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BOOK 6 ( CBSE ) / Chap 7 / Fractions
Chapter Facts :
1. A fraction is a number representing a part of a whole. The whole may be a single
object or a group of objects.
2. In
a
, the ‘
b
’ ( bar ) drawn in between is called ‘ vinculum’.
The numeral written above the vinculum is called the numerator of the fraction.
The numeral written below the vinculum is called the denominator of the fraction.
1 1 1 1
3. A fraction with numerator 1 is called a unit fraction. , , , etc. are unit fractions.
1 2 3 4
4. A fraction is said to be a proper fraction if its numerator is less than its denominator.
7 5
, etc. are proper fractions.
12 13
5. A fraction is said to be an improper fraction if its numerator is more than its
denominator.
12 6
, etc. are improper fractions.
7 5
6. An improper fraction can be written as a mixed fraction. To do so we divide the
numerator by denominator and the mixed fraction is written as : quotient
7. A mixed fraction can be converted into an improper fraction. a
remainder
.
divisor
b ac b
=
.
c
c
8. Each fraction has many equivalent fractions. To find an equivalent fraction of a given
fraction, we may multiply or divide both the numerator and the denominator of the given
fraction by the same number(other 1 and zero).
9. If two fractions are equivalent their cross products are equal. Also if two fractions are
not equivalent, their cross products are not equal.
10. If cross products of two fractions are fractions equal, they are equivalent. Also if
cross products of two fractions are not equal , they are not equivalent.
11. A fraction is said to be in the simplest (or lowest) form if its numerator and the
denominator have no common factor except 1.
12. Fractions with same denominators are called like fractions.
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13. Fractions with different denominators are called unlike fractions. Any two unlike
fractions can be converted into like fractions by writing their equivalent fractions having
denominator equal to the LCM of their denominators.
14. If two fraction have the same numerator, then the fraction having the smaller
denominator represents the greater fractional number.
15. If two fractions have the same denominator( like fractions), then the fractions having
the greater numerator represents the greater fractional number.
16. Addition (or subtraction) of like fractions can be done by adding (or subtracting) their
numerators.
17. Addition (or subtraction) of unlike fractions can be done by converting them into like
fractions.
Formative Assessment
A ) Multiple Choice Questions.
In each of the following tick the correct option.
1. The two consecutive integers between which the fraction 5/7 lies are
(a) 5 and 6
(b) 0 and 1
(c) 5 and 7
(d) 6 and 7
2. Which of the following is not in the lowest form?
(a) 7/5
(b) 15/ 20
(c) 13/ 33
(d) 27/ 28
3. Which of the following is not equal to the others?
(a) 6 /8
(b) 12 /16
(c) 15 / 25
(d) 18 / 24
4. Which of the following fractions is the smallest?
(a) 7/8
(b) 9/8
(c) 3/8
(d) 5/ 8
5. On subtracting 5/9 from 19 / 9 , the result is
(a) 24 / 9
(b) 14/9
6. The mixed fraction 5
(a) 33 /7
(c) 14/ 18
(d) 14/ 0
4
can be expressed as
7
(b) 39/ 7
(c) 33/ 4
(d) 39 / 4
7. The fraction which is not equal to 4/5 is
(a) 40/ 50
(b) 12/ 15
(c) 16/ 20
(d) 9 / 15
8. When ¼ is written with denominator as 12, its numerator is
(a) 3
(b) 8
(c) 24
(d) 12
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5 20
, then value of p is

8
p
9. If
(a) 23
(b) 2
(c) 32
(d) 16
10. Which of the following fractions is the smallest?
(a) 5/7
(b) 5/6
(c) 5/9
(d) 5/8
B ) Fill in the blanks
1. If two fractions have same denominator then the one with ____________ numerator is
greater.
2. Subtraction of like fractions can be done by ________________ their numerators.
3. 13
4.
5
is a _________ fraction.
17
12
is a/an ______ fraction.
7
5. 7/19 is a/an ______ fraction.
6. 5/8 and 3/8 are ______ proper fractions.
7. 6/11 and 6/13 are ______ proper fractions.
In each of the questions 11 to 15, fill in the blanks using ‘>’, ‘<’ or ‘=’ :
8.
14
11
_____
15
16
9.
95
8
_____
15
14
10.
12
32
_____
200
75
C ) True / False
State whether the given statements are true (T) or false (F).
1. Every fraction has a point associated with it on the number line.
2. If two fractions are not equivalent, their cross products are not equal.
3. To add or subtract to unlike fractions they must first be converted into like fractions.
4. If two fractions have the same denominator ( like fractions ), then the fractions having
the greater numerator represents the greater fractional number.
5. Fraction 18/39 is in its lowest form.
D ) True false with Justification
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Say true or false for each of the following. Justify your answer
1. Only proper fractions have equivalent fractions.
2. The sum of two fractions is always a fraction.
E ) Matching
Match the following :
1. Match each item of Column I with the corresponding item of Column II.
Column I
Column II
(i) 6/ 8
(ii) 6/10
(iii) 6/ 6
(iv) 6/16
Summative Assessment
1 mark q’s
1. Express 6
2
as an improper fraction.
3
2. Write
129
as a mixed fraction.
8
3. Write
3
as a fraction with denominator 44.
4
4. Write
5
as a fraction with numerator 60.
