Study Guide for Module 1 DBA

1. What are opposites?

  • Give an example of opposites.
  • Describe a real world situation using opposites.

2. Draw the following scenario using a vertical number line.

  • Mary climbed up a ladder 24 feet to the second story of her house. She then climbed back down.

3. Draw the following using a horizontal number line.

  • Freddie the frog hopped 5 spaces to the west and then hopped 5 spaces back east.

4. What are additive inverses?

  • Given an example determine whether two event combine to make zero.
  • Mrs. Miller rides up the elevator from the first floor to floor 12, and then back down to the first floor.
  • Johnny borrowed $9 dollars from his friend George for popcorn and a drink. He then asked George for $9 more dollars for the movie.

5. How do you use a number line to describe the answer to the following.

  • Sara received 1,000 points on Candy Crush for beating level 5. She then spent 1200 points on a power up.
  • Mark dove down 10 feet to view a turtle, and then dove 5 more feet to inspect some coral.

6. What is absolute value?

  • What symbol do we use for absolute value?
  • What is | -9| = ?| 13| = ?|-21| = ?

7. Give an example of how you use the additive ineverse property to subtract.

8. Subtraction can be rewritten as .

9. Solve the following using the additive inverse:

  • - 10 - 6 = -13 - (-3) =
  • 18 - ( -10) = 21 - 10 =

10. The of the difference between two numbers is .

11. Solve. Be careful of the signs!!!

  • | -5 - 2| = | 10 - 9 | =
  • | 3.5 - (-3.5)| = | 9 - 10 | =

12. Describe the difference between the Commutative and Associative Property of Addition. Be sure to give examples!

13. Give an example of where you would use either the Commutative or Associative Property of Addition in a real world situation.

14. Name that property.

  • ( 3 + 4) = (4 + 3)= (1 + 2) + 3 = 1 + (2+3) =
  • (5 + -5) + 8 = (-5 + 5) + 8 = -3.2 + 4 + 5.3 = 4 + 5.3 + -3.2 =

15. Signed numbers are .

16. Give an example where you have used signed numbers recently.

17. What is the general rule for multiplying signed numbers?

Positive x Positive = Negative x Negative =

Positive x Negative = Negative x Positive =

18.Work the following examples...

  • -8 x -7 = -10 x 2 =
  • 15 x 2 = 22 x -4 =

19.The product is the answer to a problem.

20.What is the rule when you multiply several factors together?

  • An EVEN number of negative signs will result in a .
  • An ODD number of negative signs will result in a .

21. What is the sign of the following product? Circle one...Don't do the multiplication!

  • (-8) x 5 x (- 6) x 2.1 x - 45 x (- 6) = Positive or Negative
  • ( -2.0) x (-12) x (-4) x (- 1/2) = Positive or Negative

22. Describe a recent situation where you multiplied or divided signed numbers. Be sure to use an example!

23. What are the rules for dividing signed numbers?

24. Work the following examples...

  • -24 / -2 = -144 / 12 =
  • 25 / 5 = 100 / -20 =

25. A is a number that can be made from dividing one integer by another.

26. Is 0 a signed number? Why or why not?

27. Can you divide by 0? Why or why not?

28. Describe and give examples of three different ways the negative sign can be placed in a division problem.

29. The average is .