NCERT Solutions for Class 6 Maths - Fractions

Exercise 7.1

Q1. Write the fraction representing the shaded portion.

Ans: 
(i) Total number of parts = 4
Number of shaded parts = 2
∴ Fraction =  2/424

(ii) Total number of parts = 9
Number of shaded parts = 8
∴ Fraction = 8/989

(iii) Total number of parts = 8
Number of shaded parts = 4
∴ Fraction = 4/848

(iv) Total number of parts = 4
Number of shaded parts = 1
∴ Fraction = 1/4 14

(v) Total number of parts = 7
Number of shaded parts = 3
∴ Fraction = 3/737

(vi) Total number of parts = 12
Number of shaded parts = 3
∴ Fraction = 3/12312

(vii) Total number of parts = 10
Number of shaded parts = 10
∴ Fraction = 10/101010

(viii) Total number of parts = 9
Number of shaded parts = 4
∴ Fraction = 4/949

(ix) Total number of parts = 8
Number of shaded parts = 4
∴ Fraction = 4/848

(x) Total number of parts = 2
Number of shaded part = 1
∴ Fraction = 1/212

Q2. Colour the part according to the given fraction.

Ans:

Q3. Identify the error, if any.

Ans: All the figures are not equally divided. For making fractions, it is necessary that figure is to be divided into equal parts.

Q4. What fraction of a day is 8 hours?
Ans: Since, 1 day = 24 hours.
Therefore, the fraction of 8 hours = (8/24)
= (1/3)

Q5. What fraction of an hour is 40 minutes?
Ans: Since, 1 hour = 60 minutes.
Therefore, the fraction of 40 minutes = (40/60)
= (2/3)

Q6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetables 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?
Ans: (a) To ensure that each person has an equal share of both sandwiches, Arya can divide each of his sandwiches into three equal parts. Therefore, each boy will receive 1/3 of each sandwich.
(b) In summary, each boy will receive:

• 1/3 of the vegetable sandwich
• 1/3 of the jam sandwich

Q7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Ans: To find the fraction of dresses that Kanchan has finished dyeing, we need to divide the number of dresses she has finished by the total number of dresses she had to dye. According to the given information, Kanchan had to dye 30 dresses and has so far finished 20 dresses. Therefore, the fraction of dresses she has finished dyeing is:  20 / 30
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 10.
20 / 30 = (20 ÷ 10) / (30 ÷ 10) = 2 / 3
Therefore, Kanchan has finished dyeing 2/3 of the dresses she had to dye.

Q8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Ans: The natural numbers from 2 to 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
To find out what fraction of these numbers are prime, we need to identify which of these numbers are prime. According to the list of prime numbers 1, the prime numbers between 2 and 12 are 2, 3, 5, 7, 11. Therefore, out of the 11 natural numbers between 2 and 12, there are 5 prime numbers. To find the fraction of these numbers that are prime, we divide the number of prime numbers by the total number of natural numbers: 5 / 11. This fraction cannot be simplified any further. Therefore, the fraction of natural numbers between 2 and 12 that are prime is 5/11.

Q9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Ans: Natural numbers from 102 to 113:
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
Prime numbers from 102 to 113:
103, 107, 109, 113
Hence fraction of prime numbers = (4/12) = 1/3

Q10. What fractions of these circles have X’s in them?

Ans: Total number of circles = 8 and number of circles having ‘X’ = 4
Hence, the fraction = (4/8)

Q11. 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?
Ans: Total number of CDs = 3 + 5 = 8
Number of CDs purchased = 3
Fraction of CDs purchased = (3/8)
Fraction of CDs received as gifts = 5/8

Exercise 7.2

Q1. Draw number lines and locate the points on them:

Ans:
(a) 

Here divide the number line from 0 to 1 into four equal parts
C = 2/4 = 1/2
B = 1/4
D = 3/4 and
E = 4/4 =1
(b)

Divide the number line from 0 to 1 into eight equal parts
B = 1/8
C =2/8
D = 3/8
H = 7/8
(c) 

From the given number line, we have
C = 2/5
D = 3/5
E = 4/5
I = 8/5

Q2. Express the following as mixed fractions:
(a) 20/3
(b) 11/5
(c) 17/7
(d) 28/5
(e) 19/6
(f) 35/9
Ans: 
(a) 

(b)

(c) 

(d) 

(e) 

(f) 

Q3. Express the following as improper fractions:

Ans:

Exercise 7.3

Q1. Write the fractions. Are all these fractions equivalent?

