The Associative Property of Multiplication

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The Associative Property of Multiplication
CCSS.MATH.CONTENT.3.OA.B.5

Information about the video The Associative Property of Multiplication

Contents

In This Video

Mr. Squeaks and Imani are preparing for a stunt, to launch Mr. Squeaks out of a cannon! They need to learn the associative property of multiplication definition first. After this, they see an example of associative property of multiplication, and then are ready to solve their problem and perform the stunt! Armed with their newfound knowledge and the associative property of multiplication definition and example firmly in their memory, Imani launches Mr. Squeaks, but there is a slight problem...

The Associative Property of Multiplication (3rd Grade)

What is the associative property of multiplication and what does the associative property of multiplication mean? 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.

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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

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  • Write the expression
  • Add parentheses around factor pair
  • Solve the parentheses and rewrite the equation
  • Calculate the product

The Associative Property of Multiplication Example Problem

What is an example of the associative property of multiplication? The following illustration shows an example of the associative property of multiplication.

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As you can see, we wrote out the expression, and we put parentheses around the factor pair four and two on the left, and then the factor pair two and three on the right. Remember, you always solve inside the parentheses first!

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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 twenty-four. The product is twenty-four!

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To solve the right side, we solve the two times three inside the parentheses first, which is six. We write 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!

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As you can see, we have circled the product of the left and right side here. It didn’t matter which factor pair 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 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 now ready for the associative property of multiplication 3rd grade worksheets below!

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The Associative Property of Multiplication Exercise

Would you like to practice what you’ve just learned? Practice problems for this video The Associative Property of Multiplication help you practice and recap your knowledge.
  • Can you help Mr. Squeaks and Imani?

    Hints

    Before 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?

    Solution

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

    1. Write the expression.
    2. Add parentheses around a factor pair you want to solve first.
    3. Solve the factor pair in parentheses 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 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?

    Hints

    First 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.

    Solution

    For 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 = 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 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

    Solution

    First, 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?

    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

    It 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.

    Hints

    Start 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.

    Solution

    Start 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
    Start by looking at the final product, 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