Introduction to study online associative theory:

Various websites are available in online to study about associative theory. Online is very useful to student studies. Online study reduces the student burdens. Many websites explain the concept of associative theory. Associative property state that alters in group does not change the answer that means the moving of brackets does not disturb the answer. Associative law contains two types of operations (addition and multiplications). Let us see study online associative theory in this article.

Study Online Associative Theory:

Associative theory:

Algebra has many laws. Associative law, distributive law and commutative law are the fundamental algebraic laws.

Associative property state that alters in group does not change the answer that means the moving of brackets does not disturb the answer. Associative law contains two types of operations.

They are

Addition
Multiplications
Associative theory of addition:

The associative property for addition state that grouping of numbers does not alter the result or answer.

x + (y + z) = (x + y) +z

Example:

5 + (1 +4) = (5 + 1) +4

LHS answer is 10 and RHS answer is 10. But the grouping of numbers is different in both sides.

Associative theory of multiplication:

Associative property for multiplication state that grouping of numbers does not alter the result or answer.

x * (y * z) = (x * y) * z

Example:

1 * (5 * 9) = (1 * 5) * 9

LHS answer is 45 and RHS answer is 45. But the grouping of numbers is different in both sides.

Associative theory is correct for both addition and multiplication operation but false for both subtraction and division.

Example Sums for Study Online Associative Theory:

Example 1:

4 + (7 + 3) = (4 + 7) + 3

4 * (7 * 3) = (4 * 7) * 3

From the above problem prove

1. Associative theory of addition

2. Associative theory of multiplication

Proof:

Associative theory of addition:

4 + (7 + 3) = (4 + 7) + 3

LHS:

4 + (7 + 3)

= 4 + (10)

= 14

RHS:

(4 + 7) + 3

=11 + 3

=14

LHS answer is 14 and RHS answer is 14. But the grouping of numbers is different in both sides. So the associative theory of addition is proved.

Associative theory of multiplication

Proof:

4 * (7 * 3) = (4 * 7) * 3

LHS:

4 * (7 * 3)

= 4 * (21)

= 84

RHS:

(4 * 7) * 3

= (28) * 3

= 84

LHS answer is 84 and RHS answer is 84. But the grouping of numbers is different in both sides. So the associative theory of multiplication is proved.

Example 2:

1 + (6 + 8) = (1 + 6) + 8

1 * (6 * 8) = (1 * 6) * 8

From the above problem prove

1. Associative theory of addition

2. Associative theory of multiplication

Proof:

Associative theory of addition:

1 + (6 + 8) = (1 + 6) + 8

LHS:

1 + (6 + 8)

= 1 + (14)

= 15

RHS:

(1 + 6) + 8

=7 + 8

=15

LHS answer is 15 and RHS answer is 15. But the grouping of numbers is different in both sides. So the associative theory of addition is proved.

Associative theory of multiplication

Proof:

1 * (6 * 8) = (1 * 6) * 8

LHS:

1 * (6 * 8)

= 1 * (48)

= 48

RHS:

(1 * 6) * 8

= (6) * 8

= 48

LHS answer is 48 and RHS answer is 48. But the grouping of numbers is different in both sides. So the associative theory of multiplication is proved.