 A fraction is a number representing a part of a whole.
Students will be made familiar with the different types of fractions in this chapter:
1. Proper Fractions: Numerator is less than the denominator.
2. Improper Fractions: Numerator is greater than the denominator
3. Mixed Fractions: An improper fraction can be written as a combination of a whole and a part.
4. Like Fractions: Fractions with same denominator
5. Unlike Fractions: Fractions with different denominator
Other than these, the concept of equivalent fractions is explained which is an important topic.
 To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator of the given fraction by the same number.
 To find an equivalent fraction, we may divide both the numerator and the denominator by the same number.
 A fraction is said to be in the simplest form if its numerator and denominator have no common factor except 1.
The addition and subtraction of fractions are explained with adequate examples and is explained under different subsections:
 Adding or subtracting like fractions
 Adding and subtracting fractions
Page No 135:
Question 1:
Write the fraction representing the shaded portion.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 


(vii) 
(viii) 
(ix) 
(x) 
Answer:
(i) The given figure represents 2 shaded parts out of 4 equal parts.
Hence,
(ii) The given figure represents 8 shaded parts out of 9 equal parts.
Hence,
(iii) The given figure represents 4 shaded parts out of 8 equal parts.
Hence,
(iv) The given figure represents 1 shaded part out of 4 equal parts.
Hence,
(v) The given figure represents 3 shaded parts out of 7 equal parts.
Hence,
(vi) The given figure represents 3 shaded parts out of 12 equal parts.
Hence,
(vii) The given figure represents 10 shaded parts out of 10 equal parts.
Hence,
(viii) The given figure represents 4 shaded parts out of 9 equal parts.
Hence,
(ix) The given figure represents 4 shaded parts out of 8 equal parts.
Hence,
(x) The given figure represents 1 shaded part out of 2 equal parts.
Hence,
Page No 135:
Question 2:
Colour the part according to the given fraction.
(i) 
(ii) 
(iii) 


(iv) 
(v) 
Answer:
(i)
(ii)
(iii)
(iv)
(v)
Page No 136:
Question 3:
Identify the error if any.
Answer:
The given figures do not represent the fractions as here each shape is not divided in equal parts.
Video Solution for knowing our numbers (Page: 136 , Q.No.: 3)
NCERT Solution for Class 6 math  knowing our numbers 136 , Question 3
Page No 136:
Question 4:
What fraction of a day is 8 hours?
Answer:
There are 24 hours in a day. Therefore, 8 hours of a day represent.
Page No 136:
Question 5:
What fraction of an hour is 40 minutes?
Answer:
There are 60 minutes in an hour. Therefore, 40 minutes of an hour represent
.
Page No 136:
Question 6:
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.
(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?
Answer:
(a) Arya will divide each sandwich in three equal parts. Then, he will
give one part of each sandwich to each one of them.
(b) Each boy will receive part of each sandwich.
Video Solution for knowing our numbers (Page: 136 , Q.No.: 6)
NCERT Solution for Class 6 math  knowing our numbers 136 , Question 6
Page No 136:
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?
Answer:
Dress dyed so far = 20
Total dresses = 30
Fraction =
Page No 136:
Question 8:
Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Answer:
Natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Prime numbers among these are 2, 3, 5, 7, and 11.
Therefore, out of 11 numbers, 5 are prime numbers. It represents a fraction.
Page No 136:
Question 9:
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Answer:
Natural numbers from 102 to 113 are 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
Among these numbers, the prime numbers are 103, 107, 109, and 113.
Therefore, out of 12 numbers, 4 are prime numbers. It represents a fraction
Page No 136:
Question 10:
What fractions of these circles have X’s in them?
Answer:
Thereare 4 circles, out of 8, having X’s in them. Therefore, it represents a
fraction .
Video Solution for knowing our numbers (Page: 136 , Q.No.: 10)
NCERT Solution for Class 6 math  knowing our numbers 136 , Question 10
Page No 136:
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?
Answer:
Total CDs Kristin had on her birthday = 3 + 5 = 8
Out of 8 CDs, she bought 3 CDs and also got 5 CDs as gifts. Therefore, she bought and received CDs as gifts in a fraction of respectively.
