The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property,
Associative Property, Identity Property and Distributive Property. In this lesson, we will learn the
associative property and identity property of numbers.
Related Topics:
Commutative Property
Distributive Property
The following table summarizes the number properties for addition and multiplication: Commutative, Associative and Identity. Scroll down the page for more examples, explanations and solutions.
The associative property states that the sum or product of a set of numbers is the same, no matter how the numbers are grouped.
An operation is associative if a change in grouping does not change the results. This means the parenthesis (or brackets) can be moved.
Numbers that are added can be grouped in any order.
For example: | (4 + 5) + 6 = 5 + (4 + 6) |
(x + y) + z = x + (y + z) |
Numbers that are multiplied can be grouped in any order.
For example: | (4 × 5) × 6 = 5 × (4 × 6) |
(x × y) × z = x × (y × z) |
Numbers that are subtracted are NOT associative.
For example: | (4 – 5) – 6 ≠ 5 – (4 – 6) |
(x – y) – z ≠ x – (y – z) |
Numbers that are divided are NOT associative.
For example: | (4 ÷ 5) ÷ 6 ≠ 5 ÷ (4 ÷ 6) |
(x ÷ y ) ÷ z ≠ y ÷ ( x ÷ z) |
When you add 0 to any a number, the sum is that number.
For example: 325 + 0 = 325.
When you multiply any number by 1, the product is that number.
For example: 65, 148 × 1 = 65, 148
The product of any number and 0 is 0
For example: 874 × 0 = 0
Identity Property of Addition & Multiplication
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