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NCERT Solutions for class 6 Maths chapter 7 – Fractions


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Exercise 7.1

Question 1.
Write the fraction representing the shaded portion.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 1
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 2
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 3
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 4

Question 2.
Color the part according to the given fraction.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 5
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 6

Question 3.
Identify the error, if any
tiwari academy class 6 maths Chapter 7 Fractions 7
Solution :
Neither of the shaded portions represents the corresponding given fractions. 4.

Question 4.
What fraction of a day is 8 hours?
Solution :
1 day = 24 hours
∴ Required fraction = 824

Question 5.
What fraction of an hour is 40 minutes?
Solution :
1 hour = 60 minutes
∴ Required fraction = 4060

Question 6.
Arya, Abhimanyu, and Vivek shared lunch. Arya brings two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?
Solution :
(a) Arya will divide each sandwich into three equal parts, and give one part of each sandwich to each one of them.
(b) Each boy will receive 13 part of a sandwich.

Question 7.
Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Solution :
She has finished 23 fraction of the dresses.

Question 8.
Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Solution :
The natural numbers from 2 to 12 are 2, 3, 4,5,6, 7, 8, 9, 10, 11 and 12
Total number of natural numbers = 11
Out of these, the prime numbers are 2, 3, 5, 7, 11

Total number of these prime numbers = 5 5
∴ Required fraction = 511.

Question 9.
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Solution :
The natural numbers from 102 to 113 are
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113
Total number of natural numbers =12
Out of these, the prime numbers are 103, 107, 109, 113.
Total number of these prime numbers = 4 . 4
∴ Required fraction = 412.

Question 10.
What fraction of these circles have X’s in them?
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 8
Solution :
Total number of circles = 8
Number of circles which have X’s in them = 4
∴ Required fraction = 48.

Question 11.
Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
Solution :
Number of CDs bought = 3
Number of CDs received as gifts = 5
∴ Total number of CDs = 3 + 5 = 8
Fraction of her total CDs that she bought 38 and, fraction of her total CDs that she received as gifts 58.

Exercise 7.2

Question 1.
Draw number lines and locate the points on them:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 9
Solution :
(a)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 10
(b)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 11
(c)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 12
Question 2.
Express the following as mixed fractions:
(a) 203
(b) 115
(c) 177
(d) 285
(e) 196
(f) 359.
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 15
tiwari academy class 6 maths Chapter 7 Fractions 16
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 17

Question 3.
Express the following as improper fractions:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 18
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 19

Exercise 7.3

Question 1.
Write the fractions. Are all these fractions equivalent?
(a)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 20
(b)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 21

Solution :
(a)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 22
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 23
(b)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 24

No ! all these fractions ae not equivalent.

Question 2.
Write the fractions and pair up the equivalent fractions from each row.
tiwari academy class 6 maths Chapter 7 Fractions 25
Solution:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 26
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 27
Equivalent fractions are
(a), (ii);
(b), (,iv);
(c), (i);
(d), (v);
(e), (iii).

Question 3.
Replace in each of the following by the correct number:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 28
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 29
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 30
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 31
Question 4.
Find the equivalent fraction of 35 having
(a) denominator 20
(b) numerator 9
(d) numerator 27
(c) denominator 30
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 32
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 33
Question 5.
Find the equivalent fraction of 3648 with
(a) numerator 9
(b) denominator 4.
Solution :
tiwari academy class 6 maths Chapter 7 Fractions 34
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 35
Question 6.
Check whether the given fractions are equivalent :
(a) 59, 3054
(b) 310, 1250
(c) 713, 511
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 36
∴ The given fractions 59 and 3054 are equivalent.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 37
∴ The given fractions 310 and 1250 are not equivalent.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 38
∴ The given fractions 73 and 511 are not equivalent.