(a) 

(b) 
Ans:
(a) 
(i) The shaded portion is 1 / 2
(ii) The shaded portion is 2/4 =  1 / 2
(iii) The shaded portion is 3 / 6 = 1 / 2
(iv) The shaded portion is 4 / 8 = I / 2
Hence, all fractions are equivalent.
(b)
(i) The shaded portion is 4/ 12 =  1 / 3
(ii)The shaded portion is 3 / 9 = I / 3
(iii) The shaded portion is 2 / 6 = I / 3
(iv) The shaded portion is 1 / 3
(v) The shaded portion is 6 / 15 = 2/5
All the fractions in their simplest form are not equal
Hence, they are not equivalent fractions

Q2. Write the fractions and pair up the equivalent fractions from each row.

Ans:

Q3. Replace  in each of the following by the correct number:





Ans:

Q4. Find the equivalent fraction of 3/5 having
(a) denominator 20 
(b) numerator 9
(c) denominator 30 
(d) numerator 27
Ans:

Q5. Find the equivalent fraction of 36/48 with
(a) numerator 9 
(b) denominator 4
Ans:

Q6. Check whether the given fractions are equivalent:



Ans:

Therefore   are equivalent

Therefore,   are not equivalent,

Therefore,    are not equivalent fraction.

Q7. Reduce the following fractions to the simplest form:
(a) 48/60
(b) 150/60
(c) 84/98
(d) 12/52
(e) 7/28
Ans:

Q8. 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 her/his pencils?
Ans:
Ramesh: 
Total pencils = 20
Pencils used = 10
Fraction = 10/20 = 1/2
Sheelu: 
Total pencils = 50
Pencils used = 25
Fraction = 25/50 = 1/2
Jamaal: 
Total pencils = 80
Pencils used = 40
Fraction = 40/80 = 1/2
Since, all of them used half of their pencils, therefore each one used up equal fraction of pencils.

Q9. Match the equivalent fractions and write two more for each.
(i) 250/400     (a) 2/3
(ii) 180/200    (b) 2/5
(iii) 660/990   (c) 1/2
(iv) 180/360   (d) 5/8
(v) 220/550    (e) 9/10
Ans:
(i)    (d) 5/8
(ii)    (e) 9/10
(iii)     (a) 2/3
(iv)        (c) 1/2
(v)   (b) 2/5

Exercise 7.4

Q1. Write the shaded portion as a fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘=’, ‘>’ between the fractions:
(a)
(b)  
(c) Show  on the number line. Put appropriate signs between the fractions given.

Ans:

Ascending order:  
Descending order:  

Ascending order:  
Descending order:
(c) Number line

Q2. Compare the fractions and put an appropriate sign.

Ans:

Q3. Make five more each pairs and put appropriate signs. 
Ans:

Q4. Look at the figures and write ‘<’ or ‘>’ between the given pairs of fractions.

Make five more such problems and solve them with your friends. 
Ans:





Five more such problems:





Ans:

Q5. How quickly can you do this? Fill appropriate sign (‘<’, ‘=’, ‘>’)











Ans:

Q6. The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
(a) 2/12
(b) 3/15
(c) 8/50
(d) 16/100
(e) 10/60
(f) 15/75
(g) 12/60
(h) 16/96
(i) 12/75
(j) 12/72
(k) 3/18
(l) 4/25
Ans:












Equivalent groups:

Q7. Find answers to the following. Write and indicate how you solved them.
(a)  
(b) 
(c) 
(d) 
Ans:

  [∴ L.C.M. of 9 and 5 is 45]


   [∴ L.C.M. of 16 and 9 is 144]


   [∴ L.C.M. of 5 and 20 is 100]


 [∴ L.C.M. of 15 and 30 is 30]

Q8. Ila read 25 pages of a book containing 100 pages. Lalita read 2/5 of the same book. Who reads less?
Ans: Ila read 25 pages out of 100 pages.
Fraction of reading the pages =  25/100 = 1/4 th part of the book
Lalita read 2/5 th part of the book  = 40/100 pages

Therefore, Ila read less.

