You and your friend are trying to solve this problem: (−4)×(5/7)×(−3/4)×(7/15) 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 convince your friend that changing the order of the numbers being multiplied is valid by using the commutative property of multiplication. This property states that the order in which two numbers are multiplied does not change the product. In other words, for any numbers a and b, the equation \(a \times b = b \times a\) holds true.

In your case, you have the expression \((-4) \times (5/7) \times (-3/4) \times (7/15)\). By rearranging the factors, you can group them in a way that simplifies the calculation. For example, you could multiply \((-4)\) with \((-3/4)\) first, which simplifies to \(3\), and then multiply \(5/7\) and \(7/15\) together, which simplifies due to the cancellation of \(7\).

Thus, you can say: "Since multiplication is commutative and associative, I can rearrange the factors to simplify the calculation without affecting the final result, allowing us to solve the problem more efficiently."