*Fractions* - *अपुर्णांक*
             __________________________
=============================
*Reading of fractions*.....

    5     <----- *Numerator*
 -------
    7     <------  *Denominator*

Reading - *5 upon 7*

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Pravin Bankar
 *Equvalent fractions*
                   - *सममुल्य अपुर्णांक*

" *Equal Value* fractions are called *equivalent fractions*  "

example  -

    4         5         6  
  ------ ,   ------ ,   -------   etc
     8        10       12
 
question  -  Find fractions equivalent to 18/60 ?

*solution ,...*

    18  ÷  2           9
    --------------  =   ------
     60  ÷  2          30

    18  ÷  3              6
   ---------------   =   ---------
     60 ÷  3              20

     18 × 2             36
    -------------     =  -------  
      60 × 2            120

So....   *18/60 ,  9/30  , 6/20 , 36/120   are equivalent fractions*

🅿....  *By multiple or division with same number to Numerator & Denominator we get equivalent fractions*

pravin bankar
============================

*Like fractions & unlike fractions*
   ( समछेद अपुर्णांक व भिन्नछेद अपुर्णांक )

🅿 *Like fractions*
       ~~~~~~~~~~~
      " *fractions with equal denominators are called like fractions* "

example .....

   4        6         7  
 -----  ,  -----  ,   ------
  8         8          8

Here denominator  8 is same hence those fractions called  *like fractions*

🅿  *Unlike fractions*
        ~~~~~~~~~~~~
  " *fractions with different denominator are called unlike fractions* "

example ...........

    4        9         14
  ----- ,   ------ ,   --------
    6         7         4  

Here denominator is different hence its called *unlike fractions*

🅿 *Converting Unlike fractions to like fractions*

example .......

*convert  9/4 & 7/5 to like fractions*

solution  

First we find common multiple for  4 & 9  ......

*multiple of 4 - 4, 8 , 12 , 16 , 20 , 24..*

*multiple of 5 - 5 , 10 , 15 , 20 , 25....*
 
here  number  20 is multiple of both  4 & 5 .....
so we *make denominator 20  both fractions*

   9 × 5             45  
-------------   =  ---------
   4 ×  5             20

    7 × 4             28
------------     =  -----------
   5 × 4               20
         
                     
*Thus  45/20  & 28/20 are like fractions*

bankar pravin
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           ⏺ *Comparing Fractions* ⏺

🅿 *When denominator Same*

   7          4      
 -----  ,    -----
   9          9      

when denominator  are same *the fractions with greater numerators is the greater fractions*

here 7 is greater than 4.....
*hence  7/9 is greater than 4/9*

🅿 *when numerators same*

   8         8
 -----  ,   ------
   3         5  

when numerators same *the fractions with smaller denominator is greater fractions*

Here 3 is smaller than 5 ....
*hence 8/3 is greater than 8/5*

pravin bankar
============================
           ⏺ *Comparing Fractions* ⏺

🅿 *When denominator Same*

   7          4      
 -----  ,    -----
   9          9      

when denominator  are same *the fractions with greater numerators is the greater fractions*

here 7 is greater than 4.....
*hence  7/9 is greater than 4/9*

🅿 *when numerators same*

   8         8
 -----  ,   ------
   3         5  

when numerators same *the fractions with smaller denominator is greater fractions*

Here 3 is smaller than 5 ....
*hence 8/3 is greater than 8/5*

🅿 *Comparing unlike fractions*

   5         7
  -----  ,  ------
   8         9

solution ....

take multiple of.....

 5 × 9   = 45

 7  × 8  =  56

here ......   *45 < 56*

hence ....   *5/8 < 7/9*  

pravin bankar
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       🅿 *Addition & substraction*
              *Unlike Fractions* 🅿

[ 1 ] example .......

   12          15
 --------  +  -------
    5            8  

do same denominator ......

    96       75       96 + 75    171
  ------  +  ------ =  ------------ = ------
   40         40          40          40

[ 2 ] example .....

   8           6
------   -   -------
   5            9  

solution ....

first do denominator same ...  

   72        30       72 - 30       42
  ------  -   -----  =  ------------  = -----
   45        45          45           45

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🅿 *Mixed Fraction*....

        3
   4 ------  
        5  

Given fraction 4 is the integer part and 3/4 is the fraction part *such fractions are called Mixed Fractons*

Reading ...
     3  
5 ------   ... *5 integer , 3 upon 8*
     8  

   °°°°° *Shri - Pravin Bankar* °°°°°°
               *E Genius Math Group*
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