Fractions

Fractions: A fraction is one whole unit divided in many parts.
2 parts shaded out of 5 so 2/5
fractions
4 parts shaded out of 7
so 4/7

Types of Fractions

Proper Fraction

Numerator is smaller than the denominator.

Ex: 3/4 , 5/6
Improper Fraction

Numerator is bigger than the denominator.

Ex. 7/2, 9/7
Mixed Fraction

Fractions that Have a whole part and a fraction part.

Ex. (1 ) 1/2,
(1) 5/7
Like Fraction

Fractions with the same denominator.

Ex. 2/4, 5/4
Unlike Fraction

Fractions with different denominators.

Ex. 1/2, 5/4
Equivalent fractions

Fractions that represent same part of a whole.

Ex. 1/2, 2/4, 4/8
Simplest form of Fractions

Numerator and denominator don´t have a common factor other than 1

Ex. 2/3, 3/5

Drag the fraction names into the correct boxes:

12 / 5
,
18 / 4
2
2 / 5
, 4
2 / 4
1 / 6
,
2 / 12
1 / 2
,
1 / 4














Simplest form of fractions
 
When the numerator and the denominator of a fraction do not have a common factor other than 1 , then the fraction is said to be in its simplest form.
 
Example: 
 6                      6/6                       1
___    =           ______       =         ___
12                    12/6                       2
Convert the following fractions to their simplest form :
No. Fraction Simplest Form
1.
2 / 8
 =
/
2.
8 / 32
 =
/
3.
15 / 60
 =
/
 Like fractions are fractions that have the same denominator.
 
Example:
1            2                            4               5                        1               3
___  ,     ____                      ____   ,    ____                   ____ ,     ____
3            3                            6              6                        9              9 
 
 Unlike fractions are fractions that don’t have the same denominator. 
1          2                            3             5                            6             7
__  ,   ___                      ____    ,   ____                      ____  ,      ___
2         3                            3             5                             9            10
 

Like fractions

Comparing like fractions
 
The fraction with a higher numerator is greater than the other fraction.
 
Example
    7                  8
_____           _____      
   10                 10 
Numerator 8 is greater than Numerator 7 , so the fraction 8/10 is greater than the fraction 7/10
 
Compare the following like fractions :
No. Fraction1 < / > Fraction2
1.
4 / 5
2 / 5
2.
1 / 6
5 / 6
3.
7 / 9
3 / 9
4.
3 / 4
1 / 4
5.
4 / 8
3 / 8
6.
5 / 5
4 / 5
Addition of  like fractions:

To add the like fractions , just add the numerators.    ( as  the denominators are the same)

Example
7            1             7  +  1            8                  
___  +   ____  =  _______  =    ____            
9            9                 9               9             
 
 2            2            2 + 2              4           
___  +   ____  =  ________  =    ____         
4        4          4            4           

 

Add the following like fractions :
1.
1 / 5
+
2 / 5
=
/
2.
6 / 9
+
5 / 9
=
/
3.
7 / 15
+
3 / 15
=
/
4.
3 / 4
+
1 / 4
=
/
5.
4 / 8
+
3 / 8
=
/
6.
1 / 18
+
4 / 18
=
/
Subtraction of  like fractions:
To subtract like fractions , just subtract the numerators as  the denominators are the same.  
Example
2            1             2  –   1            1                   
___  –   ____  =  _______  =    ____            
5            5                 5               5             
 
 9            2            9 – 2                7           
___  –   ____  =  ________  =    ____         
 10           10             10                10  
            
Subtract the following like fractions :
1.
8 / 5
–
2 / 5
=
/
2.
6 / 9
–
1 / 9
=
/
3.
14 / 15
–
7 / 15
=
/
4.
3 / 4
–
1 / 4
=
/
5.
7 / 8
–
2 / 8
=
/
6.
15 / 18
–
12 / 18
=
/

Unlike fractions

 Comparing  UnLike fractions
 
UnLike fractions are fractions that don´t have the same denominator.

Case 1:  
Unlike fractions with the same numerator but with a different denominator.

Example:
1            1                                                   
___  ,   ____                     
10          11                                                           
  
so the fraction 1/10(divided in 10 parts) is greater than the fraction 1/11 (divided in 11 parts). 
Lesser number of parts greater the fraction.

 
The fraction with a smaller denominator is greater than the other fraction.
           
Compare the following unlike fractions :
No. Fraction1 < / > Fraction2
1.
2 / 4
2 / 5
2.
1 / 5
1 / 6
3.
3 / 7
3 / 9
4.
4 / 4
4 / 2
5.
5 / 8
5 / 10
6.
11 / 5
11 / 2
 Case 2:  
Unlike fractions with the different numerators and  different denominator.

If the denominators aren’t same, Then they have to be made the same.
Example:
4          3           4*6          3*5              24      15
___  ,   ____          ______        ______              ____      ___.  
5             6                5*6             5*6                   30        30

Now the fraction with the a bigger numerator is greater than the other.  

