Explore Related Concepts

Bodmas Problems





BODMAS was introduced by Achilles Reselfelt. It is a designed to aid the memory  for solving  mathematic equation or statement. BODMAS used  to solve the equation systematically in very step of simplification by using brackets of division, multiplication, addition, subtraction. 


For example $\frac{1}{5}$ + 2$\frac{1}{2}$ * 4

In the above example the two operations are addition and multiplication, now there is a problem is whether we should add and then do multiplication  or multiply then carry on addition .Here there is a requirement for the BODMAS operation.

BODMAS Means:

B = brackets
o = of                                    (power  and square root of the terms are carried )
d = division                            (operation carried out from left- right )
m = multiplication               (operation carried out from left- right )
a = addition
s = subtraction

How to solve BODMAS problems:

Few examples are given below to show the use of BODMAS to solve the mathematical simple expression. 
  1. $\frac{50}{5}$ - 20
   The equation consists of both division and subtraction operation.

   Step1:  First divide the term before subtraction according to  BODMAS rule.

                      = 10 - 20

  Step2:  Subtraction is carried out from left to right.
         
                      =  - 10

    2.    $\frac{4}{3}$ of $\frac{4}{5}$ + 1$\frac{3}{5}*\frac{3}{3}$
  
  According to rules of BODMAS simplify and then divide

  Step1:
 First simplify and divide the term.

 $\frac{4}{3}$ 
* $\frac{4}{5}$ + $\frac{8}{5}$ * $\frac{3}{3}$

 Step 2:  Multiply the terms

 $\frac{16}{15}$ + $\frac{24}{15}$

 Step 3:  Addition is carried out from left to right and simplify.

 $\frac{40}{15}$ = $\frac{8}{3}$

3.   ( 3 + 5 - 2) * (20 - 6) * 25 - 95

    Step1:  First simplify the term inside simple bracket by BODMAS rule (addition is carried out from left to right) 

                        ( 8 - 2 ) * ( 20 - 6 ) * 25 - 95

      
Step 2:  Subtraction is carried out.
                      
                        6 * 14 * 25 - 95

     Step 3:  Multiplication is carried out between the term.
                       84 * 25 - 95
                       2100 - 95

     Step 4:  Subtract the term.
                        2005 

Simplification of Fractions including brackets using BODMAS

Example 1: 5 x [15 + {3 (6 -2 )}]

     Step 1:  Solve the inner most simple bracket first and simplify the equation
                       
                        5 x [15 + {3 x 4}]

     Step 2:  Solve the flower bracket first and simplify the equation
                       
                        5 x [15 + 12]

     Step 3:  Solve the box bracket first and simplify the equation

                        5 x 27
                       
                        = 135

Example 2:  $\frac{1}{7}+\left [\frac{7}{9}-(\frac{3}{9}+\frac{2}{9})-\frac{2}{9}  \right ]$

       Step 1: Solve the inner most simple bracket first and simplify the equation

             $\frac{1}{7}+\left [ \frac{7}{9}-\frac{5}{9}-\frac{2}{9} \right ]$
       
Step 2:  Addition and then subtraction are carried out from left to right.

            $\frac{1}{7}$ +  [$\frac{2}{9} - \frac{2}{9}$]    
                
                  $\frac{1}{7}$ + [ 0 ]    
             
Step 3:  Simplify
                                   $\frac{1}{7}$