Selina Solutions Concise Mathematics Class 6 Chapter 14: Fractions Exercise 14(B) discusses the concepts such as reducing the fractions to their lowest term, determining the greater and smaller fractions, arranging the fractions in ascending and descending order. The solutions PDF, created by our expert faculty team, helps students to ace the exam confidently. Practising these Solutions on a daily basis, helps them to enhance conceptual knowledge about the concept. Students can refer and download the Selina Solutions Concise Mathematics Class 6 Chapter 14 Fractions Exercise 14(B) PDF links, which are given below.
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Access Selina Solutions Concise Mathematics Class 6 Chapter 14: Fractions Exercise 14(B)
Exercise 14(B)
1. Reduce the given fractions to their lowest terms:
(i) 8 / 10
(ii) 50 / 75
(iii) 18 / 81
(iv) 40 / 120
(v) 105 / 70
Solution:
(i) 8 / 10
The fraction 8 / 10 can be simplified as below
8 / 10 = (8 ÷ 2) / (10 ÷ 2)
= 4 / 5
Hence 4 / 5 is the simplified form of 8 / 10
(ii) 50 / 75
The fraction 50 / 75 can be simplified as below
50 / 75 = (50 ÷ 25) / (75 ÷ 25)
= 2 / 3
Hence 2 / 3 is the simplified form of 50 / 75
(iii) 18 / 81
The fraction 18 / 81 can be simplified as below
18 / 81 = (18 ÷ 9) / (81 ÷ 9)
= 2 / 9
Hence 2 / 9 is the simplified form of 18 / 81
(iv) 40 / 120
The fraction 40 / 120 can be simplified as below
40 / 120 = (40 ÷ 40) / (120 ÷ 40)
= 1 / 3
Hence 1 / 3 is the simplified form of 40 / 120
(v) 105 / 70
The fraction 105 / 70 can be simplified as below
105 / 70 = (105 ÷ 35) / (70 ÷ 35)
= 3 / 2
Hence 3 / 2 is the simplified form of 105 / 70
2. State, whether true or false?
(i) 2 / 5 = 10 / 15
(ii) 35 / 42 = 5 / 6
(iii) 5 / 4 = 4 / 5
(iv) 7 / 9 = 
(v) 9 / 7 = 
Solution:
(i) 2 / 5 = 10 / 15
The given expression can be solved as below
2 / 5 = (10 ÷ 5) / (15 ÷ 5)
2 / 5 ≠2 / 3
Hence false
(ii) 35 / 42 = 5 / 6
The given expression can be solved as below
(35 ÷ 7) / (42 ÷ 7) = 5 / 6
5 / 6 = 5 / 6
Hence true
(iii) 5 / 4 = 4 / 5
The given expression can be solved as below
5 / 4 ≠4 / 5
Hence false
(iv) 7 / 9 = 
The given expression can be solved as below
7 / 9 = (7 × 1 + 1) / 7
7 / 9 ≠8 / 7
Hence false
(v) 9 / 7 =
The given expression can be solved as below
9 / 7 = (7 × 1 + 1) / 7
9 / 7 ≠8 / 7
Hence false
3. Which fraction is greater?
(i) 3 / 5 or 2 / 3
(ii) 5 / 9 or 3 / 4
(iii) 11 / 14 or 26 / 35
Solution:
(i) 3 / 5 or 2 / 3
The given fractions can be simplified as follows
LCM of 5, 3 is 15
Hence 3 / 5 = (3 × 3) / (5 × 3)
= 9 / 15 and
2 / 3 = (2 × 5) / (3 × 5)
= 10 / 15
We know that
10 / 15 > 9 / 15 [Numerator is greater]
Thus, 2 / 3 > 3 / 5
Hence 2 / 3 is greater fraction
(ii) 5 / 9 or 3 / 4
The given expression can be simplified as follows
First convert the given expression into like fractions
So, 5 / 9 = (5 × 4) / (9 × 4)
= 20 / 36 and
3 / 4 = (3 × 9) / (4 × 9)
= 27 / 36
We know that
27 / 36 > 20 / 36 [Numerator is greater]
Thus 3 / 4 > 5 / 9
Hence 3 / 4 is greater fraction
(iii) 11 / 14 or 26 / 35
The given expression can be simplified as follows
First convert the given expression into like fractions
So, 11 / 14 = (11 × 5) / (14 × 5)
= 55 / 70 and
26 / 35 = (26 × 2) / (35 × 2)
= 52 / 70
We know that
55 / 70 > 52 / 70 [Numerator is greater]
