Fractions (Mathematics) Class 6 - NCERT Questions

Q 1.

Write the fraction representing the shaded portion.
(I)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)

SOLUTION:

(I)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)

Q 2.

Colour the part according to the given fraction.
(I)
(ii)
(iii)
(iv)
(v)

SOLUTION:

(I)
(ii)
(iii)
(iv)
(v)

Q 3.

Identify the error, if any.

SOLUTION:

Shaded parts do not represent the given fractions, because all the figures are not equally divided. For making fractions, it is necessary that figure is to be divided in equal parts.

Q 4.

What fraction of a day is 8 hours?

SOLUTION:

Since, 1 day = 24 hours
Therefore, the fraction of 8 hours =

Q 5.

What fraction of an hour is 40 minutes?

SOLUTION:

Since, 1 hour = 60 minutes.
Therefore, the fraction of 40 minutes =

Q 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 will divide each sandwich into three equal parts and give one part of each sandwich to each one of them.
(B) Each boy will get part of a sandwich.

Q 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 = 30
she finished = 20
Fraction of finished work

Q 8.

Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

SOLUTION:

Natural numbers from 2 to 12 :
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Prime numbers from 2 to 12 :
2, 3, 5, 7, 11
Hence, fraction of prime numbers =

Q 9.

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

SOLUTION:

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 =

Q 10.

What fraction of these circles have X's in them?

SOLUTION:

Total number of circles = 8
and number of circles having 'X' = 4
Hence, the required fraction =

Q 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:

Total number of CDs = 3 + 5 = 8
Number of CDs purchased = 3
Fraction of CDs purchased =
Fraction of CDs received as gifts =

Q 12.

Draw number lines and locate the points on them :
(A)
(B)
(C)

SOLUTION:

Q 13.

Express the following as mixed fractions :
(A)
(B)
(C)
(D)
(E)
(F)

SOLUTION:

Q 14.

Express the following as improper fractions :
(A)
(B)
(C)
(D)
(E)
(F)

SOLUTION:

Q 15.

Write the fractions. Are all these fractions equivalent?

SOLUTION:

Q 16.

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

SOLUTION:

(A)
(B)
(C)
(D)
(E)
(I)
(ii)
(iii)
(iv)
(v)
Pairs of equivalent fractions are:
(A), (ii); (B), (iv); (C), (I); (D), (v); (E), (iii)

Q 17.

Replace in each of the following by correct number :
(A)
(B)
(C)
(D)
(E)

SOLUTION:

Q 18.

Find the equivalent fraction of having
(A) denominator 20
(B) numerator 9
(C) denominator 30
(D) numerator 27

SOLUTION:

(B)
(C)
(D)

Q 19.

Find the equivalent fraction of with
(A) numerator 9
(B) denominator 4

SOLUTION:

(B)

Q 20.

Check whether the given fractions are equivalent :
(A)
(B)
(C)

SOLUTION:

Q 21.

Reduce the following fractions to simplest form :
(A)
(B)
(C)
(D)
(E)

SOLUTION:

Q 22.

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?

SOLUTION:

Ramesh : Total pencils = 20

Jamaal : Total pencils = 80

Since, all of them used half of their pencils, therefore, each has used up equal fraction of pencils.

Q 23.

Match the equivalent fractions and write two more for each.

SOLUTION:

Q 24.

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.

SOLUTION:

Q 25.

Compare the fractions and put an appropriate sign.
(A)
(B)
(C)
(D)

SOLUTION:

(A) are like fractions.
Also, numerator of is greater than numerator of
(B) are unlike fractions with same numerator. Also, denominator of is greater than denominator of
(C) are like fractions.
Also, numerator of is greater than numerator of
(D) are unlike fractions with same numerator. Also, denominator of is greater than denominator of

Q 26.

Make five more such pairs and put appropriate signs.

SOLUTION:

(A)
(B)
(C)
(D)
(E)

Q 27.

Look at the figures and write '<' , '>', '=' between the given pairs of fractions.

(A)
(B)
(C)
(D)
(E)
Make five more such problems and solve them with your friends.

SOLUTION:

(A)
(B)
(C)
(D)
(E)
Five more problems :
(A)
(B)
(C)
(D)
(E)
Above problems are solved as follows :
(A)
(B)
(C)
(D)
(E)

Q 28.

