Class 6 Maths Notes for Fractions

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CLASS 6
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FRACTIONS
I – IMPORTANT BASIC CONCEPTS/RESULTS:-

1. A fraction is a number representing a part of a whole. This whole may be a single
object or a group of objects.
2. A fraction whose numerator is less than the denominator is called a Proper fraction;
otherwise it is called an improper fraction.
6 3 6 5
3. Numbers of the type 32 , 62 , 23 , 53 etc. are called mixed fractions.
4. An improper fraction can be converted into a mixed fraction and vice versa.
5. Fractions equivalent to a given fraction can be obtained by multiplying or dividing
its numerator and denominator by anon-zero number.
6. A fraction in which there is no common factor, except 1, in its numerator and
denominator is called a fraction in the simplest or lowest form.
7. Fractions with same denominators are called like fractions and if the denominators are
different, then they are called unlike fractions.
8. Fractions can be compared by converting them into like fractions and then arranging
them in ascending or descending order.
9. Addition (or subtraction) of like fractions can be done by adding(or subtracting) their
numerators.

II- EXAMPLES:-
Q1. 1. Writethefractionrepresentingtheshadedportion:

Q1. Solution:

We know that

Fraction of the shaded portion = Number of shaded parts/ Total number of parts

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(i) From the figure we know that (ii) From the figure we know that Total
Total number of parts = 3 number of parts = 15

Number of parts which are shaded = 2 So Number of parts which are shaded = 11 So we
we get get

Fraction of the shaded portion = 2/3 Fraction of the shaded portion = 11/15

(iv) From the figure we know that Total
(iii) From the figure we know that number of parts = 7
Total number of parts = 9 Number of
parts which are shaded = 8 So we get Number of parts which are shaded = 3 So we
get
Fraction of the shaded portion = 8/9
Fraction of the shaded portion = 3/7

(v) From the figure we know that (vi) From the figure we know that Total
Total number of parts = 9 number of parts = 4

Number of parts which are shaded = 4 So Number of parts which are shaded = 2 So we
we get get

Fraction of the shaded portion = 4/9 Fraction of the shaded portion = 2/4 = ½

(vii) From the figure we know that (viii) From the figure we know that Total
Total number of parts = 2 number of parts = 5

Number of parts which are shaded = 1 So Number of parts which are shaded = 1 So we
we get get

Fraction of the shaded portion = ½ Fraction of the shaded portion = 1/5

(ix) From the figure we know that
Total number of parts = 4

Number of parts which are shaded = 1 So
we get

Fraction of the shaded portion = ¼

A) MULTIPLE CHOICE QUESTIONS-

Q2. The points P,Q,R,S,T,U andV on theno. line are such that,US=SV =VR,andWT=TP
=PQ.

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1.The fraction represented by P 2.The fraction represented by U

(a) 6/5 (a) 3/5

(b) 9/5 (b) 2/5

(c ) 8/5 (c ) 4/5

(d) 7/5 (d) 1/5

Answer: (c) Answer: (d)

Q.3 1.The equivalent fraction of 3/5 with 2.The equivalent fraction of 3/5 with
denominator 20 is: numerator 9 is:

(a) 12/20 (b)20/12 (a) 15/9 (b) 9/11

(c ) 10/20 (d) 15/20 (c ) 9/15 (d) 9/5

Answer: (a) Answer: (c)

Q 4. 1.The simplest form of 48/60 is: 2. 20/3 can be written in mixed fraction as:
6 3
a) 32 (b) 62
(a) 5/4 (b) 4/5 (c) 8/10 ( d) 12/15 6 5
(c ) 23 (d) 53

Answer: (b)
Answer: (b)

Q5. 1. The sum of the fractions 1/18 & 1/18 2. The value of 12/15 – 7/15:
given by:
(a) 1/3 (b) 5/2

(c ) 5/1 (d) 1/5
(a) 1/18 (b) 1/9 (c) 2/36 (d) 36/18

Answer: (a)
Answer: (b)

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B) SHORT ANSWER TYPE QUESTIONS

Q6. What fraction of an hour is 20 minutes?

Solution: We know that Minutes in an hour = 60,

So 20 minutes of an hour = 20/ 60 = 1/3 Therefore, 1/3 of an hour is 20 minutes.

Answer: 1/3

Q7. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Solution: We know that natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12

Then prime numbers from 2 to 12 are 2, 3, 5, 7 and 11 ,So 5 numbers are prime among the 11 numbers
Therefore, 5/11 of them are prime numbers. Answer: 5/11

Q8. Represent 2/5 on a number line.

