In the problem, Kaleb's football team lost 2 yards on each of 3 consecutive plays. We are asked to complete the mathematical statement to represent the total change in position and then explain how this shows that the product of a positive number and a negative number is negative.

Step-by-Step Solution:

1. Each play results in a loss of 2 yards. A loss can be represented by the negative sign, so each play contributes $-2$ to the total change.

2. The team loses 2 yards for each of the 3 plays, so we can write the total as:

   $-2 + (-2) + (-2) = -6$

   This equation shows that the total yardage lost is $-6$ yards after 3 plays.

3. Another way to think about it is to multiply the number of plays (3) by the loss per play (−2):

   $3 \times (-2) = -6$

Explanation:

• This example illustrates that when a positive number (3 plays) is multiplied by a negative number (−2 yards per play), the result is negative (−6 yards), confirming that the product of a positive number and a negative number is negative.

Would you like more details or have any questions?

Here are 5 related questions:

1. What happens if Kaleb's team gains yards instead of losing them?
2. How would you represent a 0-yard gain on each play?
3. What is the result of multiplying two negative numbers?
4. Can you explain how adding negative numbers is similar to multiplication?
5. How would the result change if the team played 5 plays instead of 3?

Tip: Always remember, multiplying a positive number by a negative number gives a negative result, while multiplying two negative numbers gives a positive result.