The Associative Property

The associative property in math says that if you change the order of terms while doing mathematical operations, the result remains the same.

The Associative Properties:

1. The Associative Property of addition:

The associative property of addition states that changing the grouping of the addends does not change the resulting sum.

Say for example I give you 1 ice cream then 2 and then three. If you add then like (1 + 2) + 3 or 1 + (2+3) the result comes to be 6. In short, addition is associative.

is same as

Conclusion: Addition is associative. (A +B ) + C = A + (B + C)

2. The Associative Property of Subtraction:

In the case of subtraction, if the order is changed the result is different.

(1 – 2) -3 ≠ 1 – (2 – 3)

 Conclusion: Subtraction is not associative A − (B − C) ≠ (A − B) − C.

3. Multiplication:

In the case of multiplication, the property states that changing the grouping of the factors does not change the resulting product, so (2 • 3) • 4 = 2 • (3 • 4). It is a good example of associative property.

Conclusion: (A • B) • C = A • (B • C).

4. Division:

While we talk about the sequence in the case of division, let’s say I am dividing (12 ÷ 3) ÷ 2 and 12 ÷ (3 ÷ 2), these both are not equal.

Conclusion: (A ÷ B) ÷ C ≠ A ÷ (B ÷ C)

Difference between associative property and commutative property

Notice that you can distinguish the associative property from the commutative property by observing that in the associative property, the order of each of the terms is not changed.

Also as the commutative property was not satisfied by subtraction and division, the associative property couldn’t be fulfilled as well.

Distributive Property:

The distributive property involves both multiplication (or division) and addition or (subtraction) and can sometimes be used to simplify certain algebraic expressions. It states that 2(3 + 4) = 2 • 3 + 2 • 4, or 2(3 – 4) = 2 • 3 – 2 • 4. Notice that in both these cases, factor 2 is applied or distributed to each term given in parentheses.

Identity Property:

In addition to the three basic properties given above, there is an identity property for addition and multiplication. In addition, the identity property is also called the adding zero property which states the sum of any number and zero is that number, or 3 + 0 = 3. For multiplication, the identity property is also called multiplying by one property which states that the product of any number and 1 is that number, or 3 • 1 = 3.

For more details about these properties click here