8th Lesson of Mathematics Tricks and Fun

8th Lesson of Mathematics Tricks and Fun

Hello friends this is the 8 lesson of mathematics tricks and fun. I am Dr Prema B Sejekan. We are going to study in this class on squaring and multiplication of numbers with digits in random.

According to the Sutra Antyayor Dasake pe if in units place you get

  5 + 5, 7 + 3, 8 + 2 , 6 + 4 , 9 + 1 that is unit place digits added together if you get 10 and the second clause says in the tens place you get 1 + 1, 2 + 2, 3 + 3 that is the same digits .If these conditions are met with , then add 1 to tens place one digit and multiply as shown in the examples.This is a sub corollary of Ekadhikena purvena which itself is a corollary of Nikhilam sutra

Here we have to find out the square of 25 .5+5 is 10, and in ten's place it is 2 ie same digit. So we will increase one 2 to 3 and multiply straight. Ie 5×5= 25 we will write next to it in 100s place we will write 6 ie 3×2 Answer is 625. How easy and quick it is.

In the second example in units place we have 7 and 3 which gives 10 when added..Then in ten's place we have two 7s. Ie same digit . So increase one seven to 8 and multiply straight. Ie 7×3 = 21 next to it we will insert 56 ie 7×8 . So the answer is 5621.

This is multiplication by Urdhwa Tiryagbhyam Sutra. Ie multiply vertically and and crosswise.In this we are multiplying two digit number. Multiply straight on the sides and middle crosswise. So 7×6 is 42 5×6 and 7×8 added gave 86 then 8×5 is 40 Thus final answer is ,5100.

Nikhilam Sutra says all from nine and last from 10 . we find the complement of number and multiply . 98 by 97 .base is 100 here. So 100- 98 is 02 and 100 -97 is 03.We will write this as

(98- 02)× (97-03) . So multiply straight ie 02×03 = 06. Now *add or subtract crosswise accordingly’ by the Sutra. So here we have to subtract (98-03) or( 97-02 ) = 95. Thus the answer is 9506

ThisAnurupyena sutra is a sub corollary of Nikhilam sutra. Find the ratio and adjust proportionately. Here square of 54 is the question.since 54 is near 50 , we will see the ratio. Ie 100/2 is 50 or 5× 10 is 50

In this we will take base 100/2 so 54+04 .so square of o4 is 016 .Now 54+04= 58 now we will divide 58 by 2 .Thus the final answer is 2916

This is continuation of Anurupayena sutra 45 X 37 Here we take the base 5 × 10 is equal to 50. So( 45 - 5 ) and(37 - 13 )so multiply vertically straight and subtract crosswise .we get 160 and 65 . 6 is added to 160 , we get 166 so the answer is 1665.

 when we have to multiply a big number by 5 or multiples of 5 it is easy when you find its relation with next 10 or 100 or 100 etc. .Then multiply with this number and divide accordingly. Here when you have to multiply with 5 what you can do ? Multiply the number by 10 and divide the product by 2. When we have to multiply by 25 we can put two 00s to the multiplicand and the whole product can be easily divided by 4.in thecase of multiplication with 125 we have to put three 000s and divide by 8. When 625 is the multiplier then put four 0000s and divide   by 16.

  In the coming class we will

    recapitulate the various

     methods available to us in 

     the squaring of numbers.

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