Question 7.
Reduce the following fractions to simplest form:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 39
Solution :
(a) 4860
Factors of 48 are 1, 2, 3,4, 6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3,4, 5, 6, 10,12, 15, 20, 30 and 60.
∴ Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12. Highest of these common factors is 12.
∴ H.C.F. of 48 and 60 is 12.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 40
(b) 15060
Factors of 150 are 1,2,3,5,6.10,15,25,30,50, 75 and 150.
Factors of 60 are 1, 2. 3, 4. 5, 6, 10, 12, 15, 20, 30 and 60.
∴ Common factors of 150 and 60 are 1, 2, 3, 5,6, 10, 15 and 30.
Highest of these common factors is 30.
∴ H.C.F. of 150 and 60 is 30.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 41
(c) 8498
Factors of 84 are 1, 2, 3,4, 6, 7, 12, 14, 21, 28, 42 and 84.
Factors of 98 are 1, 2, 7, 14,49 and 98.
∴ Common factors of 84 and 98 are 1,7 and 14. Highest of these common factors is 14.
∴ H.C.F. of 84 and 98 is 14.
tiwari academy class 6 maths Chapter 7 Fractions 42
(d) 1252
Factors of 12 are 1, 2, 3,4, 6 and 12.
Factors of 52 are 1, 2, 4, 13, 26 and 52.
∴ Common factors of 12 and 52 are 1,2 and 4. Highest of these common factors is 4.
∴ H.C.F. of 12 and 52 is 4.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 43
(e) 728
Factors of 7 are 1 and 7.
Factors of 28 are 1, 2,4, 7, 14 and 28.
∴ Common factors of 7 and 28 are 1 and 7. Highest of these common factors is 7.
∴ H.C.F. of 7 and 28 is 7.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 44
Question 8.
Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of his/her pencils?
Solution :
For Ramesh
Number of pencils he had = 20 Number of pencils used by him =10
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 45
For Sheelu
Number of pencils she had = 50 Number of pencils used by her = 25
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 46

For Jamaal
Number of pencils he had = 80 Number of pencils used by him = 40
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 47
Yes ! each has used up an equal fraction of his/her pencils.

Question 9.
Match the equivalent fractions and write another two more for each :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 48
Solution :
(i) 250400
Factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
Factors of 400 are 1,2,4,5,8,10,16,20,25,40, 80, 100, 200 and 400.
∴ Common factors of 250 and 400 are 1,2,5, 10, 25 and 50.
Highest of these common factors is 50.
∴ H.C.F. of 250 and 400 is 50.
tiwari academy class 6 maths Chapter 7 Fractions 49

(ii) 180200
Factors of 180 are 1,2, 3,4, 5, 6,9,10,12,15, 18, 20, 30, 36, 45, 60, 90 and 180.
Factors of 200 are 1,2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
∴ Common factors of 180 and 200 are 1,2, 4, 5, 10 and 20.
Highest of these common factors is 20.
∴ H.C.F. of 180 and 200 is 20.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 50

(iii) 600990
Factors of 660 are 1,2,3,4,5,6,10,12,22,30, 66, 110, 132, 165, 220, 330 amd 660.
Factors of 990 are 1,2,3,5,6,9,10,11,30,33, 90, 99, 110, 165, 198, 330, 495 and 990.
∴ Common factors of 660 and 990 are 1,2,3, 5,6, 10, 30, 110 and 330.
Highest of these common factors is 330.
∴ H.C.F. of 660 and 990 is 330.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 51

(iv) 180360
Factors of 180 are 1, 2, 3,4, 5, 6, 9, 10, 12,15, 18, 20, 30, 36,45, 60, 90 and 180.
Factors of 360 are 1, 2, 3,4, 5, 6,9,10, 12, 15, 18, 20, 24, 30, 36,40, 60, 72, 90, 120, 180 and 360.
∴ Common factors of 180 and 360 are 1,2, 3,4,5,6,9,10,12,15,18.20, 30, 36,60,90 and 180.
Highest of these common factors is 180.
∴ H.C.F. of 180 and 360 is 180.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 52

(v) 220550
Factors of 220 are 1,2,4, 5,10,11, 20, 22,44, 55, 110 and 220.
Factors of 550 are 1, 2, 5, 10, 22, 25, 55, 110, 275 and 550.
∴ Common factors of 220 and 550 are 1,2,5, 10, 20 and 110.
Highest of these common factors is 110.
∴ H.C.F. of 220 and 550 is 110.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 53
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 54

Exercise 7.4

Question 1.
Write shaded portion as a fraction. Arrange them in ascending and descending order using correct sign ‘<‘, ‘=’, ‘>’ between the fraction:
(a)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 55
(b)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 56
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 57
appropriate signs between the fractions  given
tiwari academy class 6 maths Chapter 7 Fractions 58
Solution:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 59
(i) In ascending order, these are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 60
(ii) In descending order, these are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 61
(b)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 62

