Question
Which expression is an example of the Associative Property of Multiplication? ( 1 point) \( \begin{array}{l}7+9+8=9+7+8 \\ 7(8+9)=119 \\ (7 \times 8) \times 9=7 \times(8 \times 9) \\ 7 \times 8 \times 9=8 \times 9 \times 7\end{array} \)
Ask by Rojas Chan. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((7 \times 8) \times 9 = 7 \times (8 \times 9)\)
Solution
The **Associative Property of Multiplication** states that the way in which numbers are grouped does not change their product. Mathematically, it is expressed as:
\[
(a \times b) \times c = a \times (b \times c)
\]
Let's evaluate the options:
1. \(7 + 9 + 8 = 9 + 7 + 8\)
*This demonstrates the **Commutative Property** of addition, not the associative property.*
2. \(7(8 + 9) = 119\)
*This shows the use of the **Distributive Property**, not the associative property.*
3. \((7 \times 8) \times 9 = 7 \times (8 \times 9)\)
*This is a direct application of the **Associative Property of Multiplication**.*
4. \(7 \times 8 \times 9 = 8 \times 9 \times 7\)
*This also demonstrates the **Commutative Property** of multiplication, not the associative property.*
**Answer:**
\((7 \times 8) \times 9 = 7 \times (8 \times 9)\)
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An example of the Associative Property of Multiplication can be illustrated through the expression \((7 \times 8) \times 9 = 7 \times (8 \times 9)\). This property tells us that no matter how we group the factors in multiplication, the product remains the same! In real-world scenarios, this property can be incredibly useful. For instance, if you're calculating the total cost of multiple items, the order in which you multiply quantities doesn't matter! Whether you group the costs into smaller clusters or calculate them all at once, the final total will be the same, making budgeting and shopping much simpler.
