Multiple Representations When a movie is rented it has a due date. If the movie is not returned on time, a late fee is assessed. Kaitlyn is charged $5 each day for a movie that is 4 days late.

a. Words Explain why 4 × (-5) = -20 describes the situation.

b. Algebra Write an expression to represent the fee when the movie is x days late.

Identify Repeated Reasoning When you multiply two positive integers, the product is a positive integer. Complete the graphic organizer to help you remember the other rules for multiplying integers. Describe any patterns in the products.

Model with Mathematics Write a multiplication sentence with a product of -18.

Justify Conclusions Explain how to evaluate (-9) (-6) (15) (-7 + 7) as simply as possible.

Reason Inductively Evaluate (-1)50. Explain your reasoning.

Persevere with Problems Find values of a, b, and c that make each statement true. If no values exist, write not possible.
a. a<b and a+c<b+c

b. a<b and a+c>b+c

c. a<b and ac<bc

d. a<b and ac>bc

e. a<b and ac=bc