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Fractions

 

 




 


 

Exercise

      1.         

 

 

       2.        + - )

               

                        '

 

 

 

       3.       of (   '    )

 

 

                             

Lesson Objectives 

By the end of this lesson you should be able to:

carry out combined operations on fractions in the

correct order.

Introduction

 Evaluate:

a).  + -   b). +-

Solutions

In order to find the solution we must

find the LCM of the denominators

    2   6  3                                                                   4    8     3

2  2   3  3                                                               2  2    4     3 

3  1   1  1                                                               2  1    2     3

                                                                              2  1    1     3

                                                                              3   1    1    1

             L.C.M = 2 x 3                                      L.C.M = 2 x 2 x2 x 3

             = 6                                                                    = 24

a) + - =                                 b)   +-=

                   =                                                            =

                   ==                                                           = 

The order of operations in fractions is the same as that

used for whole numbers. 

That is working out the brackets first, then multiply,

add and subtract in that order.  Of is taken as multiplication.

Example 1.

Evaluate each of the following:

a).   - (   x    )

   Solution

  a)      ' (   x    )                              b)   x (   +    ) '  

          =  ' (   x    )                                   =  x () '  

          =  ' ()                                                =  x (')  

          =  x () =                                      =  x (x)  

                                                                             =  x  

                                                                             =

c)  + x (-)  

   =    + x ()

   =  + (x )

  =  +  

  =

  = =   

Example 2

Evaluate the following:

a).  of - x )                             b).  x ' (of )             

       =   of - x )                               =  x ' (x )  

       = x - x )                                   =  ' ()  

       = -=                                        =  x    

       =                                                        =  

Example 3

a).( ) x   x '                         b). of  -  

                x                                           -'

=   ( ) x   x '                              =  x -

                x                                               -'

=    x   x x                                        =  -

            x                                                     -x            

  =            x                                                 =  -

                                                                        -

=         x                                                     =       = '

=                                                                    

                                                                  = ' =x

                                                         = x =

Further Exercise

Evaluate the following

1

a)         +   

 

              ' -   

 

WORKING SPACE

b)   x -

  + [ - ]

 

 

 

 

 

c)          (+-) '

 

         

2. Wambui uses of her monthly salary on rent and  on fuel.

      She uses of the remainder on electricity bills and saves the

      rest. What fraction of her salary does she save?

 

 

3. The size of a farm is 270 ha.   of the farm is planted with

    maize.  Two thirds of the remaining land is under beans.  The

    rest of the farm is under grass. What area of the farm is under grass? 

 

4. A small group can empty a tank in 4 minutes and a large pump

    can empty the same tank in 3 minutes.

a).  Find the fraction of the tank that each pump will empty in one

      minute.

 

b).  Find the fraction of the tank that both pumps working

      together can empty in one minute.

c).  Find the time that both pumps working together will take on

     empty the tank.

 

END

 

FRACTIONS Fractions are quite essential in sharing things equally. Discover what they can do to your daily life.

.

 

 

 

 



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