Solution of Class 6 Fraction Mathematics (2023-24)

                                   Fractions Class 6 Ex 7.1

Question 1.
Write the fraction representing the shaded portion.

Solution:
(i) Total number of parts = 4
Number of shaded parts = 2
∴ Fraction = 

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

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

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

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

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

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

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

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

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

Question 2.
Colour the part according to the given fraction.

Solution:

Question 3.
Identify the error, if any.

Solution:
(a) Since the shaded part is not half.
∴ This is not .

(b) Since, the parts are not equal.
∴ Shaded part is not  .

(c) Since, the part are not equal.
∴ Shaded part is not .

Question 4.
What fraction of a day is 8 hours?
Solution:
Since, a day has 24 hours and we have 8 hours,
∴ Required fraction = 

Question 5.
What fraction of a hour is 40 minutes?
Solution:
Since I hours = 60 minutes
∴ Fraction of 40 minutes = 

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?
Solution:
(a) Arya has divided his sandwich into three equal parts.
So, each of them will get one part.
(b) Each one of them will receive  part.
∴ Required fraction = 

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:
Total number of dresses to be dyed = 30
Number of dresses finished = 20
∴ Required fraction =  = 

Question 8.
Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Solution:
Natural numbers between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
Number of given natural numbers = 11
Number of prime numbers = 5
∴ Required fraction = 

Question 9.
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Solution:
Natural numbers from 102 to 113 are;
102,103,104,105,106, 107,108, 109,110, 111, 112,113
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113
∴ Number of prime numbers = 4
∴ Required fraction =  = 

Question 10.
What fraction of these circles have X’s in them?

Solution:
Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction =  = 

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 by her from the market = 3
Number of CD’s received as gifts = 5
∴ Total number of CDs = 3 + 5 = 8
∴ Fraction of CD (bought) =  and the fraction of CDs (gifted) = 

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                                   Fractions Class 6 Ex 7.2

Question 1.
Draw number lines and locate the points on them.

Solution:

We have divided the number line from 0 to 1 into four equal parts.
C represents  i,e., 
B represents 
D represents 
and E represents  , i.e., 1.

We have divided the number line from 0 to 1 into eight equal parts.
B represents 
C represents 
D represents 
and H represents 

From the above number line, we have
C represents 
D represents 
E represents 
and I represents 

Question 2.
Express the following as mixed fractions:

Solution:

Question 3.
Express the following as improper fractions:

Solution:

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                                 Fractions Class 6 Ex 7.3

Question 1.
Write the fractions. Are all these fractions equivalent?

Solution:

Since all the fractions in their simplest form are not equal.
∴ They are not equivalent fractions.

 Question 2.
Write the fractions and pair up the equivalent fractions from each row.


Solution:

The following pairs fractions:represent the equivalent fractions.
(a) and (ii) = 
(b) and (iv) = 
(c) and (i) = 
(d) and (v) = 
(e) and (iii) = 

Question 3.
Replace  in each of the following by the correct number:

Solution:

Question 4.
Find the equivalent fraction of  having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27
Solution:
(a) Here, we require denominator 20.
Let N be the numerator of the fractions.

∴ The required fraction is 

(b) Here, we required numerator 9.
Let D be the denominator of the fraction.

∴ The required fraction is .

(c) Here, we required denominator 30.
Let N be the numerator of the fraction.

∴ The required fraction is .

(d) Here, we required numerator 27.
Let D be the denominator of the fraction.

∴ The required fraction is .

Question 5.
Find the equivalent fraction of  with
(a) numerator 9
(b) denominator 4
Solution:
(a) Given that numerator = 9

So, the equivalent fraction is .

(b) Given that denominator = 4
∴  =  ⇒ N x 48 = 4 x 36
⇒ N =  = 3
So, the equivalent fraction is  .

Question 6.
Check whether the given fractions are equivalent:

Solution:
(a)  and 
We have 5 x 54 = 270
and 9 x 30 = 270
Here 5 x 54 = 9 x 30
∴  and  are equivalent fractions.

(b)  and 
We have 3 x 50 = 150
and 10 x 12 = 120
Here 3 x 50 ≠ 10 x 12
∴  and  are not equivalent fractions.

(c)  and 
We have 7 x 11 = 77 and 5 x 13 = 65
Here 7 x 11 ≠ 5 x 13
∴  and  are not equivalent fractions.

Question 7.
Reduce the following fractions to simplest form:

Solution:

Question 8.
Ramesh had 28 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.
Solution:
Ramesh used up 10 pencils out of 20 pencils.

Sheelu used up 25 pencils out of 50 pencils.

Jamaal used up 40 pencils out of 80 pencils.

Yes, each has used up an equal fractions, i.e., .

Question 9.
Match the equivalent fractions and write two more for each.

Solution:


Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are

Two additional examples of equivalent fractions are


Two additional examples of equivalent fractions are

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                                Fractions Class 6 Ex 7.4

Question 1.
Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<‘, ‘=’, ‘>’ between the fractions.

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

Solution:
(a) Total number of divisions = 8
(i) Number of shaded parts = 3
∴ Fraction = 

(ii) Total number of divisions = 8
Number of shaded parts = 6
∴ Fraction = 

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

(iv) Total number of divisions = 8
Number of shaded part = 1
∴ Fraction = 
Now the fractions are:
, ,  and  with same denominator.

