To convince your friend that changing the order of the numbers being multiplied is a valid way to simplify the problem, you can use the Commutative Property of Multiplication. This mathematical property states that the order in which two numbers are multiplied does not affect the product. In other words, for any two numbers \(a\) and \(b\):
\[ a \times b = b \times a \]
This means you can rearrange the numbers being multiplied in any way that is more convenient for you to make calculations easier, without changing the result of the multiplication.
For example, if you have the expression \(2 \times 5 \times 3\), you could rearrange it to \(5 \times 3 \times 2\) or \(3 \times 2 \times 5\) if it makes it simpler to compute.
Additionally, you can use the Associative Property of Multiplication, which states that how the numbers are grouped in multiplication does not affect the result:
\[ (a \times b) \times c = a \times (b \times c) \]
This means that it's perfectly valid to group numbers in a way that makes mental calculation easier for you, as long as you multiply them all together in the end.
Together, these properties demonstrate that your approach of changing the order of operations can be a valid and sometimes more efficient strategy in solving multiplication problems, and can help make them simpler to calculate.
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