(i) In ascending order, these are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 63
(ii) In descending order, these are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 64
(c)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 65
Question 2.
Compare the fractions and put an appropriate sign.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 66
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 67

tiwari academy class 6 maths Chapter 7 Fractions 68
Question 3.
Make five more such pairs and make appropriate signs.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 69

Question 4.
Look at the figures and write ‘<’ or ‘>’, ‘=’ between the pairs of fractions.
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 70
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 71
Make five more such problems and solve them with your friends.
Solution:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 72
For the remaining part, please try yourself.

Question 5.
How quickly can you do this? Fill appropriate sign (<, =,>)
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 73
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 74
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 75
Question 6.
The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 76
Solution :
tiwari academy class 6 maths Chapter 7 Fractions 77
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 78
Question 7.
Find answers to the following. Write and indicate how you solved them.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 79
Solution :
(a) Equivalent fraction of 59 are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 80
Equivalent fraction of 45 are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 81
(b) Equivalent fraction of 916 are
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 82
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 83

Question 8.
Ila reads 25 pages of a book containing 100 pages. Lalita reads 12 of the same book. Who read less?
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 84
Question 9.
Rafiq exercised for 36 of an hour, while 6 Rohit exercised for 34 of an hour. Who exercised for a longer time?
Solution :
34 > 36
∴ Rohit exercised for a longer time.

Question 10.
In class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class was a greater fraction of students getting first class?
Solution :
tiwari academy class 6 maths Chapter 7 Fractions 85
Hence, in both the classes the same fraction (45)of total students got first class.

Exercise 7.5

Question 1.
Write these fractions appropriately as additions or subtractions:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 86
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 87
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 88
Question 2.
Solve
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 89
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 90
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 91

Question 3.
Shubham painted 23 of the wall space in his room. Her sister Madhavi helped and painted 13 of the wall space. How much did they paint together?
Solution :
tiwari academy class 6 maths Chapter 7 Fractions 92
Hence, they painted together with the complete wall space. ,

Question 4.
Fill in the missing fractions :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 93
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 94
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 95
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 96
Question 5.
Javed was given 57 of a basket of oranges. What fraction of oranges was left in the basket?
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 97
Hence, fraction 27 of oranges was left in the basket.

Exercise 7.6

Question 1.
Solve:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 98
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 99
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 100
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 101
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 0102
tiwari academy class 6 maths Chapter 7 Fractions 0103
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 104
Question 2.
Sarita bought 25 metre of ribbon and Lalita bought 34 metre of ribbon. What was the total 4 length of the ribbon they bought?
Solution :
Ribbon bought by Sarita = 25 m
Ribbon bought by Lalita = 34 m
∴ Total length of the ribbon they bought
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 105

Question 3.
Naina was given 112 piece of cake and Najma was given 113 piece of cake. Find the total amount of care given to both of them.
Solution :
Cake given to naina = 112 piece = (1×2)+12 piece
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 106
Question 4.
Fill in the boxes:
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 107

Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 108
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 109

Question 5.
Complete the addition-subtraction box.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 110
tiwari academy class 6 maths Chapter 7 Fractions 111
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 112
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 113

Question 6.
A piece of wire 78 meter long broke into two pieces. One piece was 14 metre long. How long is the other piece?
Solution :
Length of the original piece of wire = 78 metre
∴ Length of one piece = 14 metre
Length of the other piece = 78 metre – 14 metre = (7814) metre
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 114
Question 7.
Nandini’s house is ~ km from her school. She walked some distance and then took a bus for km to reach the school. How far did she walk?
Solution :
The distance of Nandini’s house from school
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 0115
Question 8.
Asha and Samuel have bookshelves of the 5 same size. Asha’s shelf is 56 the full of book and Samuel’s shelf is 25th full. Whose bookshelf is more full? By what fraction?
Solution :
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 0116
Question 9.
Jaidev takes 215 minutes to walk across 5 the school ground. Rahul takes 74 minutes to do the same. Who takes less time and by what fraction?
Solution :
Time taken by Jaidev to walk across the school ground = 215 minutes
NCERT Solutions for Class 6 Maths Chapter 7 Fractions 0117

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