Ex-6.9, Fractions, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

Q1: Add :
(i)  and
(ii)  and
(iii)  and  
(iv)  and
Ans:
(i)  and
It can be written as
3/4 + 5/6
We know that the LCM of 4 and 6 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)]
On further calculation
= 9/12 + 10/ 12
We get
= (9 + 10)/ 12 = 19/12

(ii)  and
It can be written as
7/10 + 2/15
We know that the LCM of 10 and 15 is 30
In order to convert fraction into equivalent fraction having 30 as denominator
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)]
On further calculation
= 21/30 + 4/ 30
We get
= (21 + 4)/ 30 = 25/30 = 5/6

(iii)  and  
It can be written as
8/13 + 2/3
We know that the LCM of 13 and 3 is 39
In order to convert fraction into equivalent fraction having 39 as denominator
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)]
On further calculation
= 24/39 + 26/39
We get
= (24 + 26)/ 39 = 50/39

(iv)  and
It can be written as
4/5 + 7/15
We know that the LCM of 5 and 15 is 1
In order to convert fraction into equivalent fraction having 15 as denominator
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)]
On further calculation
= 12/15 + 7/ 15
We get
= (12 + 7)/ 15 = 19/15

Q2: Subtract :
(i)  from
(ii)  from
(iii)  from
(iv)  from  
Ans:
(i)  from
It can be written as
19/21 – 2/7
We know that LCM of 21 and 7 is 21
In order to convert fraction into equivalent fraction having 21 as denominator
= [(19 × 1)/ (21 × 1)] – [(2 × 3)/ (7 × 3)]
On further calculation
= 19/21 – 6/21
We get
= (19 – 6)/21 = 13/21

(ii)  from
It can be written as
18/20 – 21/25
We know that LCM of 20 and 25 is 100
In order to convert fraction into equivalent fraction having 100 as denominator
= [(18 × 5)/ (20 × 5)] – [(21 × 4)/ (25 × 4)]
On further calculation
= 90/100 – 84/100
We get
= (90 – 84)/100 = 6/100 = 3/50

(iii)  from
It can be written as
2/1 – 7/16
We know that LCM of 1 and 16 is 16
In order to convert fraction into equivalent fraction having 16 as denominator
= [(16 × 2)/ (16 × 1)] – [(7 × 1)/ (16 × 1)]
On further calculation
= 32/16 – 7/16
We get
= (32 – 7)/16 = 25/16

(iv)  from
It can be written as
11/5 – 4/15
We know that LCM of 5 and 15 is 15
In order to convert fraction into equivalent fraction having 15 as denominator
= [(11 × 3)/ (5 × 3)] – [(4 × 1)/ (15 × 1)]
On further calculation
= 33/15 – 4/15
We get
= (33 – 4)/15 = 29/15

Q3: Find the difference of :
(i)  and  
(ii)  and  
(iii)  and  
(iv)  and
Ans:
(i)  and  
It can be written as
13/24 – 7/16
We know that LCM of 24 and 16 is 48
In order to convert fraction into equivalent fraction having 48 as denominator
= [(13 × 2)/ (24 × 2)] – [(7 × 3)/ (16 × 3)]
On further calculation
= 26/48 – 21/48
We get
= (26 – 21)/48 = 5/48

(ii)  and  
It can be written as
5/18 – 4/15
We know that LCM of 18 and 15 is 90
In order to convert fraction into equivalent fraction having 90 as denominator
= [(5 × 5)/ (18 × 5)] – [(4 × 6)/ (15 × 6)]
On further calculation
= 25/90 – 24/90
We get
= (25 – 24)/90 = 1/90

(iii)  and  
It can be written as
3/4 – 1/12
We know that LCM of 4 and 12 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(3 × 3)/ (4 × 3)] – [(1 × 1)/ (12 × 1)]
On further calculation
= 9/12 – 1/12
We get
= (9 – 1)/12 = 8/12 = 2/3

(iv)  and
It can be written as
6/7 – 2/3
We know that LCM of 7 and 3 is 21
In order to convert fraction into equivalent fraction having 48 as denominator
= [(6 × 3)/ (7 × 3)] – [(2 × 7)/ (3 × 7)]
On further calculation
= 18/21 – 14/21
We get
= (18 – 14)/21 = 4/21

Q4: Subtract as indicated :
(i)
(ii)
(iii)
(iv)
Ans:
(i)
It can be written as
8/3 – 5/9
We know that LCM of 3 and 9 is 9
In order to convert fraction into equivalent fraction having 9 as denominator
= [(8 × 3)/ (3 × 3)] – [(5 × 1)/ (9 × 1)]
On further calculation
= 24/9 – 5/9
We get
= (24 – 5)/9 = 19/9

