# The Associative Property of Multiplication

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## The Associative Property of Multiplication

What is the associative property of multiplication and what does it mean exactly? “To associate” means to connect or join with something. If you're curious and want to learn the meaning behind the associative property of multiplication and how to master it, continue reading!

### The Associative Property of Multiplication – Definition

The associative property of multiplication states that it does not matter in which order we multiply the numbers, the product will remain the same. This means we can multiply in any order and still get the same product.

## The Associative Property of Multiplication – Steps

When we are faced with problems that require us to use the associative property of multiplication, we can follow these steps:

• Write the expression
• Add brackets around one multiplication equation
• Solve inside the brackets and rewrite the equation
• Calculate the product

## The Associative Property of Multiplication – Example Problem

What is an example of the associative property of multiplication? You can see an example on the following infographic:

As you can see, we wrote out the expression, and we put brackets around the four and two on the left. There are also brackets around the two and three on the right. Remember, you always solve inside the brackets first!

To solve the left side, we solve the four times two inside the brackets first, which is eight. We rewrite this below as eight and bring down the three. Now we multiply eight times three, which gives us twenty-four. The product is twenty-four!

To solve the right side, we solve the two times three inside the brackets first, which is six. We rewrite this below as six and bring down the four. Now we multiply four times six, which gives us twenty-four. The product is twenty-four again.

On the infographic above, we have circled the product of the left and right side. It didn’t matter which pair of numbers we chose to solve first, the product was twenty-four. This is what the associative property teaches us – the order of multiplication does not change the product!

## The Associative Property of Multiplication – Review

Remember, you can define the associative property of multiplication as ordering pairs of numbers in any way you wish, because the product will not change. Now you have seen an example of the associative property of multiplication, you are ready for the associative property of multiplication worksheets!

### TranscriptThe Associative Property of Multiplication

Mr. Squeaks and Imani are preparing for a stunt! They still need to enter the power input by solving a multiplication expression. "Mr. Squeaks, we must put the brackets around five times three!" "No, we put the brackets around three times two!" Let's help them by learning about "The Associative Property of Multiplication". It doesn't matter where we put the brackets, as the product will be the SAME no matter how we solve these problems. This is what the "associative property of mutliplication" teaches us. The "order does not matter, the product will remain the SAME" To solve multiplication problems with three or more numbers, first, "write the expression". Then, "add brackets around the multiplication equation" you want to solve first. Next, "solve the brackets and rewrite the equation". Finally, "calculate the product". Remember, we can use arrays to help us solve the problems! Let's practice before we help! Here we have four times two times three. First, identify the multiplication equations we need to solve. We can use brackets HERE or HERE because the associative property states it doesn't matter which pair we solve first! Let's solve the left side first. Remember to always solve inside the brackets first. HERE we have four times two. We can set up an array with four rows of two which gives a product of eight! Rewrite the equation underneath as eight times three. We can use an array again to help us, by setting up an array with eight rows of three. The product of eight and three is twenty-four. Now let's solve the problem on the right with a different pair in brackets! This time, two times three is in brackets. Set up our array with two rows of three which gives a product of six. Next, rewrite the equation as four times six. Now we need to multiply four by six meaning we need an array with four rows of six, giving us a product of twenty-four. Even though both problems had different pairs in brackets, the product was still twenty-four. It doesn't matter which pair you multiply first, the product will always be the same! Now we can help Imani and Mr. Squeaks! To solve five times three times two, Imani said we should put brackets around five and three, and Mr. Squeaks claimed we should put brackets around three and two. Let's take a look at Imani's method first. What is the first step?

Solve inside the brackets using an array with five rows of three to help you. What is five times three?

The product is fifteen, so rewrite the equation as fifteen times two. What is the next step?

Solve fifteen times two setting up an array with fifteen rows of two. What is fifteen times two?

The product is thirty! Now we have solved the problem Imani's way... let's take a look at Mr. Squeaks' way! What is the first step?

Solve inside the brackets first, setting up an array with three rows of two. What is three times two?

The product is six, so rewrite the equation as five times six. What is the next step?

Solve five times six, setting up a new array with five rows of six. What is five times six?

