7th Lesson Mathematics Tricks and Fun squaring of same digit numbers by arithmetic progression

7th Lesson Mathematics Tricks  and Fun squaring of same digit numbers by arithmetic progression 

Hello friendds,Welcome to the 7 lesson of mathematics tricks and fun I am Dr Prema B Sejekan .In this class, we will be studying, the squaring of numbers with the same digits. In fact this is a continuation of the previous class where we have studied squaring of numbers like111, 2222 555, 4444, Here we will deal with 7777,888, and multiplication of same ddigits but unequal.!ike 7777× 77777,2222× 22:33333× 333 etcc

In this slide squaring of 777 is done. First 7 × 7= 49 . Now write 4 on the lateral side of the multiplicand and 9 on thhe lateral side of the multiplier. 4+9= 13 So start adding 13 to 4 .This is 17 Again add 13 to 17 =30. We will stop here since only 3 digits.we wtll start with 9 on the multiplier side add 13 to 9.we get 22, to this add 13 we get 35.So adding , total is 603729

  Here there are 14 digits totally. 7 on the multiplicand side 7 on the multiplier . We will start multiplying 7 with 7 . the answer is 49. We will put 4 on the lateral side of the multiplicand and 9 on the lateral side of the multiplier. Then adding 13 with 4 on the multiplicand side we get 17 . 17 + 13 is 30, 30 + 13 is 43 . 43 + 13 is 56 . 56 + 13 = 69. 69 plus 13 is. 82 . We will stop at that Then we will go to the multiplier side and 13 added to 9,=22 ,22 + 13 =35 , 35 + 13 = 48, 48 + 13 = 61, 61 + 13 =74 ,74 plus 13 =87 . then adding all the carry overs , we get the answer 6049 381 506172 9

  In this slide 888×888 we willfirdt multiply 8 ×8.we get 64..put 60 n multiplicand side laterally and 4 on multiplier side laterally.Now 6+4 is 10 . Adding 10 to 6 we 16, tthen 26. Then on multiplier side 4 + ,10 is ,14 adding 10 to 14 we ger 24 Then adding all carry overs we get 788544

  There are 14 digits 7 each on either side.we will proceed putting 6 and 4 on either side and adding 10 to all from both sides we get 6,16,26 like that till 66 on multiplicand side .Then adding 10 to 4 we get 14.24.,34 etc till 64.Adding all carry overs we get 79013329876544

  We're going to multiply 2222 with 22 . There are 2 2 extra so we group them into three groups .Extra digits we will insert in the middle group. Now we will start from the lateral siide of the multiplicand as usual . 2 into 2 is 4. So we will write zero on the lateral side of the multiplicand and 4 on the lateral side of the multiplier. Now adding from both sides 0+ 4is 4. Only 2 digits here . We will start from the multiplier side Adding 4 with 4 is 8. We will stop that . now what will we put in the middle 0 + 8 or 4 + 4 is 8 so that the digits are 88 we will write in the middle. So the answer is 04 88 84 In the other example there are four 2s X three 2s so from multiplicand side we will write 048 , then from the multiplier side we will write 4 8:12 . now the middle will be 12 as said earlier 0+ 12 or 8 plus 4 both is 12 Adding the carry overs the answer is 0493 284

  In this slide 4444 is multiplied by 44 so the answer is 1, 8 from the other side 6, 13 so the middle is occupied by 14 , 14. 1 + 13 14 or 8 + 6 is so the extra digits places are occupied by 14s adding the carry over the answer is 19 5536

   In the second example one extra digit . So the answer is 18 from the other side 6 and13 and the middle is 14 so adding 19536

   Now we will do the multiplication with 5 5555 is multiplied by 555 Here 5 into 5 is 25 so we will put 2 on multiplicand side laterally and 5 on the multiplier side laterally .Then adding 2 plus 5 is 7 then adding 7 from both side 2 + 7 is 9 and 9 + 7 is 16 will stop there.. then we will go to the multiplier side. 5 ,5 + 7 is 12, 12 + 7 is 19 now what will be the middle digit now 16 + 5 is 21 or 2 + 19 is 21 so adding over the carry overs we will get 308 3025.

    55555 X 555 . here we will start as usual to 5 into 5 is 25 . 2 on the lateral side of the multiplicand and five on the lateral side of the multiplier So 2 + 7 is 9 + 7 is 16 then from the multiplier side 5 plus 7 12 , 12 + 7 is 19 . 16+5 or 19+2 =21 . So the middle will be occupied by 21, The answer is 308 33 025.

    Here six 7s X three. 7s. 7 x 7 is 49 will put 4 on the lateral side multiplicand and 9 on the lateral side of the multiplier. 4 + 7 is 13 adding 13 with 4 we get 17, 17 plus 13 is 30 because only three digit here on the multiplicand we will stop there and go to multiplier side. 9 + 13 is 22, 22 + 13 is 35 now what will be the middle digit there are three digit so we have to fill up the middle 3 digits now 30 + 9 is 39 or 35 + 4 is 39 Three 39s will put in the middle so adding the carriy overs we will get

 604 332 729 as answer.

    888888 multiplied with 888. so the 888 are extra 8 × 8 is 64 . Now 6 will put on the multiplicand side and 4 on the multiplier side . 6 + 4 is 10. adding 6 + 10 is 16 , 16 + 10 , 26 will stop that . From the multiplier side 4 + 10 is 14, 14 + 10 is 24 now the middle digits 26 + 4 is 30 or 24 + 6 is 30 so the middle digit is 30 We will fill up 30 30 30 in the middle. Then adding the carry overs .the answer is 789 332 544 .

    In the coming classes we will study squaring and multiplication of numbers with digits in random. thank you