COMMUTATIVE AND ASSOCIATIVE PROPERTIES

About "Commutative and associative properties"

Commutative and associative properties :

The order in which you add or multiply numbers does not change their sum or product.

Commutative property of addition

Commutative property of addition is nothing but the rule which says that, when we are doing addition, it doesn't matter, in which order the numbers are.

We can add a and b or b and a  ... and we'll  get the same answer. 

More clearly,  a + b  =  b + a

Commutative property of multiplication

Commutative property of multiplication is nothing but the rule which says that, when we are doing multiplication, it doesn't matter, in which order the numbers are.  We can multiply a and b or b and a ... and we'll  get the same answer. 

More clearly,  a x b  =  b x a

Associative property

The way you group three or more numbers when adding or multiplying does not change their sum or product.

Associative property of addition

Associative property of addition is nothing but the rule which says that, when we are doing addition, it doesn't matter, in which order the numbers are.

We can add a, and c or aand c  ... and we'll  get the same answer. 

More clearly,  (a + b) + c  =  a + (b + c)

For any numbers a, b, and c,

(a + b) + c = a + (b + c)

Example :

(2 + 4) + 6  =  2 + (4 + 6)

Associative property of multiplication

Associative property of multiplication is nothing but the rule which says that, when we are doing multiplication, it doesn't matter, in which order the numbers are.  We can multiply ab and c or cb and ... and we'll  get the same answer. 

More clearly,(ab) c = a (bc)

Example :

 (3 ⋅ 5) 4  =  3 (5  ⋅ 4)

Example 1 :

Simplify 3(4x + 2) + 2x

Solution :

  =  3(4x + 2) + 2x

  =  3(4x) + 3(2) + 2x

  =  12x + 6 + 2x

  =  12x + 2x + 6

  =  14x + 6

Example 2 :

Simplify 7(ac + 2b) + 2ac

Solution :

  =  7(ac + 2b) + 2ac

  =  7(ac) + 7(2b) + 2ac

  =  7ac + 14b + 2ac

  =  7ac + 2ac + 14b

  =  9ac + 14b

Example 3 : 

Simplify 3(x + 2y) + 4(3x + y)

Solution :

  =  3(x + 2y) + 4(3x + y)

  =  3 (x) + 3 (2y) + 4 (3x) + 4 (y)

  =  3x + 6y + 12x + 4y

  =  3x + 12x + 6y + 4y

  =  15x + 10y 

Example 4 : 

Write an algebraic expression for half the sum of p and 2q increased by three-fourths q. Then simplify.

Solution :

 half the sum of p  ==>  (1/2) p

2q increased by three-fourths q  ==> 2q + (3/4) q

  =  (1/2) p +  2q + (3/4) q

  =  (p/2) +  2q + (3q/4)

  =  (p/2) +  (2q) x (4/4) + (3q/4)

  =  (p/2) +  (8q/4) + (3q/4)

  =  (p/2) +  (8q + 3q)/4

  =  (p/2) +  11q/4

Example 5 : 

Simplify 8 ⋅  1.6 ⋅  2.5

Solution :

=  8 ⋅  1.6 ⋅  2.5

=  (8 ⋅  1.6) ⋅  2.5

=  12.8 (2.5)

=  32

After having gone through the stuff given above, we hope that the students would have understood "Commutative and associative properties". 

Apart from the stuff given above, if you want to know more about "Commutative and associative properties", please click here

Apart from the stuff given on "Using properties of parallel lines", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...