Solution: The fraction 2/5 is represented on a number line as given below:

Q9.Write each fraction. Arrange them in ascending and descending order using correct sign <, =, >
between the fractions:

Solution:

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C) LONG ANSWER TYPYE QUESTIONS-

Q10. Isha read 25 pages of a book containing 100 pages. Nagma read ½ of the same book. Who
read less?

Solution: No. of pages in the
book = 100 .
We know that
Fraction of book Isha read = (25/100) ÷ (25/25) = ¼ by dividing both numerator and denominator by
HCF of 25and 100
So the fraction of book Nagma read =½
By comparing¼ and½we get the LCM of 4 and2= 4
Now convert the fraction into equivalent fraction having
denominator as 4¼ ×1/1 and ½×2/2
¼<½

Hence, Isha read less.

Answer: Isha read less.

Q11. Savita bought 2/5 m of ribbon and Kavita ¾ m of the ribbon. What was the total length of the
ribbon they bought?

Solution:

Length of ribbon Savita bought = 2/5 m Length of ribbon Kavita bought = ¾ m

So the total length of ribbon they bought = 2/5 +
¾ We know that the LCMof5 and 4is 20
So we get
= [(2×4)/(5×4)] +[(3×5)/(4×5)]
On further calculation
= 8/20+15/20
We get
= (8 +15)/20= 23/20m
Hence,thetotallengthoftheribbontheyboughtis23/20m.
D) CASE STUDY BASED QUESTION-
Q12. Ravish had 20 pencils, Shikha had 50 pencils and Priya had 80 pencils. After 4 months, Ravish
used up10 pencils, Shikha used up 25 pencils and Priya used up 40 pencils.

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(i) What fraction did each use up? (ii) Check if each has used up an equal fraction of their pencils?

Solution: (i) Number of pencils Ravish had = 20
Number of pencils Ravish used =10
By dividing the numerator and denominator by HCF of 10
and 20 We get the fraction of pencils used=
(10÷10)/(20÷10)=1/2

Number of pencils Shikha had =50
Number of pencils used by Shikha = 25
By dividing the numerator and denominator by HCF of 25
and50Wegetthefraction of pencils used = (25÷25)/(50÷25) = ½

Number of pencils Priya had =
80NumberofpencilsusedbyPriya=40
By dividing the numerator and denominator by HCF of 40 and 80
We get the fraction of pencils used = (40÷40)/(80÷40)=1/2

(ii) Yes, each has used up an equal fraction of their pencils.

III- PRACTICE QUESTIONS-
(i) MCQ QUESTIONS:-

1) Which of the following is a proper fraction?
(a) 4/3 (b)3/4 (c)13/4 (d) 21/5

2) Which of the following is an improper fraction?
(a)1/2 (b)3/7 (c)7/3 (d) 3/15

3) Which of the following is a fraction equivalent of 2/3?
(a) 4/5 (b)8/6 (c) 10/25 (d) 10/15

4) A fraction equivalent to 3/5 is:
(a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these

5) Which of the following are like fractions?
(a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4 ,4/5, 6/7 (d) None of
these

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6) If 11/4 = 77/x, then x =?
(a) 28 (b) 77/28 (c)44 (d) 308

7) If 1/3 +1/2 + 1/x = 4, then x =?
(a) 5/18 (b) 6/19 (c) 18/5 (d) 24/11
8) What is the value of (a+b) / (a−b), If a/b=4?
(a) 3/5 (b) 5/3 (c) 4/5 (d) 5/4
9) If 45/60 is equivalent to 3/x, then x =
(a )5 (b) 4 (c) 6 (d) 20
10) The correct fraction in the box □ is □ – 5/8=1/4
(a) 6/8 (b) 7/8 (c) 1/2 (d) None of these

(ii) SHORT ANSWER QUESTIONS-

1) Mukesh has a box of 24pencils.Hegives half of them to Sunita. How many does
Sunita get? How many does Mukesh still have?

2) Represent 0/10, 1/10, 5/10 and 10/10 on a number line.
3) Convert each of the following into a mixed fraction: (i) 28/9 (ii) 226/15
1 5
4) Convert each of the following into an improper fraction: (i) 74(ii) 87

5) Replace ☐ in each of the following by the correct no: (i) 2/7 = 6/ ☐ (ii) 5/8 = 10/☐

6) Find the equivalent fraction of 3/5, having: (i) Numerator 9 (ii) Denominator 30

7) Find the fraction equivalent to 45/60, having: (I) Numerator 15 (ii) Denominator 4

8) Reduce each of the following fractions to its lowest term (simplest form):

(i) 40/75 (ii) 42/28

9) Compare the following fractions and put an appropriate sign <, =, >:

(i) 3/6 …… 5/6 (ii) 4/5 …… 0/5

10) Amit was given 5/7 of a bucket of oranges.

