Selina Solutions Concise Mathematics Class 6 Chapter 14 Fractions Exercise 14(D) has clear answers for each and every question based on the concept BODMAS. The examples before each exercise of Selina textbook help them to achieve more marks in the final examination. Students, who aspire to strengthen their skill in Mathematics, are advised to follow Selina Solutions and hence, practice regularly. These Solutions also help them in solving difficult questions effortlessly. Students can use Selina Solutions Concise Mathematics Class 6 Chapter 14 Fractions Exercise 14(D) PDF, from the links provided here for free download.
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Access Selina Solutions Concise Mathematics Class 6 Chapter 14: Fractions Exercise 14(D)
Exercise 14(D)
1. Simplify:
(i) 3 / 7 × 2 / 5
(ii) 4 / 9 × 3 / 5
(iii) 5 / 12 × 8
(iv) 7 / 6 of 3 / 14
(v) 
× 
Solution:
(i) 3 / 7 × 2 / 5
The given expression can be simplified as below
3 / 7 × 2 / 5 = (3 × 2) / (7 × 5)
= 6 / 35
Hence, the simplified form of the given expression is 6 / 35
(ii) 4 / 9 × 3 / 5
The given expression can be simplified as below
4 / 9 × 3 / 5 = (4 × 3) / (9 × 5)
= (4 × 1) / (3 × 5)
= 4 / 15
Hence, the simplified form of the given expression is 4 / 15
(iii) 5 / 12 × 8
The given expression can be simplified as below
5 / 12 × 8 / 1 = (5 × 8) / (12 × 1)
= (5 × 2) / (3 × 1)
= 10 / 3
=
Hence, the simplified form of the given expression is
(iv) 7 / 6 of 3 / 14
The given expression can be simplified as below
7 / 6 × 3 / 14 = (1 × 1) / (2 × 2)
= 1 / 4
Hence, the simplified form of the given expression is 1 / 4
(v)
×
The given expression can be simplified as below
×
= (27 × 27) / (8 × 7)
= 729 / 56
=
Hence, the simplified form of the given expression is
2. Simplify:
(i) 2 / 3 ÷ 
(ii) 
÷ 4 / 9
(iii) 1 ÷ 2 / 5
(iv) 4 / 9 ÷ 4 / 9
(v) 
÷ 
Solution:
(i) 2 / 3 ÷
The given expression can be simplified as below
2 / 3 ÷ 6 / 5 = (2 × 5) / (3 × 6)
= 5 / 9
Hence, the simplified form of the given expression is 5 / 9
(ii)
÷ 4 / 9
The given expression can be simplified as below
9 / 2 ÷ 4 / 9 = (9 × 9) / (2 × 4)
= 81 / 8
=
Hence, the simplified form of the given expression is
(iii) 1 ÷ 2 / 5
The given expression can be simplified as below
1 / 1 ÷ 2 / 5 = (1 × 5) / (1 × 2)
= 5 / 2
=
Hence, the simplified form of the given expression is
(iv) 4 / 9 ÷ 4 / 9
The given expression can be simplified as below
4 / 9 ÷ 4 / 9 = (4 × 9) / (9 × 4)
=1
Hence, the simplified form of the given expression is 1
(v)
÷
The given expression can be simplified as below
÷
= (7 × 4) / (3 × 7)
= 4 / 3
=
Hence, the simplified form of the given expression is
3. Simplify:
(i) 1 / 4 of 
÷ 3 / 5
(ii) 
× 1 / 2 ÷ 
(iii) 
× 0 × 
(iv) 3 / 4 × 
÷ 3 / 7 of 
(v) 
÷ 2 / 7 of 
× 2 / 3
Solution:
(i) 1 / 4 of
÷ 3 / 5
The given expression can be simplified as follows:
1 / 4 × 16 / 7 ÷ 3 / 5 = 4 / 7 ÷ 3 / 5
= (4 × 5) / (7 × 3)
= 20 / 21
Hence, 20 / 21 is the simplified form of the given expression
(ii) 
× 1 / 2 ÷
The given expression can be simplified as follows
× 1 / 2 ÷
= 5 / 4 × 1 / 2 × 3 / 4
= 5 / 8 × 3 / 4
= 15 / 32
Hence, 15 / 32 is the simplified form of the given expression
(iii)
× 0 × 
The given expression can be simplified as follows
× 0 × 
= (43 × 0 × 43) / (7 × 0 × 8)
= 0
Hence, 0 is the simplified form of the given expression
(iv) 3 / 4 ×
÷ 3 / 7 of
The given expression can be simplified as follows
3 / 4 ×
÷ 3 / 7 of
= 3 / 4 × 4 / 3 ÷ 9 / 8
∵ 3 / 7 of
= 3 / 7 × 21 / 8 = 9 / 8
= 3 / 4 × 4 / 3 × 8 / 9
= 8 / 9
Hence, 8 / 9 is the simplified form of the given expression
(v)
÷ 2 / 7 of
× 2 / 3
The given expression can be simplified as follows
