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## Determine Property of Multiplication

#### Introduction

When you multiply numbers together, there are four key properties (or rules) you need to follow in order to make sure your answers are correct. These are:

• The cumulative property
• The associative property
• The multiplicative identity property
• Distributive property

Learning these rules will help you to manage numbers more easily and avoid small mistakes.

## Lesson

The four properties of multiplication are the commutative property, the associative property, the multiplicative identity property, and the distributive property. You have to use these each time you multiply numbers, and you can use more than one rule at a time.

### Commutative Property

The commutative property of addition means that the order you multiply numbers doesn't make a difference to the final sum.

For example: 6 x 3 x 2 = 36 3 x 2 x 6 = 36 2 x 6 x 3 = 36

Whatever order we put the numbers, we still get the same result.

### Associative Property

The associative property of multiplication means that however you group numbers (with parenthesis) the end result will not make a difference to the final sum.

For example:

4 x 5 x 2 x 3 = 120 (4 x 5) x 2 x 3 = 120 4 x (5 x 2) x 3 = 120

Also, because of the commutative property, we can shuffle the order as well and it won't change the result:

3 x 5 x (4 x 2) = 120

### Multiplicative Identity Property

The multiplicative identity property means that whatever number you multiply by 1, the answer will be the original number.

For example:

8 x 1 = 8 1 x 165 = 165 7,257,398 x 1 = 7,257,398

### Distributive Property

The distributive property means that if you multiply a number by the sum of a parenthesis, it is the same as multiplying the number by each number in the parenthesis individually.

For example:

8(3 + 4) = 8(7) = 56 (8 x 3) + (8 x 4) = (24) + (32) = 56

## Examples

(33 * 58) * 40 = 33 * (58 * 40)
When three or more numbers are multiplied, the product is the same regardless of the grouping of the numbers
This is called the Associative Property of Multiplication
41 * 43 = 43 * 41
When two numbers are multiplied, the product is the same regardless of the order of the numbers
This is called the Commutative Property of Multiplication
52 * 0 = 0
Any number times zero is zero
This is called the Multiplication by Zero