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Simplifying Using the Associative Property of Multiplication
Use the associative property of multiplication to simplify :
- Regroup the factors: Apply the associative property to move the parentheses so that the two numerical factors are grouped together:
- Multiply the numbers in parentheses: Compute :
The simplified result is .
The key observation is that regrouping lets us multiply the two known numbers ( and ) together, whereas the original grouping cannot be simplified further because and represent a product that depends on the unknown value of . This technique — pulling the numerical coefficients together using the associative property — is a common first step when simplifying algebraic expressions involving multiplication.
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Subtraction and Division Are Not Associative
Simplifying Using the Associative Property of Multiplication
True or false:
Which expression shows the associative property of multiplication for ?
The equation shows the _____ property of multiplication.
Match each term or expression with its meaning.
Which equation shows the Associative Property of Multiplication?
Put the steps in order to regroup and simplify .
Which property is shown by ?
What property is shown by ?
Name the property shown and write its formula using , , and .
What is the Associative Property of Multiplication? Show one example using three numbers and parentheses.
Learn After
A retail supervisor is calculating the total cost of an order consisting of 6 cases. Each case contains 3 items that cost x dollars each. To simplify the expression 6(3x), the supervisor uses the step (6 * 3)x. Which property of multiplication justifies this specific step?
A retail manager is organizing a shipment of 6 boxes. Each box contains 3 display cases, and each case holds x units of a product. To simplify the total units expression 6(3x) into (6 * 3)x, the manager is using the ____ Property of Multiplication.
A supervisor is simplifying the expression 6(3x) to find the total number of items in a shipment. Match each stage of the simplification process with the correct mathematical description.
A retail coordinator is calculating the total volume of a shipment consisting of 6 large containers. Each container holds 3 cases, and each case has a volume of x cubic feet. To simplify the total volume expression 6(3x) using the Associative Property of Multiplication, arrange the following steps in the correct order, starting from the initial expression.
A warehouse supervisor is calculating the total weight of an order consisting of 6 crates, where each crate contains 3 boxes weighing x pounds each. True or False: The supervisor can use the Associative Property of Multiplication to regroup the calculation from 6(3x) to (6 * 3)x.
Property Identification in Warehouse Logistics
Logistics Optimization via Algebraic Properties
Identifying Algebraic Properties in Inventory Management
A warehouse manager is calculating the total value of a shipment containing 6 cartons. Each carton holds 3 units, and each unit has a value of x dollars. The manager starts with the expression 6(3x). According to the Associative Property of Multiplication, which of the following represents the correct regrouping of factors to simplify this calculation?
A project coordinator is simplifying the expression 6(3x) to determine the total number of hours for a corporate training series. The coordinator decides to regroup the factors to create the expression (6 * 3)x. What is the primary mathematical reason for performing this regrouping step?