Mathematics Village

     Note: Pie is an  irrational number and this actvity is to understand that pie is very near to 22/7

Try Yourself How many squares, of any size, can you find on this chess board that do not contain a Rook?   Answer: There are 116 squares without a rook. 1 x 1 : 61 squares. 2 x 2 : 37 squares. 3 x 3 : 15 squares. 4 x 4 :    3 squares.  

Multiplication of 2 two-digit numbers where the first digit of both the numbers are same and the last digit of the two numbers sum to 10 Example   To calculate 56 x 54 Multiply 5 by 5+1. So, 5 x 6 = 30. Write down 30.   Multiply together the last digits: 6 x 4 = 24. Write down 24.   The product of 56 and 54 is thus 3024.   Multiplication of two numbers that differ by 2  (This trick only works if you have memorized or can quickly calculate the squares of numbers. When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1. Example   18 x 20 =( 19 x 19) - 1 = 361 - 1 = 360   25 x 27 = (26 x 26) - 1 = 676 - 1 = 675   49 x 51 = (50 x 50 ) - 1 = 2500 - 1 = 2499     Multiplication of two numbers that differ by 4 (This trick only works if you have memorized or can quickly calculate the squares of numbers.   If two ...

·          Draw a Quadrilateral ABCD on colour chart Sheet . ·          Cut such four Quadrilaterals on four different sheets. ·          Mark Ð A as Ð 1 ,   Ð B as Ð 2 , Ð C as Ð 3 and Ð D as Ð 4 on each quadrilateral as shown in fig . ·          Arrange all four angles of quadrilateral one from each colour at one point. ·          What you observe ? ·          It forms a complete angle i.e 360 0 ·          This shows that sum of all angles of quadrilateral is 360 0    

Squaring   Let us take advantage of   algebraic identity. A 2 = ( A - d )( A + d ) + d 2 Naturally, this formula works for any value of d , but we should choose d to be the distance to a number close to A that is easy to multiply. Examples. To square the number 23, we let d = 3 to get 23 2 = 20 x 26 + 3 2 = 520 + 9 = 529 :   To square 48, let d = 2 to get 48 2 = 50 x 46 + 2 2 = 2300 + 4 = 2304 :   With just a little practice, it's possible to square any two-digit number in a matter of seconds. Once you have mastered those, we can quickly square three-digit numbers by rounding up and down to the nearest hundred. Examples. 223 2 = 200 x 246 + 23 2 = 49 ; 200 + 529 = 49 ; 729 952 2 = 1000 x 904 + 48 2 = 904 ; 000 + 2 ; 304 = 906 ; 304 : To do mental calculations of this size, one needs to be quick at multiplying 2-digit and 3-digit numbers by 1-digit numbers, generating the answer from left to right.