Saturday, March 23, 2013

41-Easy Method to check your calculations

Blog-41

Dear Parents,
I delivered the lecture on Mathematical Fun.  It was delivered in Indian Language “Marathi”. If you understand Marathi, Please click here to see my Lecture on YouTube.

Secondly to think more about the studies of Mathematics, So you are requested kindly to allow your child to participate in Program of Studies for Students and Parents given in my previous Blog. (Blog-11)

1) Please tell your child to read the blog on "Simple Method of Multiplicationto learn something new concept of Multiplication.
2) Tell your child to solve the problem asked in BLOG-19 under the heading "Draw Perpendicular Bisector on Line Segment Drawn at the bottom of the page" The answer of this problem will be published on 25/03/2013.

Dear Students,

Today we will see an easy method to check your calculations.

In Number system, every number is formed by digits. For our method we require to get the digit addition (that is Addition of all the digits in the number). 

Now we will see some example of digit addition.

Example-01:  Let the given Number be 795832. The digit addition of this number means get addition of all the digit till single digit. 
      
           Digit Addition = + 9 + 5 + 8 + 3 + 2
                                    = 34
                                    = 3 + 4
                                    = 7
 So here Digit addition of the Number 795832 is 7 (which is in the lowest form)

Now we will see still easy method to do this digit addition. See the following steps to do the fast digit addition.

Step-01: Take out all 9's from the given number if any. In the given number 795832, one 9 is observed, so take it away from the number, So now we have the number for digit addition will be 75832. (Note: The removal of all 9's is only for getting digit addition. For original calculation we must take the complete number).

Step-02: Take out all the digits whose addition comes out to be 9. in our resulted number in step-01, 75832, if we observe very care fully, we will notice that the digits 7 and 2 gives addition as 9 so remove these two digits, so now we have the number for digit addition will be 583.

Step-03: Now we need to take the addition of all the remaining digits. Here we have 
           Digit Addition = (5 + 8) + 3
                                    = 16
                                    = 1 + 6
                                    =  7
Which is as the addition of all the digits calculated by adding all the digits and then redusing it till single digit.

Now we will see all above 3 steps for getting addition.

           Digit Addition = 7 + 9 + 5 + 8 + 3 + 2

                                    = (5 + 8) + 3
                                    = 13 + 3
                                    = 16
                                    = 1 + 6
                                    = 7
Example-02: Find the digit addition of the Number 543249815
           Digit Addition = 5 + 4 + 3 + 2 + 4 + 9 + 8 + 1 + 5
                                    = (5 + 4) + (3 + 2 + 4) + (9) + (8 + 1) + 5    
                                        (All terms in the brackets gives addition as 9)
                                    =  5

So the digit addition of 543249817 is 5.

Now we will see the procedure for checking our calculations.

Example-01: Add the three numbers 9432, 7859 and 8147

                         9432

                         7859
                     +  8147
                 -----------------
                       25438

Now we check our calculations by using digit addition method.

A) Digit addition of the Numbers = (9 + 4 + 3 + 2) + (7 + 8 + 5 + 9) + (8 + 1 + 4 + 7)
                                                         = (4 + 3 + 2) + (7 + 8 + 5) + (4 + 7)
                                                         = (9) + (20+ (11)
                                                         = (2 + 0+ (1 + 1)
                                                         = (2+ (2)
                                                         =  4
B) Digit addition of our result      = (2 + 5 + 4 + 3 + 8)
                                                         = (2 + 3 + 8)
                                                         = (5 + 8)
                                                         = (13)
                                                         = (1 + 3)
                                                         =  4
So our answer of addition is correct.
Example-02: Find the Multiplication of 279 and 563 
(Please Click on  "Simple Method of Multiplication" to learn new method of multiplication, We will take the same example here to check the result)


A) Digit addition of the Numbers 
            = (2 + 7 + 9) x (5 +  6 + 3
            = (9) x (5)
            = (45)
            = (4 + 5)
            = (9)
B) Digit addition of our result
            = (1 + 5 + 7 + 0 + 7 + 7)
            = (6 + 21)
            = (6 + 3)

            = (9)

So we can say the our multiplication is right.

For Subtraction also we need to transfer the negative term to other side only to check our result. 

For Example, If we would like to check the calculations for the subtraction A - B = C, then for checking purpose we need to take this subtraction as 
A = B + C .

The same thing is to be done for division. (In division, we need to transfer the division in to the product form)

For Example, If we got the result as X / Y = Z, then we need to check our calculations for 
X = YZ.

Please study the above method & try your self by doing some more operations with the help of your parents. You can also ask me your query if any by filling the Entry form available at top left tab of this blog.

Enjoy Learning Mathematics by creating such type of interesting things.

Anil Satpute