COMMUTATIVE LAW :- Commutative law states that,
a + b = b + a
For eg. 2 + 3 = 5 or
3 + 2 = 5 ( in both the cases answer is same )
a * b = b * a
For eg. 3 * 2 = 6 or
2 * 3 = 6
ASSOCIATIVE LAW :- Associative law states that,
( a + b ) + c = a + ( b + c )
For eg. ( 2 + 3 ) + 5 = 2 + ( 3 + 5 )
( a * b ) *c = a * ( b* c )
For eg. ( 2 * 4 ) * 3 = 2 * ( 4 * 3 )
DISTRIBUTIVE LAW :- Distributive law states that,
a * ( b + c ) = a * b + a * c
For eg. 3 * ( 2 + 4 ) = 18 or
3 * 2 + 3 * 4 = 6 + 12 = 18
MULTIPLICATION BY $5^{n}$ :-
Suppose we find the product, N * $5^{n}$
Method :- Put n zeros to the right of N and divide it by $2^{n}$.
For eg. 75819 * 25 = ?
75819 * $5^{2}$
= 75819 * $\left ( \frac{10}{2} \right )^{2}$
= $\frac{75819 * 100}{4}$
DIVISION ALGORITHM :- If we divide a number by other number, then
DIVIDENT = ( DIVISIOR * QUOTIENT ) + REMAINDER
SOME SERIES :-
(1.) Sum of all the first n natural numbers -
i.e. ( 1 + 2 + 3 + ......... + n ) = $\frac{1}{2}n (n+1)$
(2.) Sum of first n odd numbers -
i.e. ( 1 + 3 + 5 + ..........+ n) = $n^{2}$
(3.) Sum of first n even numbers -
i.e. ( 2 + 4 + 6 + ..........+ n) = n (n + 1)
(4.) Sum of squares of first n natural numbers -
i.e. $(1^{2}+2^{2}+3^{2}+.... +n^{2})=\frac{1}{6}n(n+1)(2n+1)$
(5.) Sum of cubes of first n natural numbers -
i.e. $(1^{3}+2^{3}+3^{3}+.... +n^{3})=\frac{1}{4}n^{2}(n+1)^{2}$
a + b = b + a
For eg. 2 + 3 = 5 or
3 + 2 = 5 ( in both the cases answer is same )
a * b = b * a
For eg. 3 * 2 = 6 or
2 * 3 = 6
ASSOCIATIVE LAW :- Associative law states that,
( a + b ) + c = a + ( b + c )
For eg. ( 2 + 3 ) + 5 = 2 + ( 3 + 5 )
( a * b ) *c = a * ( b* c )
For eg. ( 2 * 4 ) * 3 = 2 * ( 4 * 3 )
DISTRIBUTIVE LAW :- Distributive law states that,
a * ( b + c ) = a * b + a * c
For eg. 3 * ( 2 + 4 ) = 18 or
3 * 2 + 3 * 4 = 6 + 12 = 18
MULTIPLICATION BY $5^{n}$ :-
Suppose we find the product, N * $5^{n}$
Method :- Put n zeros to the right of N and divide it by $2^{n}$.
For eg. 75819 * 25 = ?
75819 * $5^{2}$
= 75819 * $\left ( \frac{10}{2} \right )^{2}$
= $\frac{75819 * 100}{4}$
= $\frac{7581900}{4}$
= 1895475.DIVISION ALGORITHM :- If we divide a number by other number, then
DIVIDENT = ( DIVISIOR * QUOTIENT ) + REMAINDER
SOME SERIES :-
(1.) Sum of all the first n natural numbers -
i.e. ( 1 + 2 + 3 + ......... + n ) = $\frac{1}{2}n (n+1)$
(2.) Sum of first n odd numbers -
i.e. ( 1 + 3 + 5 + ..........+ n) = $n^{2}$
(3.) Sum of first n even numbers -
i.e. ( 2 + 4 + 6 + ..........+ n) = n (n + 1)
(4.) Sum of squares of first n natural numbers -
i.e. $(1^{2}+2^{2}+3^{2}+.... +n^{2})=\frac{1}{6}n(n+1)(2n+1)$
(5.) Sum of cubes of first n natural numbers -
i.e. $(1^{3}+2^{3}+3^{3}+.... +n^{3})=\frac{1}{4}n^{2}(n+1)^{2}$
No comments:
Post a Comment