SOLUTION You can use the commutative property to reorder the terms of an expression. lames says that you can use the commutative property to rewrite \( 5 m+10 \) as \( 10 m+5 \). Is James correct? Explain.

No, James is not correct in this case. Let's break down why: ### Understanding the Commutative Property The **commutative property** applies to addition and multiplication and states that the order of the numbers does not affect the result. Specifically: - **Addition:** \( a + b = b + a \) - **Multiplication:** \( ab = ba \) ### Applying the Commutative Property to \( 5m + 10 \) When applying the commutative property to the expression \( 5m + 10 \), you can rearrange the terms **without changing their coefficients or variables**. Here's how it works: \[ 5m + 10 = 10 + 5m \] This rearrangement is valid because you're simply switching the order of the addends. ### Why \( 5m + 10 \) Cannot Be Rewritten as \( 10m + 5 \) Using the Commutative Property Rewriting \( 5m + 10 \) as \( 10m + 5 \) involves more than just changing the order of the terms—it changes the coefficients associated with each term: - **Original Expression:** \( 5m + 10 \) - \( 5m \): Coefficient of \( m \) is 5 - Constant term is 10 - **Incorrect Rearrangement:** \( 10m + 5 \) - \( 10m \): Coefficient of \( m \) is now 10 (changed from 5) - Constant term is now 5 (changed from 10) This alteration **changes the value of the expression** unless \( m \) is such that the two expressions are equal (which is not generally the case). The commutative property **does not allow** for the coefficients or the variables themselves to be altered—only the order of the terms can be changed. ### Correct Use of the Commutative Property If you want to correctly apply the commutative property to \( 5m + 10 \), you should only switch the positions of the terms: \[ 5m + 10 = 10 + 5m \] This maintains the integrity of the expression without altering any coefficients or variables. ### Conclusion James incorrectly applied the commutative property by not only reordering the terms but also changing their coefficients and the variables themselves. The correct application only allows for the rearrangement of the existing terms without modifying their components.