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Commutative Property of Multiplication
CCSS.MATH.CONTENT.3.OA.B.5

## Commutative Property of Multiplication

It's family movie day! But wait, something seems different today in the movie theater. The seats are set in four rows of eight and eight rows of four! So how many people can sit in each section?

In order to answer this question, we have to learn to define the commutative property of multiplication. The above video and the following text for the third grade teach us everything we need to know about the commutative property of multiplication, along with some examples. Once we find out how many people are going to watch with us, we can settle in for the movie.

## What Does the Commutative Property of Multiplication State?

The commutative property of multiplication definition states that the order of multiplication does not matter; the product will remain the same. So what exactly does commutative property of multiplication mean? It means if you rearrange a multiplication sentence, the solution will still be the same. For example, you might rewrite two times five as five times two. This would not affect the product, which is ten for both!

If you are now wondering “what is an example of commutative property of multiplication?”, then read on for a step by step example and explanation!

## Commutative Property of Multiplication – Example

Here is an example of commutative property of multiplication.

First, we write out our multiplication sentences two different ways. Here, we will use four times eight and rewrite it as eight times four: Solving four times eight first, we can see the product is thirty-two. We can even check this using the array with four rows of eight to help us: Now we can solve eight times four, which we can also see has a product of thirty-two. Again, we can check this using the array with eight rows of four to help us: As you can see, both ways of solving the problem still gave the same product. This is what the commutative property of multiplication teaches us! This means that 32 people can sit in each section of the movie theater.

Multiplication Product
4 x 8 32
8 x 4 32

## Commutative Property of Multiplication – Review

Remember, the order of multiplication will not change the product. You can rearrange multiplication sentences to make it easier for yourself, as you might know certain multiplication facts more than others.

Now you know the answer to the two questions “what is the definition of commutative property of multiplication?” and “what is the commutative property of multiplication?”. You also know how to use the commutative property of multiplication, which means you are ready to try some commutative property of multiplication example problems and worksheets on your own. Have fun!

### TranscriptCommutative Property of Multiplication

"I have never been on the red carpet for a movie before, Imani. How did you manage this?" "Oh, I just happened to get VIP tickets." "The auditorium has two sections. I wonder how many people can sit in each one?" "A quick scan tells me there are four rows of eight in the front, and eight rows of four at the back." "Hmm, I wonder how we can solve this?" To help Mr. Squeaks calculate how many people can fit in each section, we can use the commutative property of multiplication. The commutative property of multiplication is when the order of multiplication does not change the product. To use the commutative property of multiplication, we can use arrays along with following these four steps. First, write the number sentence. Next, write the number sentence in a different order. Then, set up arrays for both problems. Finally, solve and find the products of both number sentences. The commutative property of multiplication is useful because it can save time. For example, it can be quicker to multiply four by two than it is to multiply two by four. Now that we know the steps we can take to use the commutative property of multiplication, let's practice. First, write the expression six times three. Next, rewrite this as three times six. Then, set up the arrays needed. For six times three, we need six rows of three. For three times six, we need three rows of six. Now we can solve and find the products. Using the array to help, six times three gives a product of eighteen. We can also see that three times six gives a product of eighteen. The order of multiplication did not change the product. Let's look at one more example. First, write the expression two times five. Next, rewrite this as five times two. Then, set up arrays for both problems. For two times five, we need two rows of five. For five times two, we need five rows of two. Finally, calculate the product of both problems. Using the array to help, two times five gives a product of ten. We can also see that five times two gives a product of ten. The product for both problems is ten, even though we changed the order of multiplication. Now you know how the commutative property of multiplication works, let's help Mr. Squeaks. Remember, the front section had four rows of eight, so you would write this as four times eight. What is the next step? You can rewrite it as eight times four, to represent the back section. Can you remember the next step? Set up an array for both problems. How do you set up an array for four times eight? You need an array with four rows of eight. What array do you need for eight times four? You need an array with eight rows of four. Now you can find the product of both. What is the product of four times eight? Four times eight is thirty-two. What about eight times four? Eight times four also gives a product of thirty-two. That means a total of thirty-two people can fit in each section. To solve problems using the commutative property of multiplication, remember, first, write the number sentence. Then, write the number sentence in a different order. Next, set up arrays for both problems. Finally, solve and find the products of both number sentences. "I forgot to ask, what is the movie?" "Wait and see, Mr. Squeaks, wait and see." "Wait! Imani, is that? it is, It's you!"

## Commutative Property of Multiplication exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Commutative Property of Multiplication.
• ### Can you find the matching arrays?

Hints

Look at the factors in the expressions. Do you see another array whose rows and columns would give you the same factors and the same product?

Look at this example:

4 x 3

3 x 4

The expressions have the same factors, just in a different order! These expressions will have the same product.

Solution

The commutative property allows us to use factors in any order, and still end up with the same product. Each set of arrays in the picture have the same factors in a different order, and have the same product.

• ### Can you find the corresponding multiplication calculations?

Hints

Look at the factors in the equation.

Use these same factors but in a different order.

There are 3 counters from top to bottom, and then 2 counters along the top. This is the same as 3 x 2. The other array shows 2 counters from top to bottom and 3 along the top. This is the same as 2 x 3

Looking at this image you have 7 x 8. Once you have worked out the factors for an array, switch it around using the same factors.

7 x 8

8 x 7

Solution

First look at the factors, then re-arrange them.

4 x 6 = 6 x 4

12 x 5 = 5 x 12

7 x 3 = 3 x 7

6 x 5 = 5 x 6

The product of the factors can be found by multiplying the factors in any order.

• ### Can you match the corresponding array?

Hints

Write down the factors that the array is showing. Now switch it around. Can you find the matching array?

The matching arrays will have the same product.

2 x 3 = 6

3 x 2 = 6

Solution

Look at the factors in the number sentence.

Then re-arrange by swapping the factors around.

Create an array for both.

• ### Match the arrays and calculations.

Hints

Look at the digits in the calculation

Rearrange them

Solution

Write out the calculation.

Re-arrange the digits.

Create arrays to show both.

• ### Can you help Mr Squeaks by sorting the steps below.

Hints

First we need to read the question then write the calculation out.

Once we have written the calculation out, we can then re-write it in a different order.

2 x 3 = 3 x 2

6 x 4 = 4 x 6

Once both calculations are written out what do we need to do to help solve the problem?

Solution

Write the number sentence.

Write it in a different order.

Set up arrays for both problems.

• ### Can you help Imani workout how many people are in the auditorium?

Hints

What calculation must we write? What information is given away in the text?

There are 7 rows of 8 people.

Put this into a number sentence

Solution

There are 7 rows of 8 people

Using these factors to create your number sentence

7 x 8 = 56

Using the same factors, rearrange them in the number sentence

8 x 7 = 56

You can now see that by rearranging the factors the product is the same for both.