## NCERT Solutions for Class 6 Maths Chapter 7 Fractions

NCERT solutions for class 6 maths chapter 7 Fractions Exercise: 7.1

Q1 Write the fraction representing the shaded portion.

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Q2 Colour the part according to the given fraction.

Answer: The coloured parts are shown below :-

Q3 Identify the error, if any

This is

This is

This is

Answer: Yes, the above fractions are wrong. For these fractions to be correct areas of each part should be same. But clearly, in the given figure, the areas are not the same.

Q4 What fraction of a day is  hours?

Answer: Total hours in 1 day

Thus the required fraction is :-

Q5 What fraction of an hour is  minutes?

Answer: We know that 1 hour has 60 minutes.

Thus fraction of 40 minutes is :-

Q6 (a) Arya, Abhimanyu, and Vivek shared lunch. Arya has brought 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. How can Arya divide his sandwiches so that each person has an equal share?

Answer: Arya needs to divide one sandwich into 3 equal parts (as three persons are there.)

Thus each sandwich is divided into 3 parts.

Q6 (b) Arya, Abhimanyu, and Vivek shared lunch. Arya has brought 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. What part of a sandwich will each boy receive?

Answer: Since they have to distribute 1 part in 3 people, hence the fraction received by each boy will be:-

Q7 Kanchan dyes dresses. She had to dye  dresses. She has so far finished  dresses. What fraction of dresses has she finished?

Q8 Write the natural numbers from  to  What fraction of them are prime numbers?

Answer: We have :- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Prime number :- 2, 3, 5, 7, 11.

Thus the fraction of prime numbers is:-

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

Answer: The natural numbers are :- 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers are :- 103, 107, 109, 113.

Thus fraction is :-

Q10 What fraction of these circles have  ’s in them?

Answer: The number of boxes with X in them = 4

Total number of boxes = 8.

The required fraction is :

Q11 Kristin received a CD player for her birthday. She bought 3

CDs and received 5 others as gifts. What fraction of her total

Answer: The fraction of the CDs she bought is :

## NCERT Solutions for Class 6 Maths Topic: Fractions on the Number Line

Q1 Show  on a number line.

Answer: First we write  as  and divide the number line into 5 equal parts.

Q2 Show  and  on a number line.

First, we write  as  and divide the number line in 10 equal parts.

Q3 Can you show any other fraction between  and  ?Write five more fractions that you can show.

Yes. There are infinite number of fraction between  and  (Numerator is less than denominator)

Five more fractions are:

Q4 How many fractions lie between  and  ? Think, discuss and write your answer?

Answer: There are infinite number of fractions between  and  .

A fraction is of form  and for a number lying between  and  , the numerator has to be less than the denominator.

## NCERT Solutions for Class 6 Maths Topic: Proper Fractions

Q1 Give a proper fraction : (a) whose numerator is  and the denominator is
(b) whose denominator is  and the numerator is

(c) whose numerator and denominator add up to  . How many fractions of this kind can you make?

(d) whose denominator is  more than the numerator.

(Give any five. How many more can you make?)

(a) the numerator is  and the denominator is  =

(b) denominator is  and numerator is  =

(c) numerator and denominator add up to  .

Pairs of numbers having sum 10 =

Therefore, the proper fractions are

(d) denominator is  more than the numerator. =

Q2 A fraction is given. How will you decide, by just looking at it, whether, the fraction is

(a) less than  ?

(b) equal to  ?

Answer: (a) If the numerator is smaller than the denominator, then the fraction will be less than  .

(b) If the numerator is equal to the denominator, then the fraction will be equal to  .

Q3 Fill up using one of these: ‘  ’, ‘  ’ or ‘  ’

(a)

(b)

(c)

(d)

(e)

(b)

(c)

(d)

(e)

## NCERT solutions for class 6 maths chapter 7 Fractions Exercise: 7.2

Q1 (a) Draw number lines and locate the points on them :

Answer: The number line is given below:-

Q1 (b) Draw number lines and locate the points on them :

Answer: The number line is shown below with the required points marked.