6
5. Are the fractions 5/9 and 40/81 equivalent.
6. What fraction of a day is 9 hours?
7. What fraction of a straight angle is a right angle?
8. Allen divided one pizza equally among six persons. What part of the pizza did he give
to each person?
9. On an average
1
of the food eaten is turned into organism’s own body and is
10
available for the next level of consumer in a food chain. What fraction of the food eaten
is not available for the next level?
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10. A cup is
1
full of milk. What part of the cup is still to be filled by milk to make it full?
3
2 mark q’s
1. Add the fractions
2. Subtract
3
2
and .
8
3
1
1
from .
6
2
3. Add the fractions
3
3
and 6
8
4
100
1
4. Subtract 8 from
.
3
9
5. Add 1
1
1
and 6 .
4
2
6. Subtract 1
1
1
from 6 .
4
2
7. Find the fraction that represents the number of natural numbers to total numbers in the
collection 0, 1, 2, 3, 4, 5. What fraction will it be for whole numbers?
8. A rectangle is divided into certain number of equal parts. If 16 of the
parts so formed represent the fraction
1
, find the number of parts in which the rectangle
4
has been divided.
9. Mr. Raja got a job at the age of 25 years and he got retired from the job at the age of 60
years. What fraction of his age till retirement was he in the job?
10. The food we eat remains in the stomach for a maximum of 4 hours. For what fraction
of a day, does it remain there?
3 mark q’s
1. Kate rode her bicycle 6
1
3
km in the morning and 8 km in the evening. Find the
2
4
distance traveled by her altogether on that day.
2. Manu bought 3
1
3
m of lace. She used 1
m of lace for her new dress. How much
2
4
lace is left with her?
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3. When Sunita weighed herself , she found that she had lost 11
was 66
1
kg. Earlier her weight
2
3
kg. What was her weight now ?
4
1
1
4. Sunil purchased 12 litres of juice on Monday and 14 litres of juice on Tuesday.
2
4
How many litres of juice did he purchase together in two days?
5. Radha gave a wooden board of length 160
1
cm to a carpenter for making a shelf. The
4
1
carpenter cut out a piece of 60 cm from it. What is the length of the remaining piece?
5
6. Nasir traveled 3
1
1
km in a bus and then walked 1 km to reach a town. How much
8
2
did he travel to reach the town?
7. The fish caught by Karan weighs 3
1
3
kg and the fish caught by Mohit weighs 2 kg.
8
4
How much more did Karan’s fish weigh than that of Mohit’s?
8. Neelu’s father needs 1
1
3
m of cloth for her shirt and
m for the scarf. How much
4
2
cloth must he buy in all?
9. Write the fraction representing the total number of natural numbers in the collection of
numbers –3, – 2, –1, 0, 1, 2, 3. What fraction will it be for whole numbers? What fraction
will it be for integers?
10. Write a pair of fractions whose sum is
2
8
and difference is .
11
11
4 mark Q’s
1. It was estimated that because of people switching to Metro trains, about 2200 tons of
CNG, 4400 tons of diesel and 3200 tons of petrol was saved by the end of year 2014.
Find the fraction of
a) the quantity of CNG saved to the quantity of petrol saved. Is the fraction proper?
b) the quantity of diesel saved to the quantity of petrol saved. Is the fraction proper?
2. A bowl has cards with one faction out of the following written on each of them.
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2/7, 3/3 , 9/5, 8/11 , 5/ 7, 6/13 , 14/14 , 19/16, 3/4 , 19/13 .
These cards have to put in three boxes as follows : box I ( Fraction greater than 1 ) ;
box II ( Fraction equal to 1 ) ;
box III ( Fraction less than 1 )
List the cards to be put in each box.
3. Write a pair of fractions whose sum is
4. A rope was 6
7
2
and difference is .
11
11
2
2
m long. A piece 1
m long was cut out from it from one end of the
3
3
piece and a piece 3
2
m long was cut out from the other end. What is the length of the
5
rope left behind.
End ……………..
ANSWERS
Formative
MCQ’s
1
b
2
b
3
c
4
c
5
b
6
b
7
d
8
a
9
c
10
d
Fill in the blanks
1
greater
2
subtracting
3
mixed
4
improper
5
proper
6
like
7
unlike
8
>
9
<
10
=
True False
1
T
2
F
3
T
4
T
5
F
True False with Justification.
1
4
F. Consider the improper fraction . Now we can multiply both numerator and
3
8
4
denominator by say 2. We get , which is an equivalent fraction for .
6
3
2
1 3
  1 , which is not a fraction.
F.
4 4
Matching
(i) – C, (ii) – E , ( iii) – B , (iv) – A
Summative
One mark questions
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1
3
5
20
3
33
44
No
7
1
2
9
9
10
Two marks questions
1
25
24
3
1
7
8
5
3
7
4
7
5
,1
6
9
5
12
Three marks questions
1
1
15 km
4
3
1
55 kg
4
5
1
100
cm
20
7
5
1 kg
8
9
3 4 7
, ,
7 7 7
Four marks questions
1
11
11
a)
, yes
b)
, no
8
12
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
16
1
8
60
72
3
8
1
6
2
3
1
3
7
9
1
5
4
64
2
1
6
3
m
4
3
26 l
4
5
4 km
8
1
2 m
4
5
3
and
11
11
1
box I : 9/5 , 19/16, 19/13
box II : 3/3, 14/14,
box III : 2/7, 8/11, 5/ 7, 6/13, 3/4
3
9
5
and
22
22
End …….
4
3
1 m.
5
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