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Properties of Multiplication

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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)

properties of multiplication 4

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:

properties of multiplication

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:

properties of multiplication 2

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).

properties of multiplication 5

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.

properties of multiplication 3

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.

These are the five properties of multiplication. If you want to learn more elementary math,  sign up for free at Smartick.

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