The product is thirty. As you can see HERE and HERE, no matter which pair we solve first, the product is the SAME, so they are both correct! Remember, when using the associative property of multiplication, first, "write the expression". Then, "add brackets around the multiplication equation" you want to solve first. Next, "solve the brackets and rewrite the equation". Finally, "calculate the product". Remember, arrays can be a useful tool to calculate the product. Both Mr. Squeaks and Imani were correct, so they can input the power needed for the cannon! "I hope you're ready, Mr. Squeaks!" "Three, two, one!"

"Woah! Somebody help meeeee!"

## The Associative Property of Multiplication exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video The Associative Property of Multiplication.
• ### Can you help Mr. Squeaks and Imani?

Hints

Before you can solve a multiplication expression, what must you add to the equation?

Before you calculate the final product, what do you need to solve first?

Solution

Above is an example for how to solve problems with 3 or more factors.

1. First, write the expression.
2. Add brackets around one multiplication equation.
3. Solve the expression inside the brackets and rewrite the equation.
4. Calculate the final product.
• ### Which equations have the same product?

Hints

Remember, the associative property of multiplication tells you that it doesn't matter where we put the brackets, as the product will be the same.

Remember to solve the expression inside the brackets first.

Check that your equations have the same numbers.

Solution

(6 x 2) x 3 and 6 x (2 x 3) will have the same product because the associative property of multiplication tells you that it doesn't matter where we put the brackets. Since both of these equations are multiplying the same numbers, they will have the same product of 36. ___________________________________________________________________________________________________ (4 x 2) x 5 and 4 x (2 x 5) have the same product of 40.

(2 x 3) x 7 and 2 x (3 x 7) have the same product of 42.

(4 x 3) x 2 and 4 x (3 x 2) have the same product of 24.

• ### Which equations show the associative property of multiplication calculated correctly?

Hints

First solve the pair in the brackets and rewrite the equation, then calculate the final product.

Solve each equation and see if you get the same answer.

Make sure you select all of the correct equations.

Here is an example of an array for 4 x 2

Solution

For each problem, you needed to first solve the pair inside the brackets and rewrite the equation, then calculate the final product.

The first equation is solved incorrectly.
2 x (6 x 3) = 2 x 16 = 32. It should be 2 x (6 x 3) = 2 x 18 = 36

The second equation is solved correctly.
(3 x 2) x 7 = 6 x 7 = 42.

The third equation is solved incorrectly.
(2 x 4) x 8 = 8 x 8 = 34. It should be (2 x 4) x 8 = 8 x 8 = 64

The last equation is solved correctly.
5 x (3 x 3) = 5 x 9 = 45

• ### Solve the equations using the associative property of multiplication.

Hints

First, solve the pair inside the brackets, then calculate the final product.

Here is an example of an array for 5 x 3

Solution

First, solve the factor pair inside the brackets, then calculate the final product.

• (3 x 3) x 2 = 9 x 2 = 18
• 4 x (5 x 2) = 4 x 10 = 40
• (4 x 2) x 4 = 8 x 4 = 32
• 6 x (3 x 2) = 6 x 6 = 36

• ### What does the associative property of multiplication tell us?

Hints

Try solving (3 x 4) x 2 and 3 x (4 x 2).
Did you get the same answer or a different answer? What does that tell you?

Solution

The brackets can go around any pair of numbers.

It doesn't matter where we put the brackets, as the product will be the same.

For example: (3 x 4) x 2 = 24 and 3 x (4 x 2) = 24. The brackets moved, but the product remained the same.

• ### Can you find the missing numbers?

Hints

Start by looking at the final product. Then, work backwards to find out which number belongs in each space.

Once you find out the number that belongs to make the final product true, work out which number belongs in the original equation to make the rest of the equation true.

Check to make sure your equation is correct by multiplying from left to right.

Solution

Start by looking at the final product. Then, work backwards using division to work out which number makes the final product true.

Next, look at the rest of the equation and work out which number belongs in the original equation using division to make the product true.

Finally, check to make sure your equation is true by multiplying from left to right.

(3 x 2) x 4 = 6 x 4 = 24

• Start by looking at the final product, 24.
• 24 $\div$ 4 = 6
• Next, look at the product, 6.
• 6 $\div$ 2 = 3
• Finally, check to make sure your equation is correct.
• 3 x 2 = 6
• 6 x 4 = 24
___________________________________________________________________________________________________
• 5 x (3 x 3) = 5 x 9 = 45
• (3 x 4) x 3 = 12 x 3 = 36
• 6 x (4 x 2) = 6 x 8 = 48