(b)(i) Total number of divisions = 9
Number of shaded parts = 8
∴ Fraction = 
(ii) Total number of divisions = 9
Number of shaded parts = 4
∴ Fraction = 
(iii) Total number of divisions = 9
Number of shaded parts = 3
∴ Fraction = 
(iv) Total number of divisions = 9
Number of shaded parts = 6
∴ Fraction = 
∴ Fractions are , , ,  with same denominator.

Question 2.
Compare the fractions and put an appropriate sign.

Solution:

Here, denominators of the two fractions are same and 3 < 5.

Here, numerators of the fractions are same and 7 > 4.

Here, denominators of the two fractions are same and 4 < 5.

Here, numerators of the two fractions are same and 5 < 7.

Question 3.
Make five more such pairs and put appropriate signs.
Solution:

Question 4.
Look at the figures and write ’<’, or ’>’ ’=’ between the given pairs of fractions.

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

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

Question 5.
How quickly can you do this? Fill appropriate sign. ‘<‘, ‘=’, ‘>’.


Solution:



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.

Solution:

Now grouping the above fractions into equivalent fractions, we have

Question 7.
Find answers to the following. Write and indicate how you solved them.

Solution:

By cross-multiplying, we get
5 x 5 = 25 and 4 x 9 = 36
Since 25 ≠ 36

By cross-multiplying, we get
9 x 9 = 81 and 16 x 5 =80
Since 81 ≠ 80

By cross-multiplying, we get
4 x 20 = 80 and 5 x 16 = 80
Since 80 = 80

By cross-multiplying, we get
1 x 30 = 30 and 4 x 15 = 60

Question 8.
Ila read 25 pages of a book containing 100 pages.
Lalita read  of the same book. Who read less?
Solution:
Ila reads 25 pages out of 100 pages.

Lalita reads  of the same book.
Comparing  and  , we get
1 x 5 = 5 and 2 x 4 = 8
Since 5 < 8
∴  < 
Hence Ila reads less pages.

Question 9.
Rafiq exercised for  of an hour, while Rohit exercised for  of an hour. Who exercised for a longer time?
Solution:
Rafiq exercised for  of an hour.
Rohit exercised for  of an hour.
Comparing  and  , we get
3 x 4 = 12 and 3 x 6 = 18
Since 12 < 18
∴  > 
Hence Rohit exercised for longer time.

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?
Solution:
In class A, 20 students passed in first class out of 25 students.
∴ Fraction of students getting first class

In class B, 24 students passed in first class out of 30 students.
∴ Fraction of students getting first class

Comparing the two fractions, we get  = 
Hence, both the class A and B have the same fractions.

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                             Fractions Class 6 Ex 7.5

Question 1.
Write these fractions appropriately as additions or subtractions.

Solution:
(a) The given figure represents the addition of

Thus the given diagrams can be represented as

(b) The given figure represents the difference between 1 and .

Thus, the given diagrams can be represented as

(c) The given figure represents addition of  and .

Thus, the given diagrams can be represented as

 Question 2.
Solve:

Solution:

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?
Solution:
Fraction of wall painted by Shubham = 
Fraction of wall painted by Madhavi = 
Fraction of wall painted by Shubham and Madhavi

Thus the fraction of wall painted by both = 1

 Question 4.
Fill in the missing fractions.

Solution:

 Question 5.
Javed was given  of a basket of oranges. What fraction of oranges was left in the basket?
Solution:
Fraction of basket of oranges = 
Fraction of basket as a whole can be taken as 1.
∴ Fraction of basket of oranges left

Thus, the required fraction =  .

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                                            Fractions Class 6 Ex 7.6

Question 1.
Solve


Solution:




Question 2.
Sarita bought  metre of ribbon and Lalita  metre of ribbon. What is the total length of the ribbon they bought?
Solution:
Length of ribbon bought by Sarita =  metre
Length of ribbon bought by Lalita =  metre
∴ Length of ribbon bought by Sarita and Lalita

Hence, the required length =  metre

Question 3.
Naina was given 1 piece of cake and Najma was given 1 piece of cake. Find the total amount of cake was given to both of them.
Solution:
Piece of cake given to Naina = 1
Piece of cake given to Najma = 1
Piece of cake given to Naina and Najma

Hence the total amount of piece given to both = 2.

Question 4.
Fill in the boxes:

Solution:

Here, missing number is  more than  .


Here, missing number is  more than  .

Here, missing number is  less than .

Question 5.
Complete the addition-subtraction box.

Solution:

Thus the box may be completed as follows:

 Question 6.
A piece of wire  metre long broke into two pieces. One piece was  metre long. How long is the other piece?
Solution:
Total length of the wire =  metre
Length of one piece of wire =  metre
∴ Length of the other piece =  – 
LCM of 8 and 4 = 8

Hence, the length of the other piece =  metre.

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:
Total distance from house to school =  km.
Distance travelled by Nandini by bus =  km
∴ Distance travelled by her on foot

Hence, the distance travelled by her on foot = km.

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?
Solution:
Asha’s shelf is  th full
and Samuel’s shelf is  th full
Comparing  and 
LCM of 6 and 5 = 30

Hence, Asha’s shelf is full more than Samuel’s shelf.

Hence,  th fraction is more full of Asha’s shelf.

Question 9.
Jaidev takes 2 minutes to walk across the school ground. Rahul takes  minutes to do the same. Who takes less time and by what fraction?
Solution:
Jaidev takes 2 minutes 5
Rahul takes 2 minutes
Comparing 2 minutes and  minutes


So, the time take to cover the same distance by Rahul is less than that of Jaidev.

Hence, Rahul takes  minutes less to across the school ground.