(ii)
It can be written as
22/5 – 11/5
We get
= (22 – 11)/5 = 11/5

(iii)
It can be written as
41/7 – 8/3
We know that LCM of 7 and 3 is 21
In order to convert fraction into equivalent fraction having 21 as denominator
= [(41 × 3)/ (7 × 3)] – [(8 × 7)/ (3 × 7)]
On further calculation
= 123/21 – 56/21
We get
= (123 – 56)/21 = 67/21

(iv)
It can be written as
19/4 – 13/6
We know that LCM of 4 and 6 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(19 × 3)/ (4 × 3)] – [(13 × 2)/ (6 × 2)]
On further calculation
= 57/12 – 26/12
We get
= (57 – 26)/12 = 31/12

Q5: Simplify:
simplify : 
(i)  
(ii)  
(iii)  
(iv)  
(v)
(vi)  
(vii)  
(viii)  
(ix)
Ans:
(i)  
We know that the LCM of 3, 4 and 2 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(2 × 4)/ (3 × 4)] + [(3 × 3)/ (4 × 3)] + [(1 × 6)/ (2 × 6)]
On further calculation
= 8/12+ 9/12 + 6/12
We get
= (8 + 9 + 6)/ 12 = 23/12

(ii)  
We know that the LCM of 8, 5 and 4 is 40
In order to convert fraction into equivalent fraction having 40 as denominator
= [(5 × 5)/ (8 × 5)] + [(2 × 8)/ (5 × 8)] + [(3 × 10)/ (4 × 10)]
On further calculation
= 25/40 + 16/40 + 30/40
We get
= (25 + 16 + 30)/ 40 = 71/40

(iii)  
We know that the LCM of 10, 15 and 5 is 30
In order to convert fraction into equivalent fraction having 30 as denominator
= [(3 × 3)/ (10 × 3)] + [(7 × 2)/ (15 × 2)] + [(3 × 6)/ (5 × 6)]
On further calculation
= 9/30+ 14/30 + 18/30
We get
= (9 + 14 + 18)/ 30 = 41/30

(iv)  
We know that the LCM of 4, 16 and 8 is 16
In order to convert fraction into equivalent fraction having 16 as denominator
= [(3 × 4)/ (4 × 4)] + [(7 × 1)/ (16 × 1)] + [(5 × 2)/ (8 × 2)]
On further calculation
= 12/16 + 7/16 + 10/16
We get
= (12 + 7 + 10)/ 16 = 29/16

(v)
It can be written as
14/3 + 13/4 + 15/2
We know that the LCM of 3, 4 and 2 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(14 × 4)/ (3 × 4)] + [(13 × 3)/ (4 × 3)] + [(15 × 6)/ (2 × 6)]
On further calculation
= 56/12 + 39/12 + 90/12
We get
= (56 + 39 + 90)/ 12 = 185/12

(vi)  
It can be written as
22/3 + 11/3 + 31/6
We know that the LCM of 3, 3 and 6 is 6
In order to convert fraction into equivalent fraction having 6 as denominator
= [(22 × 2)/ (3 × 2)] + [(11 × 2)/ (3 × 2)] + [(31 × 1)/ (6 × 1)]
On further calculation
= 44/6 + 22/6 + 31/6
We get
= (44 + 22 + 31)/ 6 = 97/6

(vii)  
It can be written as
7/1 + 7/4 + 31/6
We know that the LCM of 1, 4 and 6 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(7 × 12)/ (1 × 12)] + [(7 × 3)/ (4 × 3)] + [(31 × 2)/ (6 × 2)]
On further calculation
= 84/12 + 21/12 + 62/12
We get
= (84 + 21 + 62)/12 = 167/12

(viii)  
We know that the LCM of 6, 1 and 4 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(5 × 2)/ (6 × 2)] + [(3 × 12)/ (1 × 12)] + [(3 × 3)/ (4 × 3)]
On further calculation
= 10/12 + 36/12 + 9/12
We get
= (10 + 36 + 9)/ 12 = 55/12

(ix)
It can be written as
7/18 + 5/6 + 13/12
We know that the LCM of 18, 6 and 12 is 36
In order to convert fraction into equivalent fraction having 12 as denominator
= [(7 × 2)/ (18 × 2)] + [(5 × 6)/ (6 × 6)] + [(13 × 3)/ (12 × 3)]
On further calculation
= 14/36 + 30/36 + 39/36
We get
= (14 + 30 + 39)/36 = 83/36