Page No 141:
Question 1:
Draw number lines and locate the points on them:
(a) (b) (c)
Answer:
(a)
(b)
(c)
Page No 141:
Question 2:
Express the following as mixed fractions:
(a) (b) (c)
(d) (e) (f)
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
Page No 141:
Question 3:
Express the following as improper fractions:
(a) (b) (c)
(d) (e) (f)
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
Page No 146:
Question 1:
Write the fractions. Are all these fractions equivalent?
(a)
(b)
Answer:
(a) In the given circles, 1 out of 2, 2 out of 4, 3 out of 6,
and 4 out of 8 equal parts are shaded respectively. Therefore, these circles represent
Also, all these fractions are equivalent.
(b)
In the given rectangles, 4 out of 12, 3 out of 9, 2 out of 6, 1 out of 3, and 6 out of 15 equal parts (i.e., circles) are shaded respectively. Therefore, these rectangles represent
No, not all of these fractions are equivalent.
Page No 146:
Question 2:
Write the fractions and pair up the equivalent fractions from each row.
Answer:
(a) Here, 1 part is shaded out of 2 equal parts (i.e., rectangle). Hence, this
figure represents a fraction.
(b) Here, 4 parts are shaded out of 6 equal parts (i.e., rectangle). Hence,
this figure represents a fraction
(c) Here, 3 parts are shaded out of 9 equal parts (i.e., squares). Hence, this
figure represents a fraction
(d) Here, 2 parts are shaded out of 8 equal parts (i.e., rectangle). Hence,
this figure represents a fraction
(e) Here, 3 parts are shaded out of 4 equal parts (i.e., squares). Hence, this
figure represents a fraction .
(i) Here, 6 parts are shaded out of 18 equal parts (i.e., triangles). Hence, this figure represents a fraction
(ii) Here, 4 parts are shaded out of 8 equal parts (i.e., rectangles). Hence, this figure represents a fraction
(iii) Here, 12 parts are shaded out of 16 equal parts (i.e., squares). Hence, this figure represents a fraction
(iv) Here, 8 parts are shaded out of 12 equal parts (i.e., rectangles). Hence, this figure represents a fraction
(v) Here, 4 parts are shaded out of 16 equal parts (i.e., triangles). Hence, this figure represents a fraction
Now, these figures can be matched correctly as
(a) (ii), (b) (iv), (c) (i), (d) (v), (e) (iii)
Page No 147:
Question 3:
Replace &mnSq2 in each of the following by the correct number:
(a) (b)
(c) (d)
(e)
Answer:
(a)
Hence, &mnSq2 can be replaced by 28.
(b)
Hence, &mnSq2 can be replaced by 16.
(c)
Hence, &mnSq2 can be replaced by 12.
(d)
Hence, &mnSq2 can be replaced by 20.
(e)
Hence, &mnSq2 can be replaced by 3.
Page No 147:
Question 4:
Find the equivalent fraction of having
(a) denominator 20 (b) numerator 9
(c) denominator 30 (d) numerator 27
Answer:
(a)
Hence, the required fraction is.
(b)
Hence, the required fraction is.
(c)
Hence, the required fraction is.
(d)
Hence, the required fraction is.
Page No 147:
Question 5:
Find the equivalent fraction of with
(a) numerator 9 (b) denominator 4
Answer:
(a)
Hence, the required fraction is.
(b)
Hence, the required fraction is.
Page No 147:
Question 6:
Check whether the given fractions are equivalent:
(a) (b)
(c)
Answer:
(a)
Clearly, both the fractions are equivalent.
(b)
Clearly, both the fractions are not equivalent.
(c)
Clearly, both the fractions are not equivalent.
Page No 147:
Question 7:
Reduce the following fractions to simplest form:
(a) (b)
(c) (d)
(e)
Answer:
(a)
(b)
(c)
(d)
(e)
Page No 147:
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 her/his pencils?
Answer:
Fraction used by Ramesh =
Fraction used by Sheelu =
Fraction used by Jamaal =
Yes, all of them used equal fraction of pencils i.e., .
