5/7
= 5 × 3/7 × 3
= 15/21
∴ fractions = 14/21, 15/21
(b) 1 3/5, 5/9
1 3/5
= 8 × 9/5 × 9
= 72/45,
5/9
= 5 × 5/9 × 5
= 25/45
∴ fractions = 72/45, 25/45
(c) 6/11, 2 11/12
6/11
= 6 × 12/11 × 12
= 72/132,
2 11/12
= 35/12
= 35 × 11/12 × 11
= 384/132
∴ fractions = 72/132, 385/132
(d) 2/7, 5/8
2/7
= 2 × 8/7 × 8
= 16/56,
5/8
= 5 × 7/8 ×7
= 35/56
∴ fractions = 16/56, 35/56
Question no – (7)
Solution :
(a) 2/5, 4/9, 1 5/6, 2 2/3, 3/4
2/5
= 2× 36/ 5×36
= 72/180,
4/9
= 4 × 20/9× 20
= 80/180,
1 5/6
= 11 × 30/6 × 30
= 330/180,
2 2/3
= 8 × 90/2 × 90
= 720/180,
3/4
= 3 × 45/4 × 45
= 135/180
∴ 720/180, 330/180, 135/180, 80/180, 72/180
Now, in ascending order,
72/180, 80/180, 135/180, 330/180, 720/180
= 2/5, 4/5, 3/4, 1 5/6, 2 2/3
(b) 11/15, 8/12, 3/4, 3/20, 8/30
11/15
= 11 × 60/15 × 60
= 660/900,
8/12
= 8 × 75/12 × 75
= 600/900,
3/4
= 3 × 225/4 × 225
= 675/900
3/20
= 3 × 45/20/45
= 135/900,
8/30
= 8 × 30/30 × 30
= 240/900
Now, in ascending order,
135/900, 240/900, 600/900, 660/900, 675/900
= 3/20, 8/30, 8/12, 11/15, ¾
Question no – (8)
Solution :
(a) 5/6, 5/8, 4/9, 1 1/3, 14/21
5/6
= 5 × 84/6 × 84
= 420/504,
5/8
= 5 × 63/8 × 63
= 315/504,
4/9
= 4 × 36/9 × 36
= 224/504,
1 1/3
= 4/3
= 4 × 165/ 3 × 168
= 672/504,
11/21
= 11 × 24/21 × 24
= 264/504
Now, in descending order:
= 672/504, 420/504, 315/504, 264/504, 224/504
= 1 4/3, 5/6, 5/8, 11/21, 4/9
(b) 4/11, 10/15, 6/18, 12/22, 15/33
4/11
= 4 × 90/11 × 90
= 360/990,
10/15
= 10 × 66/15 × 66
= 660/990,
6/18
= 6 × 55/18 × 55
= 330/990,
12/22
= 12 × 45/22 × 45
= 540/990,
15/33
= 15 × 30/33 × 30
= 450/990
Now, in Descending order
= 660/990, 540/990, 450/990, 360/990, 330/990
= 10/15, 12/22, 15/33, 4/11, 6/18
Question no – (9)
Solution :
(a) numerator 42
= 42/42 × 4
= 42/168
(b) denominator 132
= 33/132
Question no – (10)
Solution :
(a) 2/3 = …/180
2/3 = x/108
X = 2 × 108/3
= 72
(b) 6/17 = 4/…
6/17 = 48/x
X = 48 × 17/6
= 136
Question no – (11)
Solution :
(a) 6 mangoes out of 16 mangoes
= 6/168
= 3/8
(b) 10 pencils out of 18 pencils
= 10/18
= 5/9
(c) 76 caps out of 124 caps
= 76/124
= 19/31
(d) 31 boys out of 144 boys
= 31/144
(e) 24 students out of 166 students
= 24/166
= 6/29
Fractions Exercise 3B all Question Solutions :
Question no – (1)
Solution :
Let we should add x
∴ 1 2/5 + x = 3 2/7
=> 7/5 + x = 23/7
=> X = 23/7 – 7/5
