where $a$ and $b$ are real numbers
and the number above the dash line is called Numerator
and the number below the dash line is called Denominator
Different types of fractions are
LIKE FRACTIONS
Fraction with same denominator are called like fractions.
e.g 1) $1/5$ , $2/5$ , $3/5 $
In this fraction , the denominator of all the fractions is 5.
2) $1/10$ , $4/10$ , $7/10 $
In this fraction , the denominator of all the fractions is 10.
3) $1/13$ , $8/13$ , $11/13 $
In this fraction , the denominator of all the fractions is 13.
UNLIKE FRACTIONS
Fraction with different denominator are called unlike fractions.
e.g) 1) 4/5 , 8/10 , 3/7
In this fraction, the denominators are different i.e denominator are 5 , 10 and 7 .
Test your understanding.
1) Which of the following fractions are like fractions .
a) 2/3 , 4/9 , 5/9 .
b) 2/9 , 4/5 , 5/9
c) 2/9 , 4/9 , 5/9
d) 2/9 , 4/9 , 9/5
2) Which of the following fractions are like fractions .
a) 2/6 , 5/6 , 9/12 .
b) 3/5 , 1/5 , 4/5 .
c) 3/6 , 5/6 , 9/10 .
d) 1/6 , 2/6 , 9/10 .
3) Which of the following fractions are unlike fractions .
a) 2/6 , 5/6 , 9/12 .
b) 5/8 , 3/8 , 1/8 .
c) 5/9 , 1/9 , 8/9 .
d) 5/6 , 4/6 , 1/6 .
Total Correct:
UNIT FRACTIONS
Fractions having 1 as their numerator are called Unit Fractions.
e.g) $1/2$ , $1/3$ , $1/4$ and so on .
PROPER and IMPROPER FRACTIONS
Proper Fractions: When the numerator is less than denominator , it is called proper fractions.
e.g) $4/6$ , $2/5$ , $9/11$ etc .
Improper Fractions : When the numerator is equal to or greater than the denominator, it is called improper fractions.
e.g) $6/6$ , $6/4$ , $5/2$ , $11/9$ , $5/5$ etc
REPRESENTATION OF IMPROPER FRACTIONS.
$6/6$ is written as 1
$6/4$ is written as 1$1/2$
Test Your Understanding
Question
1) The improper fractions of the shaded portion is .
a) 9/8
b) 7/8
c) 15/16
d) 15/8
2)
a) 10/12
b) 6/4
c) 10/4
d) 10/2
3)
a) 7/9
b) 7/3
c) 1/3
d) 3/9
Score:/3
Mixed Fraction .
Improper fraction can also be represented as mixed number.
example of mixed number are $9{1/3}$ , and so on.
In above mixed number 9 forms the whole part and $1/3$ forms the fraction part.
Mixed numbers is alway greater than 1.
Covert improper fraction as mixed number .
| Improper Fraction | Mixed Number |
| $28/3$ | $9{1/3}$ |
| $16/5$ | $3{1/5}$ |
Concept for converting improper fraction to Mixed Number
Example 1. Convert $28/3$ into mixed number.
Eample 2. Convert $16/5$ into mixed number.
Test your understanding
Question) Convert following improper fration into mixed numbers.
1) $27/5$
2) $89/9$
3) $76/7$
4) $50/6$
How to convert Mixed Number into Improper Fraction
Since improper number is converted into improper fraction as ${Quotient}{Remainder}/{Divisor}$
Therefore mixed number are converted into improper fraction as
Improper Fraction = ${Quotient×divisor + remainder}/{divisor}$
Convert following mixed numbers into improper fraction.
1) $11{1/9}$
Ans: here Quotient = 11 ; Remainder = 1 ; and divisor = 9
hence = improper fraction = ${Quotient×divisor + remainder}/{divisor}$
= ${(11 × 9) + 1 }/ {9} $
= ${99 + 1 }/ {9} $
=$100/9$
2) $12{3/5}$
Ans: here Quotient = 12 ; Remainder = 3 ; and divisor = 5
hence = improper fraction = ${Quotient×divisor + remainder}/{divisor}$
= ${(12 × 5) + 3 }/ {5} $
= ${60+3 }/ {5} $
=$63/5$
Test your understanding
Convert following mixed numbers into improper fractions .
1) $12{2/3}$
2) $3{3/7}$
3) $4{5/8}$
4) $5{4/5}$
5) $15{4/6}$