Since 24/ 30 is greater, the corresponding fraction 4/5 is greater than 3/6

 

Compare the following unlike fractions :
No. Fraction1 < / > Fraction2
1.
4 / 6
2 / 5
2.
1 / 8
3 / 10
3.
5 / 7
3 / 9
4.
4 / 4
2 / 3
5.
3 / 8
5 / 9
6.
1 / 11
2 / 5
Addition of Unlike fractions:
To add Unlike fractions , first make the denominators same.  (Either by cross multiplying or finding a common number)
Example
2            1             2*3            1*5            6              5              11       
___  +   ____  =  ___      +     ____  =    ____   +    ____   =   ____       
5            3            5*3            3*5           15             15             15  
 
 3            2            3              2*2            3              4               7       
___  +   ____  =  ___      +     ____  =    ____   +    ____   =   ____       
 5            3           5*3           3*5             15           15             15 
     
Add the following unlike fractions :
1.
1 / 5
+
2 / 3
=
/
2.
6 / 10
+
5 / 9
=
/
3.
7 / 8
+
3 / 4
=
/
4.
1 / 4
+
3 / 5
=
/
5.
4 / 6
+
1 / 8
=
/
6.
1 / 2
+
4 / 9
=
/
Subtraction of Unlike fractions:
To subtract Unlike fractions , first make the denominators same.  (Either by cross multiplying or finding a common number)
Example
2             1            2*5            1*3           10              3              7       
___  –   ____  =  ___       –     ____  =    ____   –    ____   =   ____       
3            5            3*5            5*3          15              15             15  
 
 7            2            7              2*2            7               4                3       
___  –   ____  =  ___      –     ____  =    ____   –    ____   =   ____       
10            5           10            5*2            10             10             10 
 
      
Subtract the following unlike fractions :
1.
2 / 6
–
1 / 5
=
/
2.
4 / 5
–
6 / 9
=
/
3.
3 / 5
–
1 / 3
=
/
4.
2 / 4
–
1 / 8
=
/
5.
4 / 6
–
3 / 8
=
/
6.
4 / 10
–
1 / 18
=
/

Mixed Fraction

Mixed fraction can be formed only when the
numerator is higher than the
denominator.
Improper fractions to Mixed fractions
To convert 3/2 , an improper fractions to Mixed fraction 
                                                              Remainder
Mixed fraction = quotient(whole part) ___________
                                                                Divisor
Example:                                                   
    
  3                    1
  __  =      1      ____         
   2                   2
      
Convert the following improper fractions to mixed fractions :
No. Improper Fraction Mixed Fraction
1.
18 / 5
/
2.
12 / 7
/
3.
20 / 9
/
4.
11 / 5
/
5.
17 / 3
/
Mixed Fractions to Improper fractions
                       3
To convert 1  — , a Mixed fraction  to Improper fractions.
                       2                                         
Improper fraction = 
                                                      
Example:                                                   
      3              5           
1  —-    =  —–     
      2             2                               
   
Convert the following mixed fractions to improper fractions :
1.
4
3 / 5
=
* + /
=   
/
2.
5
5 / 7
=
* + /
=   
/
3.
5
3 / 4
=
* + /
=   
/
4.
1
6 / 10
=
* + /
=   
/
5.
1
2 / 3
=
* + /
=   
/
Addition of  Mixed  fractions:
To add Mixed fractions , 
1. Convert the mixed fractions into improper fraction

2. Make the denominators same
3. Add the improper fractions
4. Convert the result into mixed fractions

Example
       
Add the following mixed fractions
4
3 / 5
+ 5
5 / 7
=
* + /
+
* + /
=
/
+
/
=
* / *
+
* / *
=
/
+
/
=
/
=
/
Subtraction of  Mixed  fractions:
To subtract  Mixed fractions , 
1. Convert the mixed fractions into improper fraction

2. Make the denominators same
3. Subtract the improper fractions
4. Convert the result into mixed fractions

Example
 
Subtract the following mixed fractions
5
5 / 7
– 4
3 / 5
=
* + /
–
* + /
=
/
–
/
=
* / *
–
* / *
=
/
–
/
=
/
=
/
Multiplication of  fractions:
To multiply fractions, multiply the numerators and multiply the denominators separately
Example
 2             1            2*1               2                
___  *   ____  =  _____    =    ____       
 3            5            3*5              15  
 
   3            2            3*2               6                   
____  *   ____  =    _____    =    ____              
   4            5            4*5               20             
      
Multiply the following fractions :
1.
1 / 5
*
2 / 3
=
/
2.
6 / 10
*
5 / 9
=
/
3.
7 / 8
*
3 / 4
=
/
4.
1 / 4
*
3 / 5
=
/
5.
4 / 6
*
1 / 8
=
/
6.
1 / 2
*
4 / 9
=
/
Multiplication of  mixed fractions:
To multiply mixed fractions,
convert to improper fractions and multiply the denominators separately
Example              
1
2 / 3
* 2
2 / 5
=
3 * 1 + 2 / 3
*
5 * 2 + 2 / 5
=
5 / 3
*
12 / 5
=
60 / 15
= 4
1
2 / 3
*
1 / 4
=
3 * 1 + 2 / 3
*
1 / 4
=
5 / 3
*
1 / 4
=
5 / 12
2 * 2
2 / 5
=
2 / 1
*
5 * 2 + 2 / 5
=
2 / 1
*
12 / 5
=
24 / 5
= 4
4 / 5
Multiply the following mixed fractions
4
3 / 5
* 5
5 / 7
=
* + /
*
* + /
=
/
*
/
=
/
=
/
Division of  mixed fractions:
Example              
1
2 / 3
2
2 / 5
=
3 * 1 + 2 / 3
5 * 2 + 2 / 5
=
5 / 3
12 / 5
=
5 / 3
*
5 / 12
=
25 / 36
1
2 / 3
1 / 4
=
3 * 1 + 2 / 3
1 / 4
=
5 / 3
1 / 4
=
5 / 3
*
4 / 1
=
20 / 3
= 6
2 / 3
2 2
2 / 5
=
2 / 1
5 * 2 + 2 / 5
=
2 / 1
12 / 5
=
2 / 1
*
5 / 12
=
10 / 12
Divide the following mixed fractions
4
3 / 5
5
5 / 7
=
* + /
* + /
=
/
/
=
/
*
/
=
/