SIMPLIFICATION..............

Distributive property for multiplication over addition:

 The product of a number ‘a’ with the sum of two numbers (b &c ) is equal to                       

 the sum of the products ab and ac.          a x (b + c ) = a x b + a x c        

 e.g. 2 x (3 + 4) = 2 x 3 + 2 x 4 = 14

Rules of Signs:

* To add two numbers with similar signs, add their absolute values and prefix the common sign.

   Thus: 2 + 5 = 7,      (- 4) + (- 5) = -9

* To add two numbers with opposite signs, find the difference between their absolute values and

   prefix the sign of the number with greater absolute value.

   Thus: 18 + (-7) = 11,         (-6) + 3 = -3,         (-18) + 12 = -6

* To subtract one number ‘x’ from another number ‘y’, change the operation to addition and

   replace ‘y’ by its opposite, - y. 

   Thus, 11 – (7) = 11 + (-7) = 4,

            (-9) – (5) = - 9 + (-5) = - 14

            2 – (-9) 2 + 9 = 11

* To multiply (or divide) two numbers having similar signs, multiply (or divide) their absolute

    values and prefix a plus sign (or no sign) e.g.

(4) (3) = 12,        (-5) (-4) = 20,               

* To multiply (or divide) two numbers having opposite signs, multiply (or divide) their absolute

   values and prefix a minus sign, e.g.

            (-3) (7) = - 21,                  (3) (-7) = - 21,    

Some Rules on Counting Numbers:

 1. Sum of the first n natural numbers = n x n+1

                                                               2

         For example:  1+2+3+4…….+108 = 108 x 109 = 5886                                                                          

                                                                  2

2. Sum of the first n odd numbers = n2

       For example:  1 + 3 + 5 + 7 + 9 + 11 = 36 (as there are 6 odd numbers).

3. Sum of the first n even numbers = n (n+1)

      For example: 2 + 4 + 6 + 8 +……..50 (or, 25th even number)

                              25 (25 + 1) = 650