What fraction of oranges was left in the basket?

(iii) LONG ANSWER QUESTIONS-

1) Match the equivalent fractions and write another 2 for each:

(i) 250/400 (a) 2/3

(ii) 180/200 (b) 2/5

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(iii) 660/990 (c)1/2

(iv) 180/360 (d) 5/8

(v) 220/550 (e) 9/10

2) The following fractions represent just three different numbers. Separate them in to three
groups of equal fractions by changing each one to its simplest form:

(i) 2/12 (ii)3/15 (iii)8/50 (iv) 16/100 (v) 10/60 (vi) 15/75 (vii)12/60 (viii)16/96 (ix) 12/75

3) Arrange the following fractions in the ascending order: (i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9

(ii) 7/8, 7/25, 7/11, 7/18, 7/10(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41

(iv) 3/5, 1/5, 4/5, 2/5 (v) 2/5, 3/4, 1/2, 3/5 (vi) 3/8, 3/12. 3/6, 3/4 (vii) 4/6, 3/8, 6/12, 5/16

4) Ravish‟s house is 9/10 km from his school. He walked some distance and then took a bus
for 1/2km upto the school. How far did he walk?

5) A piece of a wire 7/8 metres long broke into two pieces. One piece was ¼ meter long. How
long is the other piece?

6) Find the difference of:

(i) 13/24 and 7/16 (ii) 5/18 and 4/15 (iii) 1/12 and 3/4 (iv) 2/3 and 6/7

(iv) CASE STUDY QUESTIONS:

1) 10. Shikha and Priya have bookshelves of the same size Shikha‟s shelf is 5/6 full of book
and Priya‟s shelf is 2/5 full.

(i) Whose bookshelf is more full?

(ii) By what fraction?

(iii) Why keep books bookself

2) 7. Akash bought vegetables weighing 10kg.Out of this 3kg 500g is onions, 2kg 75g is
tomatoes and the rest is potatoes.

(i) What is the weight of the potatoes?

(ii) What is the weight of the Onions?

(iii) What is the weight of the Tomatoes?

ANSWERS:

(i) MCQ QUESTIONS:-

1) (b) 2) (c) 3) (d) 4) (c) 5) (b) 6) (a) 7) (b) 8) (b) 9) (b) 10) (b)

(ii) SHORT ANSWER QUESTIONS-

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1) 12Pencils 2)

1 1
3) (i) 39 (ii) ) 1515 , 4) (i) 29/4 (ii) ) 61/7 , 5) (i) 21 (ii) 16 , 6) (i) 27/45 (ii) 18/30,

7) (i) 15/20 (ii) ) 3/4 , 8) (i) 40/75 (ii) 42/28 , 9) (i) 3/6 < 5/6 (ii) 4/5 > 0/5 , 10) 2/7

(iii) LONG ANSWER QUESTIONS-

1) (i) (d), (ii) (e), (iii) (a), (iv) (c), (v) (b)

2) 1st Group- { 2/12,10/60,16/96 }, 2nd Group- { 3/15, 15/75,12/60 },

3rd Group- { 8/50,16/100,12/75 }

3) (i) 1/9,2/9,3/9,4/9,5/9,6/9,7/9 (ii) 7/25,7/18,7/11,7/10,7/8

iii) 37/1000,37/100,37/85,37/50,37/47,37/41 (iv) 1/5,2/5,3/5,4/5

(v) 2/5,1/2,3/5,3/4 (vi) 3/12,3/8,3/6, 3/4 (vii) 5/16, 3/8,6/12, 4/6

4) Distance covered by Ravish is 2/5 km , 5) Length of Second Piece is 5/8 m

6) (i)5/48 (ii) 1/90 (iii) 2/3 (iv) 4/21

(iv) CASE STUDY QUESTIONS:

1) (i) Shikha book self is more full, (ii) By 13/30, (iii) Keep safe the books.

2) (i) 4Kg425gm (ii) 3Kg500gm (iii) 2Kg75gm

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CLASS TEST – 1 -
TIME- 45 MIN. M.M. 20

General Instructions:

i. All questions are compulsory.
ii. This paper consists of 12 questions divided into 4 sections: A, B, C, D
iii. Sections A contain 7 questions of MCQ type and of 1 mark each .
iv. Section B contains 3 questions of 2 marks each.
v. Section C contains 1 question of 3 marks.
vi. Section D contains 1 question of 4 marks.

SECTION – A –
Q1. Write the fraction representing the shaded region in the adjoining figure.

