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 119 + a + 271 + b. 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. travel fund friend amount (dollars) a 119 b a c 271 d b which expressions below are equivalent to 119 + a + 271 + b by a commutative property? select all that apply. a. 119 + a + b + 271 b. 119 + a + 271 + b c. 119 + 271 + a + b d. a + 119 + 271 + b

Explanation:

The Commutative Property of Addition states that the order of adding numbers can be changed without changing the sum, i.e., \(x + y = y + x\). We analyze each option:

• Option A: \(119 + a + b + 271\) swaps the order of \(271\) and \(b\) (since original is \(119 + a + 271 + b\)), so this uses the Commutative Property.
• Option B: \(119 + a + 271 + b\) is the same as the original expression, so it does not use the Commutative Property to create a new equivalent expression (it's identical).
• Option C: \(119 + 271 + a + b\) swaps the order of \(a\) and \(271\), so this uses the Commutative Property.
• Option D: \(a + 119 + 271 + b\) swaps the order of \(119\) and \(a\), so this uses the Commutative Property.

Answer:

A. \(119 + a + b + 271\)
C. \(119 + 271 + a + b\)
D. \(a + 119 + 271 + b\)