Page No 147:
Question 9:
Match the equivalent fractions and write two more for each.
(i) (a) (iv) (d)
(ii) (b) (v) (e)
(iii) (c)
Answer:
(i)
Two more fractions are .
(ii)
Two more fractions are .
(iii)
Two more fractions are .
(iv)
Two more fractions are .
(v)
Two more fractions are .
Now, these can be matched as
(i) (d), (ii) (e), (iii) (a), (iv) (c), (v) (b)
Page No 152:
Question 1:
Write shaded portion as 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.
Answer:
(a)
Here, 1^{st} circle represents 3 shaded parts out of 8 equal parts. Therefore, it represents a fraction .
Here, 2nd circle represents 6 shaded parts out of 8 equal parts. Therefore, it represents a fraction .
Here, 3rd circle represents 4 shaded parts out of 8 equal parts. Therefore, it represents a fraction .
Here, 4^{th} circle represents 1 shaded part out of 8 equal parts. Therefore, it represents a fraction .
Now, these fractions may be arranged as
(b)
Here, 1^{st} square represents 8 shaded parts out of 9 equal parts. Therefore, it represents a fraction.
Here, 2nd square represents 4 shaded parts out of 9 equal parts. Therefore, it represents a fraction .
Here, 3rd square represents 3 shaded parts out of 9 equal parts. Therefore, it represents a fraction .
Here, 4th square represents 6 shaded parts out of 9 equal parts. Therefore, it represents a fraction .
Now, these fractions can be arranged as
(c) To represent the given fractions on number line, each unit length should be divided in 6 equal parts. Now, these fractions can be represented as
Page No 153:
Question 2:
Compare the fractions and put an appropriate sign.
(a) (b)
(c) (d)
Answer:
(a)
Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
(b)
As 4 < 7,
(c)
Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
(d)
Here, the numerators are same. Therefore, the fraction having lesser denominator will be greater.
Page No 153:
Question 3:
Make five more such pairs and put appropriate sign.
Answer:
(i)
Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
(ii)
Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
(iii)
Here, numerators are same. Therefore, the fraction having the lesser denominator will be greater.
(iv)
Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
(v)
Here, the numerators are same. Therefore, the fraction having the lesser denominator will be greater.
Page No 153:
Question 4:
Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.
(a)
(b)
(c)
(d)
(e)
Answer:
(a) Here, the numerators are same. Therefore, the fraction having the
lesser denominator will be greater.
Hence,
(b)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(c) Here, the numerators are same. Therefore, the fraction having the lesser denominator will be greater.
Hence,
(d) As ,
(e) Here, the numerators are same. Therefore, the fraction having the lesser denominator will be greater.
Hence,
Page No 153:
Question 5:
How quickly can you do this? Fill appropriate sign (‘<’, ‘=’, ‘>’)
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(k)
Answer:
(a) Here, the numerators are same. Therefore, the fraction having the
lesser denominator will be greater.
Hence,
(b)
Hence,
(c)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(d)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(e) Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
Hence,
(f) Here, the denominators are same. Therefore, the fraction having the greater numerator will be greater.
Hence,
(g)
Hence,
(h)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(i)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(j)
As the denominators of are same, the fraction having the greater numerator will be greater.
Hence,
(k)
Hence,
Page No 154:
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.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(k) (l)
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
There are 3 groups of equivalent fractions
(a), (e), (h), (j), (k)
(b), (f), (g)
(c), (d), (i), (l)
Page No 154:
Question 7:
Find answers to the following. Write and indicate how you solved them.
(a) ? (b) ?
(c) ? (d) ?
Answer:
(a)
Converting these into like fractions,
Therefore,
(b)
Converting these into like fractions,
(c)
Therefore,
(d)
Page No 154:
Question 8:
Ila read 25 pages of a book containing 100 pages. Lalita read of the same book. Who read less?
Answer:
Numbers of pages read by Lalita == 40
Number of pages read by Ila = 25
Hence, Ila has read less number of pages.