Q1 (c) Draw number lines and locate the points on them :

Answer: The number line locating the given fraction is shown below:-

Q2 Express the following as mixed fractions :

(a)

(b)

(c)

(d)

(e)

(f)

(b)

(c)

(d)

(e)

(f)

Q3 Express the following as improper fractions :

(a)

(b)

(c)

(d)

(e)

(f)

Answer: The improper fractions of the mixed fractions are given below :-

(a)

(b)

(c)

(d)

(e)

(f)

## NCERT Solutions for Class 6 Maths Topic: Simplest Form of a Fraction

Q1 Write the simplest form of :

(i)

(ii)

(iii)

(iv)

(v)

(ii)

(iii)

(iv)

(v)

Q2 Is  in its simplest form?

Answer: Yes,  is in its simplest form because 49 and 64 has no common divisor.

## NCERT Solutions for Class 6 Maths Topic: Equivalent Fractions

Q1 Are  and  ;  and  ;  and  and equivalent? Give reason

Answer:  and  ;  and  are not equivalent because

and

but

Q2 Give example of four equivalent fractions.

Answer: Four example of equivalent fractions are :

Q3 Identify the fractions in each. Are these fractions equivalent?

(i)  (ii)  (iii)  (iv)

all fractions in it simplest form is

So all fractions are equivalent

Q1 Find five equivalent fractions of each of the following:

(i)

(ii)

(iii)

(iv)

(ii)

(iii)

(iv)

## NCERT Solutions for Class 6 Maths Exercise: 7.3

Q1 Write the fractions. Are all these fractions equivalent?

Answer: In the case of (a), we have:-

(i)

(ii)

(iii)

(iv)

Hence all fractions are equal in this case.

In the case of (b), we have:-

(i)

(ii)

(iii)

(iv)

(v)

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

Answer: The fractions of each are given below :-

(a)

(b)

(c)

(d)

(e)

Similarly,

(i)

(ii)

(iii)

(iv)

(v)

Q3 (a) Replace  in each of the following by the correct number :

Answer: The correct number is 28.

Thus  .

Q3 (b) Replace  in each of the following by the correct number :

Q3 (c) Replace  in each of the following by the correct number :

Answer: The required value is 12.

Q3 (d) Replace in each of the following by the correct number :

Answer: The required value is 20.

Q3 (e) Replace  in each of the following by the correct number :

Answer: The correct number is  .

Multiplying numerator and denomenator by  .

We have :-

Hence

Q4 Find the equivalent fraction of  having

(a) denominator

(b) numerator

(c) denominator

(d) numerator

Answer: (a) Multiply numerator and denominator by 4, we have :

(b) Multiply numerator and denominator by 3, we have :

(c) Multiply numerator and denominator by 6, we have :

(d) Multiply numerator and denominator by 9, we have :

Q5 Find the equivalent fraction of  with

(a) numerator

(b) denominator

Answer: The required equivalent fractions are given below :-

(a) Divide both numerator and denomenator by 4.

(b) Divide both numerator and denomenator by 12.

Q6 (a) Check whether the given fractions are equivalent :

Answer: Multiply both numerator and denominator by 6.

Q6 (b) Check whether the given fractions are equivalent :

Multiply both numerator and denominator by 4, we get :

Q6 (c) Check whether the given fractions are equivalent :

Answer: Multiply both numerator and denominator by  , we get :

Hence these two fractions are not the same.

Q7 Reduce the following fractions to simplest form :

(a)

(b)

(c)

(d)

(e)

(b)

(c)

(d)

(e)

Q8 Ramesh had  pencils, Sheelu had  pencils and Jamaal had  pencils. After  months, Ramesh used up  pencils, Sheelu used up  pencils and Jamaal used up  pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Answer: The fraction of pencils used by Ramesh is:-

The fraction of pencils used by Sheelu is:-

The fraction of pencils used by Jamaal is:-

Thus, the fractions of pencils used by each are the same.

Q9 Match the equivalent fractions and write two more for each.

(i)  (a)

(ii)  (b)

(iii)  (c)

(iv)  (d)

(v)  (e)

(ii)

(iii)

(iv)

(v)

## NCERT Solutions for Class 6 Maths Topic: Comparing Fractions

Q1 You get one-fifth of a bottle of juice and your sister gets one-third of the same size of a bottle of juice. Who gets more?