(a) 3 /7 (b) 5 /7 (c) 4 /7 (d) none of these

Q2. Fill in the boxes with the correct symbol: 3/4 ☐ 5/2
(a) > (b) < (c) = (d) none of these
Q3. What fraction of an hour is 45 minutes?

(a) 4/3 (b) 3/4 (c) 3/1 (d) 1/ 3
Q4. The points P,Q,R,S,T,U andV on thenumber line are suchthat,US=SV =VR,&
WT=TP =PQ.

Then value of (U+R) is:

(a) 1/5 (b) 4/5 (c) 5/5 (d) 6/5

Q5. The simplest form of 48/60 is:

(a) 3/5 (b) 4/5 (c) 5/4 (d) 5/3
1
Q6. 74can be written in improper fraction
(a) 4/29 (b) 11/4 (c) 29/4 (d) 8/4
Q7. Which of the following can be written in the box 2/7 = 8/?
(a) 16 (b)13 (c) 28 (d) 35
SECTION – B –
Q8. Show 7/4 on the Number Line.
Q9. Give a proper fraction:
(a) Whose numerator is 5 and denominator is 7.
(b) Whose denominator is 9 and numerator is 5.

1 3
Q10. Simplify: [74 + 84 ]

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SECTION- C –
Q11.My elder sister divided the watermelon into 16 parts. I ate 7 out them. My friend ate 4. 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?

SECTION – D –
Q12.It was estimated that because of people switching to Metro trains, about 33000 tonnes of CNG, 3300
tonnes of diesel and 21000 tonnes of petrol was saved by the end of year 2007. Find the fraction of :
(i) the quantity of diesel saved to the quantity of petrol saved. (1 mark)
(ii) the quantity of diesel saved to the quantity of CNG saved. (1 mark)
(iii) Why CNG preferred to use as fuel in Vehicles? (2 marks)

CLASS TEST – 2 -

TIME- 90 MIN. M.M. 30

General Instructions:

i. All questions are compulsory.
ii. This paper consists of 18 questions divided into 4 sections: A, B, C, D
iii. Sections A contain 10 questions of MCQ type and of 1 mark each.
iv. Section B contains 5 questions of 2 marks each.
v. Section C contains 2 questions of 3 marks.
vi. Section D contains 1 question of 4 marks.

SECTION – A –
Q1. Write the fraction representing the shaded region in the adjoining figure.

(a) 3 /7 (b) 5 /7 (c) 4 /7 (d) none of these

Q2. Fill in the boxes with the correct symbol: 3/4 ☐ 5/4
(a) > (b) < (c) = (d) none of these

Q3. What fraction of an hour is 20 minutes?

(a) 4/3 (b) 3/4 (c) 3/1 (d) 1/ 3

Q4. The points P,Q,R,S,T,U and V on the number line are such that, US=SV =VR,&
WT=TP =PQ.

Then value of (R+W) is:

(a) 1/5 (b) 4/5 (c) 5/5 (d) 10/5
Q5. The simplest form of 36/60 is:

(a) 3/5 (b) 4/5 (c) 5/4 (d) 5/3

59

1
Q6. 75can be written in improper fraction
(a) 5/36 (b) 11/5 (c) 36/5 (d) 13/5
Q7. Which of the following can be written in the box 2/7 = 12/?
(a) 16 (b) 42 (c) 28 (d) 35
Q8. Which of the following is a smaller fraction?
(a) 5/6 (b) 4/5 (c) 5/2 (d) 5/3
Q9. 11. The value of 1+ 2/3 is:
(a) 5/6 (b) 4/5 (c) 5/2 (d) 5/3
Q10. Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the
basket?
(a) 4/7 (b) 2/7 (c) 5/7 (d) 12/7

SECTION – B –
Q11. Show 3/5 on the Number Line.
Q12. Give a proper fraction:
(a) Whose Numerator is 3 and Denominator is 13.
(b) Whose Denominator is 7 and Numerator is 11.
1 3
Q13. Simplify: [74 - 8 ]
4
Q14.Fill up using one of these: „>‟, „<‟ or „=‟

Q15. Two equivalent fractions of each of the following:

(a) 5/ 9 (b) 2/ 7

SECTION- C –
Q16.17. 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?
1 3 1
Q17. Simplify: [64 - 5 +7 ]
4 4

SECTION – D –
Q12.It was estimated that because of people switching to Metro trains, about 33000 tons of CNG, 3300 tons
of diesel and 21000 tons of petrol was saved by the end of year 2007. Find the fraction of:
(i) What is Ratio of the quantity of diesel saved to the quantity of petrol saved? (1 mark)
(ii) What is Ratio of the quantity of diesel saved to the quantity of CNG saved. (1 mark)
(iii) Why METRO preferred by the people? (2 marks)

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