Video Solution for knowing our numbers (Page: 154 , Q.No.: 8)
NCERT Solution for Class 6 math  knowing our numbers 154 , Question 8
Page No 154:
Question 9:
Rafiq exercised for of an hour, while Rohit exercised for of an hour.
Who exercised for a longer time?
Answer:
Rafiq exercised for and Rohit exercised for
Converting these into like fractions,
Hence, Rohit exercised for a longer time.
Page No 154:
Question 10:
In a 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?
Answer:
Fraction of students of class A who passed in Ist class =
Fraction of students of class B who passed in Ist class =
From both classes, an equal fraction of students passed in first class.
Video Solution for knowing our numbers (Page: 154 , Q.No.: 10)
NCERT Solution for Class 6 math  knowing our numbers 154 , Question 10
Page No 157:
Question 1:
Write these fractions appropriately as additions or subtractions:
(a)
(b)
(c)
Answer:
(a) Here, it can be observed that 1^{st}, 2^{nd}, and 3^{rd} rectangles are representing 1, 2, and 3 shaded parts out of 5 equal parts respectively. Clearly, the fraction represented by 3^{rd} rectangle is the sum of the fractions represented by 1^{st} and 2^{nd} rectangles.
Hence,
(b) Here, it can be observed that 1^{st}, 2^{nd}, and 3^{rd} circles are representing 5, 3, and 2 shaded parts out of 5 equal parts respectively. Clearly, the fraction represented by 3^{rd} circle is the difference between the fractions represented by 1^{st} and 2^{nd} circles.
Hence,
(c) Here, it can be observed that 1^{st}, 2^{nd}, and 3^{rd} rectangles are representing 2, 3, and 5 shaded parts out of 6 equal parts respectively. Clearly, the fraction represented by 3^{rd} rectangle is the sum of the fractions represented by 1^{st} and 2^{nd} rectangles.
Hence,
Page No 158:
Question 2:
Solve:
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Page No 158:
Question 3:
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:
Space painted by Shubham = of the room
Space painted by Madhavi = of the room
Hence, together they painted =of the room
= 1 = the complete wall
Page No 158:
Question 4:
Fill in the missing fractions.
(a) (b)
(c) (d)
Answer:
(a)
(b)
(c)
(d)
Page No 158:
Question 5:
Javed was given of a basket of oranges. What fraction of oranges was left in the basket?
Answer:
Fractions given to Javed =
Fraction left in the basket = =
Page No 160:
Question 1:
Solve
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(k) (l)
(m) (n)
Answer:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
Page No 160:
Question 2:
Sarita bought metre of ribbon and Lalita metre of ribbon. What is the total length of the ribbon they bought?
Answer:
Length of ribbon bought by Sarita =
Length of ribbon bought by Lalita =
Total length of ribbon bought by them =
Page No 160:
Question 3:
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:
Fraction Naina got =
Fraction Najma got =
Page No 161:
Question 4:
Fill in the boxes: (a) (b) (c)
Answer:
(a)
(b)
(c)
Page No 161:
Question 5:
Complete the additionsubtraction box.
(a)
(b)
Answer:
(a)
Hence, the given box can be completed as
(b)
Hence, the given box can be completed as
Page No 161:
Question 6:
A piece of wire metre long broke into two pieces. One piece was metre long. How long is the other piece?
Answer:
Length of one piece =
The length of the other piece of wire will be the difference of the lengths of the original wire and this piece of wire.
Hence, length of the other piece of wire =
Page No 161:
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?
Answer:
Distance walked by Nandini = Total distance − Distance for which she took the bus
Page No 161:
Question 8:
Asha and Samuel have bookshelves of the same size partly filled with books.
Asha’s shelf is th full and Samuel’s shelf is th full. Whose bookshelf is more full? By what fraction?
Answer:
Fraction of Asha’s shelf =
Fraction of Samuel’s shelf =
Converting these into like fractions,
Clearly, Asha’s bookshelf is more full.
Difference =
Page No 161:
Question 9:
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:
Time taken by Jaidev = minutes = min
Time taken by Rahul = min
Converting these into like fractions,
Hence, Rahul takes lesser time.
Difference =
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