Associative Property Formula

Associative Property

A fundamental idea in mathematics, the associative property demonstrates a characteristic of some binary operations. Associativity is a legitimate rule of replacement for expressions in logical proofs in propositional logic. No matter how the numbers are grouped, you can add or multiply, according to the associative property. In layman’s terms, associative property is the grouping of numbers. Any type of computation that requires regrouping depends on the application of this technique.

What is Associative Property?

A mathematical principle known as the associative property explains the significance of grouping numbers together while performing mathematical operations. The associative property of mathematical operations is the property of numbers that states that no matter how the numbers are ordered while adding, subtracting, or multiplying, the overall result of the operations will not change. ‘The way we employed brackets’ is implied by the phrase ‘here ordered’. In other words, regardless of how the numbers are organised or parenthesized, the result of adding three or more numbers is the same.

One of the three key characteristics of mathematical operations, and particularly for addition, is the associative feature. We will learn the associative property formula, associative property formula, and associative property in this post.

Formula of Associative Property

Mathematical operations like addition, multiplication, subtraction, and others are all about playing with numbers. Even these basic operations are subject to a set of restrictions, just like any other operation. One such crucial requirement that needed to be adhered to throughout addition and multiplication is the associative property. No matter how the numbers are arranged or how the brackets are used between the numbers, we can multiply and add the numbers in an equation. The formula used to prove this rule is called the associative law formula.

As a result, only addition and multiplication operations are compatible with the associative attribute. The associative property of multiplication formula and the associative property of addition formula are corresponding associative property equations.

Associative Property of Addition Formula

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

Associative Property of Multiplication Formula

                                                                             (a × b) × c = a × (b × c)

Difference between Associative Property and Commutative Property

Commutative Property

 The term “commutative property” refers to the idea that no matter how two numbers are arranged, when they are multiplied or added, the result is always the same.

Now that you are aware of both features, you must have deduced that the only distinction is the quantity of numbers required to carry out the operation.

Commutative property involves two numbers, while associative property involves more than two numbers.

Does division and subtraction fall under the associative property?

You must be asking why division and subtraction are exempt from these properties. Let’s use an illustration to address this “Why?”

Fun Fact!

The word “associate” serves as the basis for the name of the associative property, which describes how numbers are grouped.

Question 1

If (42 × 15) × 87 = 55125, then use associative property to find (15 × 42) × 87.

Solution: 

To the associative property of multiplication, (42 × 15) × 87 = (15 × 42) × 87.

Given that (42 × 15) × 87 = 55125,

(15 × 42) × 87 = 55125.

Question 2

According to the associative property, fill in the missing number.

(12 + 27) + 8 = (12 + 8) + __ = 27

Solution:

According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped. Hence, (12 + 27) + 8 = (12 + 8) + 27 = 47.

Question 3

Solve 4 × (5 × 3) using Associative Property of Multiplication.

Solution:

4 × (5 × 3)

= (4 × 5) 3

= 20 × 3

= 60