Question

How is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.

Answer 1

The product of 3 and -2 can be shown using integer tiles in the following ways:

1. 3 positive tiles and 2 negative tiles:
This can be represented by placing 3 green tiles and 2 red tiles. The presence of a negative tile switches the sign of the product.

2. 3 negative tiles and 2 positive tiles:
This can be represented by placing 3 red tiles and 2 green tiles. Again, the presence of a negative tile switches the sign of the product.

3. 3 sets of 2 negative tiles:
This can be represented by arranging 3 sets of 2 red tiles each. Each set of 2 red tiles represents -2, and when multiplied by 3, the final product is -6.

4. 3 sets of 2 positive tiles:
This can be represented by arranging 3 sets of 2 green tiles each. Each set of 2 green tiles represents 2, and when multiplied by 3, the final product is 6.