To convince your friend that changing the order of the numbers being multiplied is a valid way to solve the problem, you can refer to the commutative property of multiplication. The commutative property states that the order in which two numbers are multiplied does not change the product; in other words, \(a \times b = b \times a\).
Additionally, you can also mention the associative property of multiplication, which states that how the numbers are grouped in multiplication does not affect the product. This means that for any numbers \(a, b, c\), the equation \((a \times b) \times c = a \times (b \times c)\) holds true.
Since multiplication is both commutative and associative, you are allowed to rearrange and group the factors in a way that may simplify the calculations. In this case, rearranging the order of the factors to make the multiplication easier to compute is a valid approach. This flexibility can help you simplify calculations by pairing values that make the arithmetic simpler. For instance, you can multiply the fractions and whole numbers in a way that simplifies them before multiplying everything together.