Fraction in Maths Arithmetic

Review :  Basic Rules of  Fraction ,  Types of Fraction ,  Special  Fraction

The fraction is how many parts of a whole . It is being written  as  m/n .  Where is numerator and n  is denominator,
both are integers and n ≠ 0.

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In above figure we can understand  like ;  Fraction 1/3 that is  – one whole is divided into three parts and out of these three take one part.

Fraction 7/10 – One whole is divided into ten parts and out of these ten take 7 parts.

Now find out yourself what will be the fraction of following figures.

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Basic Rules of Fraction

  • If we multiply numerator ‘m’ and denominator ‘n’  with the same  number the resultant will be equivalent to m/n .

                          Ex.1      5/6 = (5 x 3 )/(6 x 3)  = 15/18 ;           Ex.2           2/3 = ( 2x 4)/(3 x 4) = 8/12

  • A fraction can be reduced to a lowest term by dividing numerator and denominator with same number.

                         Ex.1         12/64   =  3/16 ;                                Ex. 2            25/35 = 5/7

  • Two add  or subtract two fraction first take common denominator by taking LCM , and convert it to equivalent fraction.

                         Ex. 1     2/3  + 5/6

        LCM of denominator  3,6 is 6

       = (4 + 5)/6

      = 9/6

      = 3/2

                            Ex. 2              7/8   –   3/4

                  LCM of numerator  8 and 4 is 8

                    = (7 – 6)/8

            =   1/8

  • A negative sign  in numerator or denominator will be written in front of fraction .

                          Ex. 1         -4/5   =     -4/5                                 Ex.2       6/-7    = -6/7

  • Multiplication of two fractions can be done directly by taking product of numerator and denominator.

                        Ex. 1               (2/3) x  (1/2 ) = (2 x1 )/ ( 3 x 2 )  = 2/6

                        Ex. 2               (-4/7) x (2/8)    = – 8/56

  • To divide one fraction with another fraction first revert the second fraction ( or take reciprocal inverse of second fraction )and then multiply with first fraction.

                      Ex. 1   7/9  ÷   4/3   = 7/9 x 3 /4    = 7/12

                       Ex. 2     – 9/15   ÷   1/3    = (- 9/15)  x (3/1)  = -9/5

Types of Fraction

  1. Proper Fraction –  When numerator is smaller than denominator then we call the fraction as proper fraction

2/5, -4/9  , 1/2   ,  5/6 …etc

  1. Improper Fraction –  When numerator is equal to or bigger than denominator than we say it as improper fraction.

5/2 , 9/5 , -6/5 ,  7/3…… etc.

  1. Mixed Fraction –  The combination of a whole number and the proper fraction is Mixed Fraction.

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  1. Like Fraction – Fractions with same denominator is known as Like Fractions.

2/7,   5/7,    1/7 ,  11/7,    18/7 125/7 ……………etc.

  1. Unlike Fraction –  Fractions with different denominators are known as Unlike Fractions.

2/3, 7/9  , 35/6 ,      2/11,   5/18 …………..etc.

Special Fractions

When for any  fraction m/n ;  ‘m’ and ‘n’ are  not integers and n ≠ 0, we manipulate the expression as fractions only .

Ex. 1      a/2  +  a/ 3    =  (3a + 2a) / 6    =  5a/6

Ex. 2      √3 / 5   ÷  2/ √3              =  √3   / 5    x  √3  /2              =  3/10

Ex. 3    π/6  +  π/2  =  ( π  + 3 π) / 6   =  4 π/6  =  2 π/3

                                                                                  

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