Thus, 11 / 14 > 26 / 35
Hence 11 / 14 is greater fraction
4. Which fraction is smaller?
(i) 3 / 8 or 4 / 5
(ii) 8 / 15 or 4 / 7
(iii) 7 / 26 or 10 / 39
Solution:
(i) 3 / 8 or 4 / 5
The given expression can be simplified as follows
First convert the given expression into like fractions
So, 3 / 8 = (3 × 5) / (8 × 5)
= 15 / 40 and
4 / 5 = (4 × 8) / (5 × 8)
= 32 / 40
We know that
15 / 40 < 32 / 40 [Numerator is smaller]
Thus, 3 / 8 < 4 / 5
Hence 3 / 8 is the smaller fraction
(ii) 8 / 15 or 4 / 7
The given expression can be simplified as follows
First convert the given expression into like fractions
So, 8 / 15 = (8 × 7) / (15 × 7)
= 56 / 105 and
4 / 7 = (4 × 15) / (7 × 15)
= 60 / 105
We know that
56 / 105 < 60 / 105 [Numerator is smaller]
Thus, 8 / 15 < 4 / 7
Hence 8 / 15 is the smaller fraction
(iii) 7 / 26 or 10 / 39
The given expression can be simplified as follows
First convert the given expression into like fractions
So, 7 / 26 = (7 × 3) / (26 × 3)
= 21 / 78 and
10 / 39 = (10 × 2) / (39 × 2)
= 20 / 78
We know that
20 / 78 < 21 / 78 [Numerator is smaller]
Thus, 10 / 39 < 7 / 26
Hence 10 / 39 is the smaller fraction
5. Arrange the given fractions in descending order of magnitude:
(i) 5 / 16, 13 / 24, 7 / 8
(ii) 4 / 5, 7 / 15, 11 / 20, 3 / 4
(iii) 5 / 7, 3 / 8, 9 / 11
Solution:
(i) 5 / 16, 13 / 24, 7 / 8
The given expression can be simplified as follows
LCM of 16, 24, 8 = 2 × 2 × 2 × 2 × 3
= 48
Converting given expression into like fractions, we get
5 / 16 = (5 × 3) / (16 × 3)
= 15 / 48 and
13 / 24 = (13 × 2) / (24 × 2)
= 26 / 48 and
7 / 8 = (7 × 6) / (8 × 6)
= 42 / 48
Hence, fractions in descending order are 7 / 8, 13 / 24, 5 / 16
(ii) 4 / 5, 7 / 15, 11 / 20, 3 / 4
The given expression can be simplified as follows
LCM of 5, 15, 20, 4 = 4 × 5 × 3
= 60
Converting the given expression into like fractions, we get
4 / 5 = (4 ×12) / (5 × 12)
=48 / 60 and
7 / 15 = (7 × 4) / (15 × 4)
= 28 / 60 and
11 / 20 = (11 × 3) / (20 × 3)
= 33 / 60 and
3 / 4 = (3 × 15) / (4 × 15)
= 45 / 60
Hence, fractions in descending order are 4 / 5, 3 / 4, 11 / 20, 7 / 15
(iii) 5 / 7, 3 / 8, 9 / 11
The given expression can be simplified as follows
LCM of 5, 3, 9 = 3 × 3 × 5
= 45
Converting the given expression into like fractions, we get
5 / 7 = (5 × 9) / (7 × 9)
= 45 / 63 and
3 / 8 = (3 × 15) / (8 × 15)
= 45 / 120 and
9 / 11 = (9 × 5) / (11 × 5)
= 45 / 55
The fraction with the smallest denominator is the biggest fraction if the numerator is same
Hence, fractions in descending order are
45 / 55, 45 / 63, 45 / 120 i.e
9 / 11, 5 / 7, 3 / 8
6. Arrange the given fractions in ascending order of magnitude:
(i) 9 / 16, 7 / 12, 1 / 4
(ii) 5 / 6, 2 / 7, 8 / 9, 1 / 3
(iii) 2 / 3, 5 / 9, 5 / 6, 3 / 8
Solution:
(i) 9 / 16, 7 / 12, 1 / 4
The given fractions can be simplified as follows
LCM of 16, 12, 4 = 48
Converting the given expression into like fractions, we get
9 / 16 = (9 × 3) / (16 × 3)
= 27 / 48 and
7 / 12 = (7 × 4) / (12 × 4)
= 28 / 48 and
1 / 4 = (1 × 12) / (4 × 12)
= 12 / 48
