Multiplication can be thought of as the first number telling how much to make of the second number. So 2(-5) is like making 2 groups of (-5). There are 10 negative unit tiles in total, so 2(-5) = -10. A negative first factor can be thought of as the first number telling how much to remove of the second number. So -2 (-5) is like removing 2 groups of (-5). Recall that zero pairs have no value, so add zero pairs until there are enough negative tiles to be able to remove 2 groups of (-5). After removing 2 groups of (-5) there are 10 positive tiles remaining, so -2 (-5) = 10. Notice that the negative sign can also be thought of as taking the “opposite” of 2(-5).

Multiplying Integers using the Brainingcamp Algebra Tiles virtual manipulative.

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