The Associative Property of Multiplication
Basics on the topic The Associative Property of Multiplication
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 the order of factor pairs does not matter, 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 as outlined in the illustration below:
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 parentheses around the factor pair four and two on the left. There are also parantheses around the factor pair two and three on the right. Remember, you always solve inside the parentheses first!
To solve the left side, we solve the four times two inside the parentheses first, which is eight. We rewrite this below as eight and bring down the three. Now we multiply eight times three, which gives us twentyfour. The product is twentyfour!
To solve the right side, we solve the two times three inside the parentheses first, which is six. We rewrite this below as six and bring down the four. Now we multiply four times six, which gives us twentyfour. The product is twentyfour again.
On the infographic above, we have circled the product of the left and right side. It didn’t matter which factor pair we chose to solve first, the product was twentyfour. 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 factor pairs 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 3rd grade worksheets!
Transcript The 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 parentheses around our factor pair five and three!" "No, we put the parentheses around the factor pair three and two!" Let's help them by learning about the associative property of multiplication. It doesn't matter where we put the parentheses, as the product will be the same no matter how we solve these problems. This is what the associative property of multiplication teaches us. The order of factor pairs does not matter, the product will remain the same. To solve multiplication problems with three or more factors, first write the expression. Then, add parentheses around a factor pair you want to solve first. Next, solve the parentheses 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 factor pairs to solve. We can use parentheses here or here because the associative property states it doesn't matter which factor pair we solve first. Let's solve the left side first. Remember to always solve inside the parentheses 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 twentyfour. Now let's solve the problem on the right with a different factor pair in parentheses. This time, two times three is in parentheses. 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 twentyfour. Even though both problems had different factor pairs in parentheses the product was still twentyfour. It doesn't matter which factor 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 parentheses around the factor pair five and three and Mr. Squeaks claimed we should put parentheses around the factor pair three and two. Let's take a look at Imani's method first. What is the first step? Solve inside the parentheses, 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 parentheses 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 factor 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 parentheses around a factor pair you want to solve first. Next, solve the parentheses 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 me!"
The Associative Property of Multiplication exercise

Can you help Mr. Squeaks and Imani?
HintsBefore you can solve the factor pair, what must you add to the equation?
Before you calculate the final product, what do you need to solve first?
SolutionAbove is an example for how to solve problems with 3 or more factors.
 Write the expression.
 Add parentheses around a factor pair you want to solve first.
 Solve the factor pair in parentheses and rewrite the equation.
 Calculate the final product.

Which equations have the same product?
HintsRemember, the associative property of multiplication tells you that it doesn't matter where we put the parentheses, as the product will be the same.
Remember to solve the factor pair in parentheses 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 parentheses. 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?
HintsFirst solve the factor pair in the parentheses and rewrite the equation, then calculate the final product.
Solve each equation and see if you get the same answer.
Try using arrays to help you solve the equations.
Here is an example of an array for 4 x 2
Make sure you select all the correct equations.
SolutionFor each problem, you needed to first solve the factor pair in the parentheses 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 = 36The 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 = 64The last equation is solved correctly.
5 x (3 x 3) = 5 x 9 = 45 
Solve the equations using the associative property of multiplication.
HintsFirst solve the factor pair in the parentheses, then calculate the final product.
Try using arrays to help you solve the equations.
Here is an example of an array for 5 x 3
SolutionFirst solve the factor pair in parentheses, 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?
HintsTry 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?SolutionIt doesn't matter where we put the parentheses, as the product will be the same.
For example: (3 x 4) x 2 = 24 and 3 x (4 x 2) = 24. The parentheses moved, but the product remained the same.

Figure out the missing numbers.
HintsStart by looking at the final product. Then work backwards, figuring out which number belongs in each space.
Once you figure out the number that belongs to make the final product true, figure out which number belongs in the original equation to make the factor product true.
Check to make sure your equation is true by multiplying from left to right.
SolutionStart by looking at the final product. Then, work backwards using division to figure out which number makes the final product true. Next, look at the factor product. Then, figure out which number belongs in the original equation using division to make the factor product true. Lastly, check to make sure your equation is true by multiplying from left to right.
 (3 x 2) x 4 = 6 x 4 = 24
24 $\div$ 4 = 6
Next, look at the factor product, 6.
6 $\div$ 2 = 3
Lastly, check to make sure your equation is true.
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
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