Answer: My sister gets more because

## NCERT Solutions for Class Maths Topic: Comparing Like Fractions

Q1 Which is the larger fraction?

(i)  or

(ii)  or

(iii)  or

Answer: The fractions are shown below using greater than or less than sign

(i)

(ii)

(iii)

Q2 Write these in ascending and also in descending order.

(a)

(b)

(c)

(b)

(c)

## NCERT class 6 maths chapter 7 Fractions Topic: Arrangement of Fractions

Q1 (1) Arrange the following in ascending and descending order :

and

Q1 (b) Arrange the following in ascending and descending order :

Answer: The following in ascending and descending order are :

(b)

Q1 (c) Arrange the following in ascending and descending order :

Write 3 more similar examples and arrange them in ascending and descending order.

Answer: The following in ascending and descending order are:

(i)

and

(ii)

and

(iii)

and

## NCERT solutions for class 6 maths chapter 7 Fractions Exercise: 7.4

Q1 Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign  between the fractions:

(c) Show  on the number line. Put appropriate signs between the fractions given

(b)

(c)

From the above number line we can compare the given numbers easily.

Q2 Compare the fractions and put an appropriate sign.

(a)

(b)

(c)

(d)

Answer: The comparison is given below :-

(a)

(b)

(c)

(d)

Q3 Make five more such pairs and put appropriate signs.

Answer: The five pairs can be :-

,

Q4 (a) Look at the figures and write  between the given pairs of fractions.

(a)

Answer: With the help of given diagram :

Thus

Q4 (b) Look at the figures and write  between the given pairs of fractions.

(b)

Answer: From the diagram it is cleat that :

Q4 (c) Look at the figures and write  between the given pairs of fractions.

(c)

Answer: From the given diagram, we can clearly say that :-

Q4 (d) Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(d)

Answer: From the diagram it is clear that :-

Q5 How quickly can you do this? Fill appropriate sign.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

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)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

( j)

(k)

(l)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

Q7 (a) Find answers to the following. Write and indicate how you solved them.

Is  equal to

Multiply numerator and denomenator by  .

We have :

Hence

Q7 (b) Find answers to the following. Write and indicate how you solved them.

Is  equal to  ?

Q7 (c) Find answers to the following. Write and indicate how you solved them.

Is  equal to

By multiplying numerator and denominator by 5, we get :

Q7 (d) Find answers to the following. Write and indicate how you solved them.

Is  equal to  ?

Multiply both numerator and denomenator by 2, we get :-

Q8 Ila read  pages of a book containing  pages. Lalita read  of the same book. Who read less?

So we can compare the fraction now:-

Q9 Rafiq exercised for  of an hour, while Rohit exercised for  of an hour. Who exercised for a longer time?

Answer: Who exercised for a longer time can be found by comparing the fraction of their work time.

Hence Rohit exercised for a longer time.

Q10 In a class A of  students,  passed with  or more marks; in another class B of  students,  passed with  or more marks. In which class was a greater fraction of students getting with  or more marks?

Answer: In class A, the fraction of students passed with  or above marks :

And, in class B, the fraction is :

Hence the required fraction is same in both the classes.

## NCERT class 6 maths chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 My mother divided an apple into  equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?

Answer: mother gave to me  part

mother gave to my brother  part

She gave both off us

part

Q2 Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one-fourth of the total stones in it and her brother also picked up one-fourth of the stones. What fraction of the stones did both pick up together?

brother picked up the stones

The total fraction of the stones they both pick up together

of total stones.

Q3 Sohan was putting covers on his note books. He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?

Answer: He put covers on Monday=

He put the cover on Tuesday =

and the remaining on Wednesday.

Thus, the fraction of the covers he put on Wednesday =

## NCERT class 6 maths chapter 7 Fractions Topic: Adding or Substracting like Fractions

Q1 Find the difference between  and  .

Answer: The difference between  and  is given by

Q2 Mother made a gud patti in a round shape. She divided it into  parts. Seema ate one piece from it. If I eat another piece then how much would be left?

