RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.9 help students with a clear and detailed understanding of fractions and their operations. This exercise focuses on important concepts such as addition and subtraction of fractions with like and unlike denominators, simplifying fractions, and converting mixed numbers to improper fractions and vice versa.
The exercise also includes problems on comparing fractions, finding equivalent fractions, and applying these skills to solve word problems. The step-by-step solutions help students build a solid grasp of fraction concepts, enhance their problem-solving abilities, and prepare them for more advanced topics in mathematics.
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.9 Introduction
Exercise 6.9 in Chapter 6 of RD Sharma Class 6 Maths focuses on the addition and subtraction of fractions. This exercise is designed to help students understand how to add and subtract fractions with both like and unlike denominators.
Students will learn important steps such as:
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Finding a common denominator when the denominators are different.
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Converting fractions to equivalent fractions with the same denominator.
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Adding or subtracting the numerators while keeping the denominator the same.
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Simplifying the resulting fraction to its lowest terms.
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Applying these methods to solve word problems and practical examples involving fractions.
Access Answers to Maths RD Sharma Solutions for Class 6 Chapter 6 Fractions Exercise 6.9
Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 6 Exercise 6.9 on Fractions.
1. Add:
(i) 3/4 and 5/6
(ii) 7/10 and 2/15
(iii) 8/13 and 2/3
(iv) 4/5 and 7/15
Solution:
(i) 3/4 and 5/6
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) 7/10 and 2/15
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) 8/13 and 2/3
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) 4/5 and 7/15
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
2. Subtract:
(i) 2/7 from 19/21
(ii) 21/25 from 18/20
(iii) 7/16 from 2
(iv) 4/15 from 2 1/5
Solution:
(i) 2/7 from 19/21
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) 21/25 from 18/20
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) 7/16 from 2
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) 4/15 from 2 1/5
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
3. Find the difference of:
(i) 13/24 and 7/16
(ii) 5/18 and 4/15
(iii) 1/12 and 3/4
(iv) 2/3 and 6/7
Solution:
(i) 13/24 and 7/16
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) 5/18 and 4/15
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) 1/12 and 3/4
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) 2/3 and 6/7
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
4. Subtract as indicated:
(i) 8/3 – 5/9
(ii) 4 2/5 – 2 1/5
(iii) 5 6/7 – 2 2/3
(iv) 4 3/4 – 2 1/6
Solution:
(i) 8/3 – 5/9
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) 4 2/5 – 2 1/5
It can be written as
22/5 – 11/5
We get
= (22 – 11)/5 = 11/5
(iii) 5 6/7 – 2 2/3
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) 4 3/4 – 2 1/6
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
5. Simplify:
(i) 2/3 + 3/4 + 1/2
(ii) 5/8 + 2/5 + 3/4
(iii) 3/10 + 7/15 + 3/5
(iv) 3/4 + 7/16 + 5/8
(v) 4 2/3 + 3 1/4 + 7 1/2
(vi) 7 1/3 + 3 2/3 + 5 1/6
(vii) 7 + 7/4 + 5 1/6
(viii) 5/6 + 3 + 3/4
(ix) 7/18 + 5/6 + 1 1/12
Solution:
(i) 2/3 + 3/4 + 1/2
We know that the LCM of 3, 4 and 2 is 12
In order to convert fraction into equivalent fraction having 12 as denominator
= [(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) 5/8 + 2/5 + 3/4
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) 3/10 + 7/15 + 3/5
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) 3/4 + 7/16 + 5/8
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) 4 2/3 + 3 1/4 + 7 1/2
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) 7 1/3 + 3 2/3 + 5 1/6
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) 7 + 7/4 + 5 1/6
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) 5/6 + 3 + 3/4
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) 7/18 + 5/6 + 1 1/12
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
6. Replace ☐ by the correct number:
(i) ☐ – 5/8 = 1/4
(ii) ☐ – 1/5 = 1/2
(iii) 1/2 – ☐ = 1/6
Solution:
(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
7. Savita bought 2/5 m of ribbon and Kavita 3/4 m of the ribbon. What was the total length of the ribbon they bought?
Solution:
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.
8. Ravish takes 2 1/5 minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?
Solution:
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.
9. A piece of a wire 7/8 metres long broke into two pieces. One piece was ¼ meter long. How long is the other piece?
Solution:
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.
10. Shikha and Priya have bookshelves of the same size Shikha’s shelf is 5/6 full of book and Priya’s shelf is 2/5 full. Whose bookshelf is more full? By what fraction?
Solution:
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.
11. Ravish’s house is 9/10 km from his school. He walked some distance and then took a bus for 1/2km upto the school. How far did he walk?
Solution:
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.
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.9 PDF Download
Students looking to master the addition and subtraction of fractions can refer to the detailed solutions provided in this exercise.
These solutions are explained step-by-step to help students understand the concepts easily and improve their problem-solving skills.
You can download the PDF of RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.9 from the link given below and study anytime, even without an internet connection.