How quickly can you do this? Fill appropriate sign. ( '<', '=', '>')
(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)
(J)
(K)

SOLUTION:

are unlike fractions with same numerator. Also, denominator of is greater than denominator of .

(B) are unlike fractions with different numerator.

(C) are unlike fractions with different numerator.

(D) are unlike fractions with different numerators.

(E) are like fractions. Also, numerator of is greater than numerator of .

(F) are like fractions. Also, numerator of is greater than numerator of .

(G) are unlike fractions with different numerators.

(H) are unlike fractions with different numerator.

(I) are unlike fractions with different numerators.

(J) are unlike fractions with different numerators.

(K) are unlike fractions with different numerators.

Q 29.

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)

SOLUTION:

(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)
(J)
(K)
(L)
Equivalent groups :
I group : [(B), (F), (G)]
II group : [(A), (E), (H),(J),(K)]
III group : [(C), (D), (I),(L)]

Q 30.

Find answers to the following. Write and indicate how you solved them.
(A) Is
(B) Is
(C) Is
(D) Is

SOLUTION:

(A)
[∴ L.C.M. of 9 and 5 is 45]

(B)
[∴ L.C.M. of 16 and 9 is 144]

(C)
[∴ L.C.M. of 5 and 20 is 20]

(D)
[∴ L.C.M. of 15 and 30 is 30]

Q 31.

Ila read 25 pages of a book containing 100 pages. Lalita read of the same book. Who read less?

SOLUTION:

Ila read 25 pages out of 100 pages.
Fraction of reading the pages

Comparing Ila and Lalita pages

[∴ L.C.M. of 5 and 4 is 20]

Therefore, Ila read less.

Q 32.

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

SOLUTION:

Rafiq exercised of an hour.
Rohit exercised of an hour.
Therefore, Rohit exercised for a longer time.

Q 33.

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 passed in first class out of 25.
∴ Fraction of first class passed students

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

Hence, both classes have same fraction of student getting first class.

Q 34.

Write these fractions appropriately as additions or subtractions :
(A)
(B)
(C)

SOLUTION:

(A)
(B)
(C)

Q 35.

Solve :
(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)

SOLUTION:

(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)

Q 36.

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
Total painting by both of them

Therefore, they painted complete wall.

Q 37.

Fill in the missing fractions.
(A)
(B)
(C)
(D)

SOLUTION:

(A)
(B)
(C)
(D)

Q 38.

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

SOLUTION:

Consider the total number of oranges to be the whole portion or 1.
Fraction of oranges left

Thus, oranges was left in the basket.

Q 39.

Solve :
(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)
(J)
(K)
(L)
(m)
(n)

SOLUTION:

(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) L.C.M. of 7 and 3 is 21,

(E) L.C.M. of 5 and 6 is 30,

(F) L.C.M. of 5 and 3 is 15,

(G) L.C.M. of 4 and 3 is 12,

(H) L.C.M. of 6 and 3 is 6,

(I) L.C.M. of 3, 4 and 2 is 12,

(J) L.C.M. of 2, 3, and 6 is 6,

(K) L.C.M. of 3 and 3 is 3,

(L) L.C.M. of 3 and 4 is 12,

(m) L.C.M. of 5 and 5 is 5,

(n) L.C.M. of 3 and 2 is 6,

Q 40.

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

SOLUTION:

Ribbon bought by Sarita
And Ribbon bought by Lalita
Total length of ribbon
[∴ L.C.M. of 5 and 4 is 20]

Therefore, they bought of ribbon.

Q 41.

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.

SOLUTION:

Cake taken by Naina
And cake taken by Najma
Total cake taken

[∴ L.C.M. of 2 and 3 is 6]

Therefore, total amount of cake given to both of them

Q 42.

Fill in the boxes :
(A)
(B)
(C)

SOLUTION:

(A)
(B)
(C)

Q 43.

Complete the addition-subtraction box.
(A)
(B)

SOLUTION:

(A)
(B)

Q 44.

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 wire
Length of first part
Remaining part
[∴ L.C.M. of 8 and 4 is 8]

Therefore, the length of remaining part is

Q 45.

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 between school and house
Distance covered by bus
Remaining distance
[∴ L.C.M. of 10 and 2 is 10.]

Therefore, distance covered by walking is

Q 46.

Asha and Samuel have book shelves 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?