Check for accuracy of a product

Subject:  How to check for the accuracy of product of two numbers.
                   Example           123476
                                              x 654879
                                            7645983254
      Now to check for the accuracy no need to go to the actual product. Follow the following simple steps.
1.    add all the digits of the first number i.e. 1+2+3+4+7+6= 23
2.  divide it by 9 and record the remainder i.e. 23 /9 , remainder = 5
3. add all the digits of second number 6+5+4+8+7+9 = 39
4.  divide it by 9 and record the remainder i.e. 39 /9 , remainder = 3
5.  multiply the two remainders i.e. 5x3 = 15
6.  divide the number obtained in step 5 by 9 and record the remainder. i.e. 15/9, remainder = 6
7.  add all the digits of the product of two numbers i.e. 7645983254 you get
      7+6+4+5+9+8+3+2+5+4= 53
8.  divide it by 9 and record the remainder i.e. 53 /9 , remainder = 8
Conclusion: If remainders obtained in step 6 and 8 are equal then your product is correct otherwise wrong.
Clearly above product is wrong. As remainder in step 6 is and that in step 8 is 8 , unequal. 

Vedic Mathematics

How to multiply two numbers which are near 100.

Example:  1.   95x96

                       95       -5

                   X  96      -4               either 95 – 4 = 91

                     9120                       Or       96 – 5 = 91

                                                    And   -5x-4 = 20

Example:  2.   102x105

                       102       +2

                   X  105      +5            either 102 + 5 = 107

                     10510                     Or       105 + 2 = 107

                                                    And   5x2 = 10

Now multiply 96 and 99

          Multiply 89 and 97

                  Vedic Mathematics

Subject:         How to square a number ending with 5

Formula:       Ekadiken purven

Meaning:      One more than the previous one.

Method:       To make square of  a number which has 5 at its unit place, take the number leaving out 5 , add one in it. Now multiply them and write 25 after the product so obtained. You will get the square of that number.

Example:           (25)² = (2x3)25 = 625

                        (35)² = (3x4)25 = 1225

                        (45)² = (4x5)25 = 2025  e.t.c

                        Now make practice for other numbers yourself i.e.

                      Find square of 55

                      Find square of 75

                      Find square of 85

PARABOLA

What is parabola? Where this appear? What is the use of  it? Why we study conic sections and the parabola? These are the general question arise in students mind. And the answer is just question and answer of various label i.e. easy to very difficult. After doing a lot of problem students get nothing. As a result students lose their interest and forget in time span.
Study of parabola , ellipse and hyperbola must be based on reality. Teacher must visualize these conics in their surrounding. For example, there is a hanging bridge on the river Ganga in Rishikesh. The bridge has no pillars. A long iron rope is tied with two poles situated on two banks of the river and the whole bridge is hanging with some vertical supporting ropes. The long iron rope which is tied with two pillars and the vertical ropes takes the shape of a parabola.