# What Are The Five Properties of Multiplication – Examples

Learners!! you will find the answer of the question “what are the five properties of multiplication” here in this article. So start reading, five key properties of multiplication in mathematics are:

1. Commutative property: changing the order of the factors in a multiplication problem does not affect the result.. (a × b = b × a)
2. Associative property: changing the grouping of the factors does not change the product. ((a × b) × c = a × (b × c))
3. Distributive property: multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products. In mathematical terms, for any numbers a, b, and c, a × (b + c) = a × b + a × c.
4. Identity property: multiplying any number by 1 gives the same number. (a × 1 = a)
5. Zero property: multiplying any number by 0 gives 0. (a × 0 = 0)

## What Are The Five Properties of Multiplication

1. Commutative Property:
• Example: To find 7 x 8
• Step 1: Multiply 7 and 8 as 7 x 8 = 56
• Step 2: Reverse the order of numbers and multiply 8 and 7 as 8 x 7 = 56
• Result: The product remains the same, regardless of the order of numbers, which shows the Commutative Property of multiplication.
1. Associative Property:
• Example: To find (2 x 3) x 4
• Step 1: Multiply 2 and 3 as 2 x 3 = 6
• Step 2: Multiply the result (6) and 4 as 6 x 4 = 24
• Result: The product remains the same, regardless of grouping, which shows the Associative Property of multiplication.
1. Distributive Property:
• Example: To find 2 x (3 + 4)
• Step 1: Add 3 and 4 as 3 + 4 = 7
• Step 2: Multiply 2 and the result (7) as 2 x 7 = 14
• Result: The product of 2 and (3 + 4) can be found by distributing 2 to each addend and then adding the products, which shows the Distributive Property of multiplication.
1. Identity Property:
• Example: To find 5 x 1
• Step 1: Multiply 5 and 1 as 5 x 1 = 5
• Result: The product of 5 and 1 is the original number 5, which shows the Identity Property of multiplication.
1. Zero Property:
• Example: To find 3 x 0
• Step 1: Multiply 3 and 0 as 3 x 0 = 0
• Result: The product of any number and 0 is always 0, which shows the Zero Property of multiplication.

### Properties of Multiplication

The five properties of multiplication have numerous applications in mathematics, including:

• Simplifying expressions: By using the Commutative and Associative properties, the expressions can be rearranged to make the calculation process easier.
• Solving equations: By using the Distributive Property, the equations can be simplified and solved more efficiently.
• Multiplying decimals: The properties of multiplication can be used to perform operations with decimals, such as finding the product of a decimal and an integer.
• Multiplying fractions: The properties of multiplication can be used to perform operations with fractions, such as finding the product of two or more fractions.
• Word problems: The properties of multiplication can be applied to real-life scenarios, such as finding the total cost of items or the total distance traveled.
• Understanding patterns and relationships in numbers: By using the properties of multiplication, patterns and relationships in numbers can be explored and understood, which is important for further studies in mathematics.

In conclusion, the five properties of multiplication (Commutative, Associative, Distributive, Identity, and Zero) play a crucial role in mathematics.