I eat =

Total part eaten is

The left part would be

Q3 My elder sister divided the watermelon into  parts. I ate  out of them. My friend ate  . How much did we eat between us? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?

My friend ate =

we both eat

the watermelon more I eat than my friend is

The portion of the watermelon remained

## NCERT solutions for class 6 maths chapter 7 Fractions Exercise: 7.5

Q1 Write these fractions appropriately as additions or subtractions :

case (b) - Subtraction

Q2 Solve :

(a)

(b)

(c)

(d)

(e)

(f)

(g)

( h)

(i)

(b)

(c)

(d)

(e)

(f)

(g)

( h)

(i)

Q3 Shubham painted  of the wall space in his room. His sister Madhavi helped and painted  of the wall space. How much did they paint together?

Answer: Total wall painted = Wall painted by Subham + Wall pained by Madhavi

Hence the whole wall is painted by them.

Q4 Fill in the missing fractions.

(a)

(b)

(c)

(d)

or

(b)

or

(c)

(d)

or

Q5 Javed was given  of a basket of oranges. What fraction of oranges was left in the basket?

Thus the fraction of oranges left is :

## NCERT class 6 maths chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q2 Subtract  from  .

Answer: Subtraction of  from  is given by

## NCERT solutions for class 6 maths chapter 7 Fractions Exercise: 7.6

Q1 Solve

(a)  (b)  (c)

(d)  (e)  (f)

(b)

(c)

(d)

(e)

(f)

Q1 Solve

(g)  (h)  (i)

(j)  (k)  (l)

(m)  (n)

(h)

(i)

(j)

(k)

(l) \

(m)

(n)

Q2 Sarita bought  metre of ribbon and Lalita  metre of ribbon. What is the total length of the ribbon they bought?

Answer: The total length of ribbon is given :-

Thus total length of ribbon is  .

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.

Answer: Total amount of cake given to both = Cake given to Naina + Cake given to Najma

Q4 Fill in the boxes :

(a)

(b)

(c)

(b)  :-

(c)  :-

Answer: The required table is shown below:-

Answer: The required box is given below :-

Q6 A piece of wire  metre long broke into two pieces. One piece was  metre long. How long is the other piece?

Answer: Let the length of another piece of wire be x.

Thus,

Hence the length of other part is  .

Q7 Nandini’s house is  from her school. She walked some distance and then took a bus for  to reach the school. How far did she walk?

Answer: The distance Nandini walked is given by :-

Hence she walked  .

Q8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is  full and Samuel’s shelf is  full. Whose bookshelf is more full? By what fraction?

Answer: If we compare the bookshelves of both, we obtain that :

Also,

Hence the bookshelf of Asha is more full and by  fraction.

Q9 Jaidev takes  minutes to walk across the school ground. Rahul takes  minutes to do the same. Who takes less time and by what fraction?

Answer: Firstly, let us convert the time taken by Jaidev in the improper fraction from mixed fraction.

Now, comparing both, we have :

Also,

Hence Rahul takes less time as compared to Jaidev by  a fraction.

Chapter No. Chapter Name
Chapter 1 NCERT Solutions for class 6 maths chapter 1 Knowing Our Numbers
Chapter 2 NCERT solutions for class 6 maths chapter 2 Whole Numbers
Chapter 3 NCERT solutions for class 6 maths chapter 3 Playing with Numbers
Chapter 4 NCERT Solutions for class 6 maths chapter 4 Basic Geometrical Ideas
Chapter 5 NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes
Chapter 6 NCERT solutions for class 6 maths chapter 6 Integers
Chapter 7 NCERT Solutions for class 6 maths chapter 7 Fractions
Chapter 8 NCERT solutions for class 6 maths chapter 8 Decimals
Chapter 9 NCERT solutions for class 6 maths chapter 9 Data Handling
Chapter 10 NCERT solutions for class 6 maths chapter 10 Mensuration
Chapter 11 NCERT Solutions for class 6 maths chapter 11 Algebra
Chapter 12 NCERT solutions for class 6 maths chapter 12 Ratio and Proportion
Chapter 13 NCERT solutions for class 6 maths chapter 13 Symmetry
Chapter 14 NCERT Solutions for class 6 maths chapter 14 Practical Geometry

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