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## Properties of Multiplication

###### The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

We are dedicating this post to examining the properties of multiplication, which are the following:

• Distributive property: The multiplication of a number by a sum is equal to the sum of the multiplications of this number by each one of the amounts to be added.

Lets take for example: 2 x (3 + 5) According to the distributive property 2 x (3 + 5) will be equal to 2 x 3 + 2 x 5.

Lets check if this is true.

2 x (3 + 5) = 2 x 8 = 16

2 x 3 + 2 x 5 = 6 + 10 = 16

Both give us 16 as a result, which shows that the distributive property of multiplication works.

• Commutative property: The order of the factors does not change the product.

Let’s look at an example of the commutative property: The result of multiplying 10 x 3 will be equal to multiplying 3 x 10. Although we change the order of the factors, the result is still 30.

• Associative property: The mode of grouping the factors does not change the result of the multiplication.

Let’s take an example of the associative property of multiplication: In this case, as we show in the image, it gives us the same result if we multiply 3 x 2 and then multiply the result by 5 as if we multiply 2 x 5 and then multiply the result by 3.

• Removing a common factor: This is the inverse property of the distributive property. If various addends have a common factor, we can transform the sum into a product by taking out this factor.

Let’s look at an example of removing a common factor. If we have the operation (2 x 7) + (3 x 7), which has 7 as a common factor, we can transform this operation into 7 x (2 + 3). Let’s check that removing the common factor gives us the same result:

(2 x 7) + (3 x 7) = 14 + 21 = 35

7 x (2 + 3) = 7 x 5 = 35

This shows that this property of multiplication works.

• Neutral Element: 1 is called the identity of multiplication because every number multiplied by itself is just the same number. In the example that we show in the image, we see that if we multiply 5 or 7 by 1, we get as a result 5 or 7. So any number that we multiply by 1 gives us, as a result, the same number.