define -fractions and fractional

1. Amit Kumar Singh
M.Ed 1st Year
2016-17

2.  In this figure, a strip has been divided into 7 equal parts .
4
7
 Out of these 7 equal parts, 4 parts have been shaded.
 Here
𝟒
𝟕
is a fraction and four-sevenths is fractional
number.
 Clearly, the shaded portion represents four-sevenths.
In numeral, we denote it by
𝟒
𝟕
(read as ‘four by seven’).

3. Fractions on number line
Suppose we want to denote the fraction
𝟒
𝟕
on number line.
Take a line segment OA of unit length.
p
O A4
7
Dived OA into 7 equal parts and take 4 parts out of it to reach the point P.
Then ,the point P represents the number
𝟒
𝟕
.

4. Some more examples of fraction
are given below.
Fraction Fractional Number
𝟏
𝟐
One-half
𝟏
𝟒
One-quarter
𝟐
𝟑
Two-thirds
𝟑
𝟓
Three-fifths
𝟓
𝟖
Five-eighths

5. Definition
The number of the form
𝐚
𝐛
, 𝐰𝐡𝐞𝐫𝐞 a and b are natural numbers ,
are called fractions.
Here a is called the numerator and b is called the
denominator of the fraction
𝐚
𝐛
.
Example

𝟓
𝟗
is a fraction with numerator = 5 and
denominator = 9

𝟖
𝟓
is a fraction with numerator = 8 and
denominator = 5

6. Example(1)
 What fraction of a day is 8 hours ?
Solution : We know that 1 day = 24 hours.
∴ the required fraction =
𝟖
𝟐𝟒
.
Example(2)
 What fraction of an hour is 40 minutes?
Solution : We know that 1 hour = 60 minutes.
∴ the required fraction =
𝟒𝟎
𝟔𝟎
.

7. Type of fractions
Proper Fractions :
Improper Fractions :
A fraction whose numerator is greater than or equal to its denominator
is called an improper fraction.
Example :
𝟓
𝟒
,
𝟔
𝟓
,
𝟖
𝟓
,
𝟓
𝟓
,
𝟏𝟎
𝟏𝟎
,
𝟏𝟏
𝟔
,etc… are all improper fractions.
A fraction whose numerator(a) is less than its denominator(b)is called a
proper fraction.
i.e
𝒂
𝒃
where (a , b) ∈ ℕ and a < b
Example :
𝟐
𝟒
,
𝟑
𝟓
,
𝟓
𝟖
. etc… are all proper fractions.
NOTE Each proper fraction is less than 1.

8. Vulgar fraction
A combination of natural number and a proper fraction is called mixed
fraction.
Example : 1
𝟑
𝟒
, 4
𝟓
𝟕
, 5
𝟕
𝟗
, etc … are all mixed fractions.
Mixed Fractions
A fraction whose denominator is a natural number, other than
10, 100, 1000 etc… is called a vulgar fraction.
Examples:
𝟐
𝟗
,
𝟓
𝟏𝟑
,
𝟗
𝟐𝟎
, etc … are all vulgar fraction.

9. Decimal fraction
A fraction whose denominator is s10 , 100 ,1000 etc… is
called a decimal fraction .
Examples
Each of the fractions
𝟑
𝟏𝟎
,
𝟓
𝟏𝟎𝟎
,
𝟗
𝟏𝟎𝟎𝟎
, etc. ... is a decimal
fraction.

10. TO convert an improper fraction into a
mixed fraction
Example : Convert
𝟐𝟗
𝟖
into a mixed fraction .
Solution : On dividing 29 by 8 , we get quotient = 3 and
remainder = 5
∴
𝟐𝟗
𝟖
= 3+
𝟓
𝟖
= 3
𝟓
𝟖
similarly ,
𝟑𝟖
𝟗
= 4+
𝟐
𝟗
=4
𝟐
𝟗

11. TO convert a mixed fraction into an
improper fraction
 Example : convert 3
𝟓
𝟖
into an improper fraction.
Solution : 3
𝟓
𝟖
=
𝟑×𝟖 +𝟓
𝟖
=
𝟐𝟒+𝟓
𝟖
=
𝟐𝟗
𝟖
.
similarly, 4
𝟐
𝟗
=
𝟒×𝟗 +𝟐
𝟗
=
𝟑𝟔+𝟐
𝟗
=
𝟑𝟖
𝟗
.