Question
2 Cheryl wrote the expression \( (7 \times k) \times 5 \) to help her solve a math problem. Which of these is equivalent to the expression? F \( (k+7) \times 5 \) \( \begin{array}{ll}\text { G } 7 k+5 & \text { J } 7 \times(k \times 5)\end{array} \) Answer: Property Used:
Ask by Rose Bartlett. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( 7 \times (k \times 5) \).
Solution
**Answer:**
J. \( 7 \times (k \times 5) \)
**Property Used:**
Associative Property of Multiplication
**Explanation:**
The **Associative Property** states that the way in which numbers are grouped in a multiplication problem does not change the product.
Given the original expression:
\[
(7 \times k) \times 5
\]
Using the Associative Property, you can regroup the numbers:
\[
7 \times (k \times 5)
\]
This shows that option **J** is equivalent to the original expression.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
First, let's talk about how Cheryl's expression, \( (7 \times k) \times 5 \), can be rearranged using the associative property of multiplication. The associative property allows us to regroup the numbers we are multiplying. So, we can rewrite it as \( 7 \times (k \times 5) \), which is option J in your choices! Now, a classic mistake with expressions like these is not recognizing that while multiplying, the order doesn't change the result (thanks to the commutative property). For example, thinking \( 7 \times k + 5 \) would be the same as Cheryl’s original expression is incorrect, because here we're adding 5 instead of multiplying! Keep those properties in mind to avoid any confusion!
