Final answer:
The multiplication expressions that can potentially be modeled by the tiles for a total of 24 tiles are 8(3) = 24, 6(4) = 24, 3(8) = 24, and 2(12) = 24, as these products match a possible tile quantity.
Step-by-step explanation:
The question requires us to determine which of the given multiplication expressions can be represented by a set of tiles. Since we do not have a visual representation of the tiles, we will evaluate the expressions based on the product they yield, which should match the quantity of tiles if the expression is correct. The products of the given expressions are:
- 8(3) = 24
- 6(4) = 24
- (3)(12) = 36
- 24(3) = 72
- 3(8) = 24
- 2(12) = 24
Expressions a), b), e), and f) all yield a product of 24, which implies that these could potentially be modeled by the tiles if there are 24 tiles in total. Expression c) yields a product of 36 and d) yields a product of 72, so they cannot be modeled by the tiles if we are only considering a total of 24 tiles.
It is important to note that multiplication is commutative, meaning that the order of the factors does not affect the product. Therefore, 8(3) and 3(8) will yield the same result. Multiplying two positive numbers results in a positive product, and multiplying two numbers with opposite signs gives a negative product, but these rules are not directly applicable to the provided expressions as we are only dealing with positive factors here.