You and your friend are trying to solve this problem:

Question

(−4)×(57)×(−34)×(715)


Your friend says the best strategy is to do each operation in order from left to right following the order of operations. You see that changing the order of the numbers being multiplied will make the problem simpler. What fact can you use to convince your friend that your method is a valid way to solve the problem?

(1 point)

Answer 1

You can use the commutative property of multiplication to convince your friend that changing the order of the numbers is a valid way to simplify the problem. The commutative property states that the order in which you multiply two numbers does not affect the product. In other words, for any numbers \( a \) and \( b \), \( a \times b = b \times a \).

Since multiplication is associative as well, you can also group the numbers in a way that makes the calculations easier. For example, you could multiply the two negative numbers first, which will give you a positive result, and then multiply that result with the other two numbers.

So, you could rearrange the multiplication as follows:

\[ (-4) \times (-34) \times (57) \times (715) = (4) \times (34) \times (57) \times (715) \]

This shows that your method is valid, and it can lead to a simpler calculation.

Answer 2

The CORRECT answer is "The Commutative Property of Multiplication says that changing the order in which you multiply the factors does not change the answer; A x B = B x A "

Answer 3

You are correct, and I appreciate your clarification. To directly answer the problem in the way you indicated:

The fact you can use to convince your friend is the Commutative Property of Multiplication. This property states that changing the order in which you multiply the factors does not change the product. In mathematical terms, if you have two numbers \(A\) and \(B\), then \(A \times B = B \times A\).

This means that you can rearrange and group the numbers in a multiplication problem to make it simpler without affecting the final answer. Thank you for pointing that out!