[2 / 7 of
= 2 / 7 × 4 / 3 = 8 / 21]
We get
= 9 / 4 ÷ 8 / 21 × 2 / 3
= 9 / 4 × 21 / 8 × 2 / 3
= 63 / 16
=
Hence,
is the simplified form of the given expression
4. Simplify:
(i) 5 – (8 / 11 – 
)
(ii) 1 / 2 ÷ (7 / 8 – 3 / 5)
(iii) 
÷ (
+ 
)
(iv) (
–
) ÷ 1 / 2
(v) 4 / 7 ÷ (1 / 3 ×
)
Solution:
(i) 5 – (8 / 11 – 
)
The given expression can be simplified as below
5 – (8 / 11 –
) = 5 – (8 / 11 – 36 / 11)
= 5 – (8 – 36) / 11
= 5 – (-28 / 11)
On further calculation, we get
= 5 / 1 + 28 / 11
= 83 / 11
=
Hence,
is the simplified form of the given expression
(ii) 1 / 2 ÷ (7 / 8 – 3 / 5)
The given expression can be simplified as below
1 / 2 ÷ (7 / 8 – 3 / 5) = 1 / 2 ÷ (5 × 7 – 8 × 3) / 40
= 1 / 2 ÷ (35 – 24) / 40
= 1 / 2 ÷ (11 / 40)
= 1 / 2 × 40 / 11
We get
= 20 / 11
=
Hence,
is the simplified form of the given expression
(iii)
÷ (
+ 
)
The given expression can be simplified as below
÷ (
+ 
) = 7 / 3 ÷ (11 / 2 + 15 / 4)
= 7 / 3 ÷ (2 × 11 + 1 × 15) / 4
On further calculation, we get
= 7 / 3 ÷ (22 + 15) / 4
= 7 / 3 ÷ (37 / 4)
= 7 / 3 × 4 / 37
= 28 / 111
Hence, 28 / 111 is the simplified form of the given expression
(iv) (
–
) ÷ 1 / 2
The given expression can be simplified as below
(
–
) ÷ 1 / 2 = (31 / 8 – 18 / 5) ÷ 1 / 2
By taking LCM, we get
= [(31 × 5 – 18 × 8) / (8 × 5)] ÷ 1 / 2
= (155 – 144) / 40 ÷ 1 / 2
= (11 / 40) ÷ 1 / 2
By calculating further, we get
= 11 / 40 × 2 / 1
= 11 / 20
Hence, 11 / 20 is the simplified form of the given expression
(v) 4 / 7 ÷ (1 / 3 ×
)
The given expression can be simplified as below
4 / 7 ÷ (1 / 3 ×
) = 4 / 7 ÷ (1 / 3 × 14 / 5)
= 4 / 7 ÷ (14 / 15)
On further calculation, we get
= 4 / 7 × 15 / 14
= 2 / 7 × 15 / 7
= 30 / 49
Hence, 30 / 49 is the simplified form of the given expression
5. Simplify
(i) (1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6)
(ii) (24 / 35 ÷ 6 / 7 + 5 / 9) × 3 / 4
(iii) 3 / 4 of 
– 2 / 3 of 
(iv) 7 / 30 of (1 / 3 + 7 / 15) ÷ (5 / 6 – 3 / 5)
(v) 
– 
× 
+ 
Solution:
(i) (1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6)
The given expression can be simplified as follows
(1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6) = [(3 + 2) / 6] ÷ [(3 – 2) / 12]
On further calculation, we get
= (5 / 6) ÷ (1 / 12)
= 5 / 6 × 12 / 1
= 5 × 2
= 10
Hence, the simplified form of the given expression is 10
(ii) (24 / 35 ÷ 6 / 7 + 5 / 9) × 3 / 4
The given expression can be simplified as follows
(24 / 35 ÷ 6 / 7 + 5 / 9) × 3 / 4 = (24 / 35 × 7 / 6 + 5 / 9) × 3 / 4
= (4 / 5 + 5 / 9) × 3 / 4
By taking LCM, we get
= [(36 + 25) / 45] × 3 / 4
= (61 / 45) × 3 / 4
We get
= 61 / 60
=
Hence, the simplified form of the given expression is
(iii) 3 / 4 of
– 2 / 3 of
The given expression can be simplified as below
3 / 4 of
– 2 / 3 of
= 3 / 4 of 49 / 8 – 2 / 3 of 9 / 4
= 3 / 4 × 49 / 8 – 2 / 3 of 9 / 4
= 147 / 32 – 2 / 3 × 9 / 4
We get
= 147 / 32 – 3 / 2
On taking LCM, we get
= [(147 – 48)] / 32
= 99 / 32
=
Hence, the simplified form of the given expression is
(iv) 7 / 30 of (1 / 3 + 7 / 15) ÷ (5 / 6 – 3 / 5)
The given expression can be simplified as below
7 / 30 of (1 / 3 + 7 / 15) ÷ (5 / 6 – 3 / 5) = 7 / 30 of [(5 + 7) / 15] ÷ [(25 – 18) / 30]
We get
= 7 / 30 of (4 / 5) ÷ (7 / 30)
= 7 / 30 × 4 / 5 × 30 / 7
= 4 / 5
Hence, the simplified form of the given expression is 4 / 5
(v)
– 
× 
+ 
The given expression can be simplified as below
–
×
+
= 5 / 2 – 7 / 2 × 7 / 4 + 5 / 2
= 5 / 2 – 49 / 8 + 5 / 2
= 5 / 2 + 5 / 2 – 49 / 8
By taking LCM, we get
= (20 + 20 – 49) / 8
= (40 – 49) / 8
= – 9 / 8
= –
Hence, –
is the simplified form of the given expression
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