Distributive Laws

It says that multiplying a number by a group of numbers added together is same as doing each multiplication separately. 

1. a * ( b + c ) = a * b + a * c

Examples : 

1. 7 * (50 - 2 )
   = 7 * 48
   = 336
lets rearrange
( 7 * 50 ) - (7*2)        [ here, a * ( b - c ) = a * b - a * c]
=350 -14
= 336 

2. 625 * (-35) + ( -625 ) * 65 
 that is ,  [ 625 * (-35) ] +  [ ( -625 ) * 65 ]
              = (-21,875 ) + ( -40,625 )
              = - 62,500
lets rearrange
[ 625 * (-35) ] +  [ ( -625 ) * 65 ]
here, 625 is common in both , so lets take 625 out
that is, 625 * ( -35 - 65 ) 
          = 625 * -100
          = - 62,500

Associative Laws

Associative Laws

It means that it doesn't matter how we group the numbers.

1. ( a + b ) + c = a + ( b + c )
2. ( a * b ) * c = a * ( b * c ) 

Examples :

1. ( 3 + 2 ) + 5
   = 5 + 5
   = 10
lets regroup it,
 3 + ( 2 + 5 )
= 3 + 7
= 10

2. ( 3 * 2 ) * 5
   = 6 * 5
   = 30 
lets regroup it,
3 * ( 2 * 5 )
= 3 * 10
 = 30 

Commutative Law

Commutative Law

The Commutative laws which means we can swap numbers over and still get the same answer when we add or multiply.

1. a + b = b + a
2. a * b = b * a

Examples : 

1. 3 + 4 = 7
now, lets swap
  4 + 3 = 7
even if we swap we are getting same answer 7.
 
2. 3 * 4 = 12
    4 * 3 = 12
 
3. 8 * 53 * (-125)
   = 424 * (-125)
   = -53,000
lets swap
   53 * (8*(-125))
 = 53 * (-1000)
 = -53,000
even if we swap we are getting same answer -53,000

NOTE :
 - *- = + 
 + * + = +
 + * - = -
 - *+ = -

4. 15 * (-25) * (-4) * (-10)
   = [15 * (-25) * (-4) ] * (-10)
   = 1500 * (-10)
   = -15,000 
lets swap
15 * (-25) * (-4) * (-10)
   =  (-25) * [15 * (-4)  * (-10)]
   =  -25 * 600
   = -15,000