The nature of multiplication room distributive, commutative, associative, remove a common factor and the neutral element.

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We are dedicating this article to assessing the nature of multiplication, which room the following:

Distributive property: The multiplication of a number through a amount is equal to the sum of the multiplications of this number by each among the amounts to it is in added.

Lets take for example: 2 x (3 + 5)


According come the distributive home 2 x (3 + 5) will certainly be same 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 offer us 16 together a result, which mirrors that the distributive home of multiplication works.

Commutative property: The stimulate of the factors does not readjust the product.

Let’s look at an example of the commutative property:


The result of multiplying 10 x 3 will certainly be equal to multiplying 3 x 10. Return we adjust the bespeak of the factors, the result is tho 30.

Associative property: The mode of group the factors does not adjust the result of the multiplication.

Let’s take an example of the associative building of multiplication:


In this case, as we display in the image, it offers us the same result if us multiply 3 x 2 and then main point the an outcome by 5 together if we multiply 2 x 5 and then multiply the result by 3.

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

Let’s look at an instance of removed a usual factor. If we have the operation (2 x 7) + (3 x 7), which has actually 7 together a usual factor, we can transform this operation into 7 x (2 + 3).


Let’s examine that removing the common factor provides us the same result:

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

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

This mirrors that this property of multiplication works.

Neutral Element: 1 is called the identity of multiplication due to the fact that every number multiplied by chin is simply the very same number.


In the example that we display in the image, we view that if us multiply 5 or 7 by 1, we acquire as a an outcome 5 or 7. So any kind of number that us multiply by 1 provides us, together a result, the very same number.

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These space the five properties of multiplication. If you desire to learn more elementary math, authorize up for totally free at