Q9. Rafiq exercised for 3/6 of an hour, while Rohit exercised for 3/4of an hour. Who exercised for a longer time?
Ans: Rafiq exercised 3/6 of an hour.
Rohit exercised 3/4 of an hour.

Therefore, Rohit exercised for a longer time.

Q10. 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?
Ans: In class A, 20 passed out of 25, i.e., 20/25 = 4/5
In class B, 24 passed out of 30, i.e., 24/30 = 4/5
Hence, each class have the same fraction of student getting a first class.

Exercise 7.5

Q1. Write these fractions appropriately as additions or subtractions:
(a)
(b) 
(c) 
Ans:

Q2. Solve:









Ans:

Q3. Shubham painted 2/3of the wall space in his room. His sister Madhavi helped and painted 1/3 of the wall space. How much did they paint together?
Ans: Fraction of wall painted by Shubham = 2/3
Fraction of wall painted by Madhavi = 1/3
Total painting by both of them =
Therefore, they painted the complete wall.

Q4. Fill in the missing fractions.

Ans:
(a) 4/10
(b) 8/21
(c) 6/6
(d) 7/27

Q5. Javed was given a basket of oranges. What fraction of oranges was left in the basket?
Ans:
Total = 1
Fraction of Orange left  

Thus, 2/7 oranges were left in the basket.

Exercise 7.6

Q1. Solve














Ans:
(a) L.C.M. of 3 and 7 is 21

(b) L.C.M. of 10 and 15 is 30

(c) L.C.M. of 9 and 7 is 63
 
(d)
 
(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

Q2. Sarita bought 2/5 metre of ribbon and Lalita 3/4 metre of ribbon. What is the total length of the ribbon they bought?
Ans: Ribbon bought by Sarita = 2/5 m and Ribbon bought by Lalita = 3/4 m
The total length of ribbon =

Therefore, they bought    of ribbon.

Q3. Naina was given  piece of cake and Najma was given  piece of cake. Find the total amount of cake was given to both of them.
Ans: Cake taken by Naina =  piece and Cake taken by Najma  piece
Total cake taken

Therefore, the total consumption of cake is  

Q4. Fill in the boxes: 



Ans:

Q5. Complete the addition-subtraction box.

Ans:

Q6. A piece of wire 7/8 metre long broke into two pieces. One piece was 1/4 metre long. How long is the other piece?
Ans:
The total length of wire = 7/8 meter
Length of first part = 1/4 meter
Remaining part     [∴ L.C.M. of 8 and 4 is 8]

Therefore, the length of the remaining part is 5/8 meter.

Q7. Nandini’s house is 9/10 km from her school. She walked some distance and then took a bus for 1/2 km to reach the school. How far did she walk?
Ans:
The total distance between school and house 9/10 km
Distance covered by bus = 1/2 km
Remaining distance  [∴ L.C.M. of 10 and 2 is 10]

Therefore, the distance covered by walking is 2/5 km.

Q8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5/6 th full and Samuel’s shelf is 2/5 th full. Whose bookshelf is more full? By what fraction?
Ans:

⇒   [∴ L.C.M. of 6 and 5 is 30]
∴    
⇒  
∴ Asha’s bookshelf is more covered than Samuel.


Q9. Jaidev takes minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?
Ans:
Time taken by Jaidev =  minutes = 11/5 minutes
Time taken by Rahul =  7/4 minutes
Difference   [∴ L.C.M. of 5 and 4 is 20]

Thus, Rahul takes less time, which is 9/20 minutes.