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Math for Kids23 chapters | 325 lessons

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Instructor:
*Audrey Akins*

Audrey has more than a decade of experience teaching elementary. She has a bachelor's in journalism and a master's in education.

In this lesson, we'll discuss multiplications properties. You'll learn about the four properties of multiplication and how they work, then you can test your knowledge with a quick quiz.

Learning how to multiply doesn't have to be hard. There are four **multiplications properties** that can help make the process easier: the identity, commutative, associative and distributive properties. They provide rules for quickly solving multiplication problems according to properties that always apply to certain equations. Let's explore these multiplications properties below.

The rule for the identity property is that a number multiplied by 1 will always yield that number as the answer, or product. Think of it like this: When multiplied by 1, a number does not change its identity--it always stays the same.

Imagine a superhero named 7 Man, dressed up in a mask and cape. When 1 comes at him to try and change him, 7 Man goes unaltered. He comes out of the multiplication problem just the same, wearing his mask and cape. So, 7 x 1 = 7.

Commutative property states that two numbers multiplied together will always produce the same answer no matter which number is first or second in the problem. This means 12 x 3 = 36 and 3 x 12 = 36. The same for 7 x 9 = 63 and 9 x 7 = 63. The rule works for any two numbers being multiplied together.

Similar to the commutative property is the associative property. The rule for the associative property is that when three numbers are multiplied together, the product will always be the same no matter which number is first, second, or third. For example, 2 x 3 x 5 = 30 and 5 x 3 x 2 = 30. Also, 3 x 5 x 2 = 30.

Distributive property says that when you have an equation such as 2 x (3 + 4), the answer will be the same, whether or not you choose to solve it the way it's written or to distribute before solving: (2 x 3) + (2 x 4). We'll solve the problems both ways to clarify.

- For the problem 2 x (3 + 4), you will first add 3 + 4 to get 7. Then, you'll multiply 7 x 2 to get 14.
- For the distributed version of this problem, (2 x 3) + (2 x 4), you will multiply each side: 2 x 3 = 6, while 2 x 4 = 8. The, simply add the two products: 6 + 8 = 14.

So, when you see an equation that requires you to distribute the number outside the parenthesis, you can solve the problem two different ways and still get the same answer.

The identity property means that a number multiplied by 1 will always stay the same. The commutative property says that when you're multiplying two numbers, you'll get the same answer no matter which number comes first in the problem, and similarly, the associative property says you'll get the same answer when multiplying three numbers no matter what order they're in. The distributive property states that you can either solve a problem in the parenthesis or distribute before solving to get the same answer.

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Math for Kids23 chapters | 325 lessons

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