= 11 – 49/35
= 66/35
Question no – (2)
Solution :
Let, we should subtract x
=> 12 1/5 – x = 11 3/4
=> 61/5 – x = 47/4
=> x = 61/5 – 47/7
= 244 – 235/20
= 9/20
Question no – (3)
Solution :
(a) 13/24 × 8/11
= 13/33
(b) 12/15 × 1 2/7
= 12/15 × 9/7
= 36/35
(c) 10/13 × 1 3/5
= 10/13 × 8/5
= 16/13
(d) 2 5/7 × 3 4/9
= 19/7 × 31/9
= 589/63
Question no – (4)
Solution :
(a) 4/5 by 10/15
= 4/5 ÷ 10/15
= 4/5 × 15/10
= 6/5
(b) 1 4/7 by 3/20
= 11/7 × 20/3
= 220/21
(c) 17/33 by 2 1/2
= 17/3 × 2/5
= 34/15
(d) 5 8/15 by 6 9/11
= 83/15 × 11/75
= 913/1125
Question no – (5)
Solution :
(a) 6/7 + 21/23 × 5/42 ÷ 15/7 – 1/6
= 6/7 + 21/23 × 5/42 × 7/15 – 1/6
= 6/7 = 7/138 – 1/6
= 828 + 49/966 – 1/6
= 877 – 966/966
= – 89/966
(b) 5/6 ÷ [(13/15 – 10/75) + 3/8] × 2/7
= 5/6 ÷ [(65/- 10/75) + 3/8] × 2/7
=5/6 ÷ [55/75 + 3/8] × 2/7
= 5/9 ÷ [11/15 + 3/8] × 2/7
= 5/9 ÷ 88 + 45/120 × 2/8
=5/9 ÷ 133/120 × 2/8
= 5/9 × 120/133 × 2/8
= 150/1197
(c) (10/15 – 1/3) ÷ 1/5 + 22/30 – 38/45
(10/15 – 1/3) ÷ 1/5 + 22/30 – 38/45
= 1/3 ÷ 1/5 + 22/30 – 38/45
= 5/3 + 22/30 – 38/45
= 75 + 33 – 38/45
= 70/45
= 14/9
(d) (4/5 + 2/3 – 14/27) + 5/6 ÷ 7/12 × 24/35
= 4/9 + 5/6 × 12/7 × 24/35
= 4/9 + 48/49
= 196 + 432/441
=628/441
(e) 1/3 × 5/6 ÷ (11/17 + 13/17) – 5/34
= 1/3 × 5/6 ÷ 24/17 – 5/34
= 1/3 × 5/6 × 17/24 – 5/34
= 85/432 – 5/34
= 1445 – 1080/7344
= 365/7344
(f) [{(1/2 + 7/9) ÷ 23/18} – 1 + 1/2 – 3/6] + 4
= [{(9 + 14/18) ÷ 23/18} – 2 + 1/2 – 3/6] + 4
= [23/18 × 18/23 – 3/2 – 3/6] + 4
= [1 – 3/2 – 1/2] + 4
= 2 – 3 – 1/2 + 4
= – 2/2 + 4
= – 1 + 4
= 3
Fractions Exercise 3C all Question Solutions :
Question no – (1)
Solution :
Road length – 16 8/11m
= 184/11m
Cut length – 4/11m
∴ we cut = 184/11 × 11/4
= 46 pieces
Question no – (2)
Solution :
Water in the container – 3 3/9 L = 97/3L bottles capacity = 3/5 L
∴ 97/3 × 5/3
= 485/9
∴ 53 8/9 bottles filled.
Question no – (3)
Solution :
Weight of the packet – 83 8/13kg
= 1087/13kg
∴ weight of 15 1/6
= 91/6 packets will be – 1087/13 × 91/6
= 7609/6
∴ 1268 1/6kg
Question no – (4)
Solution :
One bottles holds – 38/43kg
∴ 25 bottles holds = 25 × 38/43
= 350/43kg
Question no – (5)
Solution :
Price of 1 L Juice = 98 1/2
= 197/2 Rs
34 1/4 L = 137/4 L juice price = 197/2 × 137/4
= 26989/8
∴ 1268 1/6kg
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