Hence, fractions in ascending order are
12 / 48, 27 / 48, 28 / 48 i.e
1 / 4, 9 / 16, 7 / 12
(ii) 5 / 6, 2 / 7, 8 / 9, 1 / 3
The given fractions can be simplified as follows
LCM of 6, 7, 9, 3 = 3 × 3 × 2 × 7
= 126
Converting the given expression into like fractions, we get
5 / 6 = (5 × 21) / (6 × 21)
= 105 / 126 and
2 / 7 = (2 × 18) / (7 × 18)
= 36 / 126 and
8 / 9 = (8 × 14) / (9 × 14)
= 112 / 126 and
1 / 3 = (1 × 42) / (3 × 42)
= 42 / 126
Hence, fractions in ascending order are
36 / 126, 42 / 126, 105 / 126, 112 / 126 i.e
2 / 7, 1 / 3, 5 / 6, 8 / 9
(iii) 2 / 3, 5 / 9, 5 / 6, 3 / 8
The given fractions can be simplified as follows
LCM of 3, 9, 6, 8 = 72
Converting the given expressions into like fractions, we get
2 / 3 = (2 × 24) / (3 × 24)
= 48 / 72 and
5 / 9 = (5 × 8) / (9 × 8)
= 40 / 72 and
5 / 6 = (5 × 12) / (6 × 12)
= 60 / 72 and
3 / 8 = (3 × 9) / (8 × 9)
= 27 / 72
Hence, fractions in ascending order are
27 / 72, 40 / 72, 48 / 72, 60 / 72 i.e
3 / 8, 5 / 9, 2 / 3, 5 / 6
7. I bought one dozen bananas and ate five of them. What fraction of the total number of bananas was left?
Solution:
Given
Number of bananas bought = 1 dozen
We know there are 12 bananas in a dozen
Number of bananas eaten = 5
Number of bananas left = 12 – 5
= 7
Therefore, the required fraction is 7 / 12
8. Insert the symbol ‘=’ or ‘>’ or ‘<’ between each of the pairs of fractions, given below:
(i) 6 / 11 …. 5 / 9
(ii) 3 / 7 ….. 9 / 13
(iii) 56 / 64 …. 7 / 8
(iv) 5 / 12 …. 8 / 33
Solution:
(i) 6 / 11 …. 5 / 9
LCM of 11, 9 = 99
Converting the given expression into like fraction
We get
6 / 11 = (6 × 9) / (11 × 9)
= 54 / 99 and
5 / 9 = (5 × 11) / (9 × 11)
= 55 / 99
Therefore,
54 / 99 < 55 / 99 i.e
6 / 11 < 5 / 9
(ii) 3 / 7 ….. 9 / 13
LCM of 7, 13 = 91
Converting the given expression into like fraction
We get
3 / 7 = (3 × 13) / (7 × 13)
= 39 / 91 and
9 / 13 = (9 × 7) / (13 × 7)
= 63 / 91
Therefore,
39 / 91 < 63 / 91 i.e.
3 / 7 < 9 / 13
(iii) 56 / 64 …. 7 / 8
LCM of 64, 8 = 64
Converting the given expression into like fraction
We get
56 / 64 = (56 × 1) / (64 × 1)
= 56 / 64 and
7 / 8 = (7 × 8) / (8 × 8)
= 56 / 64
Therefore,
56 / 64 = 56 / 64 i.e.
56 / 64 = 7 / 8
(iv) 5 / 12 …. 8 / 33
LCM of 12, 33 = 132
Converting the given expression into like fractions
We get
5 / 12 = (5 × 11) / (12 × 11)
= 55 / 132 and
8 / 33 = (8 × 4) / (33 × 4)
= 32 / 132
55 / 132 > 32 / 132 i.e
5 / 12 > 8 / 33
9. Out of 50 identical articles, 36 are broken. Find the fraction of:
(i) The total number of articles and the articles broken.
(ii) The remaining articles and total number of articles.
Solution:
(i) Given
Total number of articles = 50
Number of articles broken = 36
Remaining articles = 50 – 36
= 14
The fraction of total number of articles and articles broken = 50 / 36
= 25 / 18
(ii) Given
Total number of articles = 50
Number of articles broken = 36
Remaining articles = 50 – 36
= 14
The fraction of remaining articles and total number of articles = 14 / 50
= 7 / 25
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