Question - Analyzing Math Questions from a Worksheet

We are given the operation \((6 + (9 \times 8)) \div 3\) and asked to apply the Associative Law of Multiplication to it.

The Associative Law states that for any numbers \(a\), \(b\), and \(c\), the multiplication operation is associative, i.e., \((a \times b) \times c = a \times (b \times c)\).

By applying the Associative Law to the given expression we have:

\((6 + (9 \times 8)) \div 3 = 6 + ((9 \times 8) \div 3)\)

So applying the Associative Law does not affect the brackets here, because it's related to the order of the multiplication operation within them. We might also consider that in the absence of brackets, division and multiplication should be carried out before addition and subtraction, from left to right. Thus, no change in the placement of brackets is needed in this case due to the associative law itself. We simplify it instead:

\(6 + (72 \div 3) = 6 + 24 = 30\)

The value after applying the associative law is \(30\).