challenge to rent a car for a trip, 4 friends are combining their money. the table shows the amount of money that each puts in. one expression for their total amount of money is 138 + v + 237 + w. use a commutative property to find equivalent expressions.

use pencil and paper. if they need $500 to rent a car, find at least two different pairs of numbers that friends b and d must put in.

which expressions below are equivalent to 138 + v + 237 + w by a commutative property? select all that apply.

a. 138 + 237 + v + w
b. 138 + v + 237 + w
c. v + 138 + 237 + w
d. 138 + v + w + 237

Question

challenge to rent a car for a trip, 4 friends are combining their money. the table shows the amount of money that each puts in. one expression for their total amount of money is 138 + v + 237 + w. use a commutative property to find equivalent expressions.

use pencil and paper. if they need $500 to rent a car, find at least two different pairs of numbers that friends b and d must put in.

which expressions below are equivalent to 138 + v + 237 + w by a commutative property? select all that apply.

a. 138 + 237 + v + w
b. 138 + v + 237 + w
c. v + 138 + 237 + w
d. 138 + v + w + 237

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equivalent Expressions", "Associative Property" ], "new_concepts": [ "Commutative Property" ], "current_concepts": [ "Equivalent Expressions", "Associative Property", "Commutative Property" ] } ## Identify equivalent expressions using the Commutative Property of Addition $$ \begin{aligned} &\text{Original expression: } 138 + v + 237 + w\ &\text{Commutative Property allows changing the order of terms.}\ &\text{Option A: } 138 + 237 + v + w \quad (\text{reordered } v \text{ and } 237)\ &\text{Option B: } 138 + v + 237 + w \quad (\text{identical to original, order unchanged})\ &\text{Option C: } v + 138 + 237 + w \quad (\text{reordered } 138 \text{ and } v)\ &\text{Option D: } 138 + v + w + 237 \quad (\text{reordered } 237 \text{ and } w) \end{aligned} $$ ## Determine valid reorderings $$ \begin{aligned} &\text{A, C, and D are equivalent by changing the order of terms.}\ &\text{B is identical, which does not demonstrate a change in order via the Commutative Property.} \end{aligned} $$

(A) $138 + 237 + v + w$

(B) $138 + v + 237 + w$

(C) $v + 138 + 237 + w$

(D) $138 + v + w + 237$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Equivalent Expressions" ] }

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Question

Explanation:

Identify equivalent expressions using the Commutative Property of Addition

Determine valid reorderings

Answer: