Mathematics Village

·          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.