## A Negative Times a Negative

## Work Time

# A Negative Times a Negative

The rule “a negative times a negative equals a positive” can be represented by the equation (−*a*) ⋅ (−*b*) = *ab*. The following proof shows that this equation is true.

- Work on the table and justify each step using the properties of operations for addition or multiplication to prove that if the values for
*a*and*b*are positive, then both (−*a*) and (−*b*) are negative and*ab*is positive.

HANDOUT: Multiplying a Negative by a Negative

## Hint:

- The
*addition property of equality*states that you can add any quantity to both sides of an equation without changing the equation. - The
*multiplication property of equality*states that you can multiply both sides of an equation by any quantity without changing the equation. - The
*addition property of zero*states that*a*+ 0 =*a*. You can rewrite this equation as*a*+ ( −*a*) = 0 .