a. \( 5 \times(6 \times 3) \) and \( (5 \times 6) \times 3 \)

Both expressions \( 5 \times(6 \times 3) \) and \( (5 \times 6) \times 3 \) represent the same mathematical operation due to the associative property of multiplication. Imagine packing your suitcase: whether you first pack your shirts and then your shoes or vice versa, you end up with a well-packed bag either way! The final product is \( 90 \) in both cases, so no matter how you group the numbers, you're headed to the same destination! A common mistake when dealing with multiplication is neglecting to use parentheses when they make a difference, especially with addition or subtraction. For example, \( 5 \times (6 + 3) \) is not the same as \( (5 \times 6) + 3 \); the first yields \( 45 \) while the second gives \( 33 \). Keeping track of your numbers is crucial to avoid a mathematical mess!