Q6: Replace * by the correct number:
(i) * – 5/8 = 1/4
(ii) * – 1/5 = 1/2
(iii) 1/2 – * = 1/6
Ans: 
(i) * – 5/8 = 1/4
It can be written as
* = 1/4 + 5/8
On further calculation
* = [(1 × 2)/ (4 × 2)] + [(5 × 1)/ (8 × 1)]
We get
* = 2/8 + 5/8
By addition
*= (2 + 5)/ 8 = 7/8

(ii) * – 1/5 = 1/2
It can be written as
* = 1/2 + 1/5
On further calculation
* = [(1 × 5)/ (2 × 5)] + [(1 × 2)/ (5 × 2)]
We get
* = 5/10 + 2/10
By addition
* = (2 + 5)/ 10 = 7/10

(iii) 1/2 – * = 1/6
It can be written as
* = 1/2 – 1/6
On further calculation
* = [(1 × 3)/ (2 × 3)] – [(1 × 1)/ (6 × 1)]
We get
* = 3/6 – 1/6
By addition
* = (3 – 1)/ 6 = 2/6 = 1/3

Q7: Savita bought  m of ribbon and kavita  m of ribbon. What was the total length of the ribbon they bought ? 
Ans:
Length of ribbon Savita bought = 2/5 m
Length of ribbon Kavita bought = 3/4 m
So the total length of ribbon they bought = 2/5 + 3/4
We know that the LCM of 5 and 4 is 20
So we get
= [(2 × 4)/ (5 × 4)] + [(3 × 5)/ (4 × 5)]
On further calculation
= 8/20 + 15/20
We get
= (8 + 15)/20 = 23/20 m
Hence, the total length of the ribbon they bought is 23/20 m.

Q8: Ravish takes  minutes to walk across the school ground. Rahul takesminutes to do the same. Who takes less time and by what fraction ? 
Ans: Time taken by Ravish to walk across the school ground = 2 1/5 minutes = 11/5 minutes
Time taken by Rahul to walk across the school ground = 7/4 minutes
By comparing 11/5 and 7/4 minutes
We know that LCM of 4 and 5 is 20
In order to convert fraction into equivalent fraction having 20 as denominator
[(11 × 4)/ (5 × 4)], [(7 × 5)/ (4 × 5)]
So we get 44/20 > 35/20
So Rahul takes less time
It can be written as
44/20 – 35/20 = (44 – 35)/20 = 9/20 minutes
Hence, Rahul takes less time by 9/20 minutes.

Q9: A piece of a wire  metres long broke into two pieces. One piece was  meter long. How long is the other piece ?
Ans:
It is given that
Length of wire = 7/8 m
Length of first piece = 1/4 m
Consider x m as the length of second piece
It can be written as
Length of wire = Length of first piece + Length of second piece
By substituting the values
7/8 = 1/4 + x
On further calculation
x = 7/8 – 1/4
We know that the LCM of 8 and 4 is 8
x = [(7 × 1)/ (8 × 1)] – [(1 × 2)/ (4 × 2)]
We get
x = 7/8 – 2/8
By subtraction
x = (7 – 2)/ 8 = 5/8 m
Hence, the length of second piece of wire is 5/8 m.

Q10: Shikha and priya have bookshelves of the same size shikha’s shelf is  full of book and priya’s shelf is full. Whose bookshelf is more full ? By what fraction ? 
Ans: Fraction of Shikha’s shelf filled with books = 5/6
Fraction of Priya’s shelf filled with books = 2/5
We know that LCM of 5 and 6 is 30
In order to convert fraction into equivalent fraction having 30 as denominator
= [(5 × 5)/ (6 × 5)], [(2 × 6)/ (5 × 6)]
So we get 25/30 > 12/30
So Shikha’s shelf is more full.
It can be written as
25/30 – 12/30 = (25 – 12)/ 30 = 13/30
Hence, Shikha’s bookshelf is more full by 13/30.

Q11: Ravish’s house is Km from his school. He walked some distance and then took a bus for  Km. How far did he walk?
Ans:
It is given that
Distance of Ravish’s house from his school = 9/10 km
Distance covered by bus = 1/2 km
It can be written as
Distance between house and school = Distance covered by walking + Distance covered by bus
So we get
Distance covered by walking = Distance between house and school – Distance covered by bus
Substituting values
Distance covered by walking = 9/10 – 1/2
We know that LCM of 10 and 2 is 10
In order to convert fraction into equivalent fraction having 10 as denominator
Distance covered by walking = [(9 × 1)/ (10 × 1)] – [(1 × 5)/ (2 × 5)]
We get
Distance covered by walking = 9/10 – 5/10
By subtraction
Distance covered by walking = (9 – 5)/ 10 = 4/10 = 2/5 km
Hence, the distance covered by Ravish by walking is 2/5km.