Question

for exercises 9-12, find the product.

1. $-4(-9)$
2. $-8(-12)$
3. $-4.1(-5)$
4. $-12.6(-5)$

for exercises 13 and 14, answer the question.

1. a community pool is being drained at a rate of 0.5 foot per hour. how much deeper was the water in the pool 4 hours ago? write an expression that represents this situation and evaluate the expression.

1. kiara is participating in a sack race. each time she jumps, her distance from the finish line decreases by 1.5 feet. write an expression that represents how much farther kiara was from the finish line 8 jumps earlier, then evaluate the expression.

for exercise 15, answer the question.

1. stem connection a manufacturing company is trying to reduce the amount plastic they use in their packaging. they find that a new method of packaging will reduce their plastic use by 286 pounds per month. what is the amount the companys plastic use will be reduced in one year using this method? explain.

reflect
how can you explain to a classmate how to determine the sign of the product when multiplying negative numbers?

Explanation:

Step1: Multiply two negatives (9)

$(-4) \times (-9) = 36$

Step2: Multiply two negatives (10)

$(-8) \times (-12) = 96$

Step3: Multiply two negatives (11)

$(-4.1) \times (-5) = 20.5$

Step4: Multiply two negatives (12)

$(-12.6) \times (-5) = 63$

Step5: Set up pool depth expression (13)

Expression: $0.5 \times 4$
Evaluate: $0.5 \times 4 = 2$

Step6: Set up race distance expression (14)

Expression: $1.5 \times 8$
Evaluate: $1.5 \times 8 = 12$

Step7: Calculate annual plastic reduction (15)

Expression: $286 \times 12$
Evaluate: $286 \times 12 = 3432$

Step8: Explain sign rule for multiplication

When multiplying two negative numbers, the product is positive; a negative times a positive is negative, and positive times positive is positive. For negatives: the two negative signs "cancel out" to make a positive result.

Answer:

1. 36
2. 96
3. 20.5
4. 63
5. Expression: $0.5 \times 4$; Value: 2 feet
6. Expression: $1.5 \times 8$; Value: 12 feet
7. 3432 pounds. The monthly reduction is 286 pounds, and there are 12 months in a year, so multiply 286 by 12 to get the total annual reduction.

Reflect: When multiplying negative numbers, if there is an even number of negative factors, the product is positive; if there is an odd number of negative factors, the product is negative. For two negatives specifically, their product is positive because the negative signs offset each other.