1. Exploring, Adding, Subtracting, Multiplying, and Dividing Real Numbers

4. Examples

5. I

6.  The Venn Diagram below shows the relationships of the sets of numbers that make up real numbers.

7. Inequality  An inequality is a mathematical sentence that compares the value of two expressions using an inequality symbol, such as.

8.  The number line below shows how values of numbers increase as you go to the right on a number line.  To compare fractions, you may find it helpful to write the fractions as decimals and then compare the decimals.

10.  Two numbers that are the same distance from zero on a number line but lie in opposite directions are opposites.

11.  The absolute value of a number is its distance from 0 on a number line. Both -3 and 3 are 3 units from zero. Both have an absolute value of 3. You write “the absolute value of -3” as |-3|.

12. Adding Real #s  Identity Property of Addition  For every rational number n, n + 0 = n and 0 + n = n.  Examples: -5 + 0 = -5and 0 + 5 = 5  The opposite of a number is its additive inverse. The number line shows the sum of 4 + (-4).

13.  The additive inverse of a negative number is a positive number. The number line below shows the sum of -5 and 5.  Inverse Property of Addition  For every real number n, there is an additive inverse –n such that n + (-n) = 0.  Examples: 17 + (-17) = 0 and -17 + 17 = 0

17. Matrices

18.  Matrices are equal if the elements in corresponding positions are equal.  You add matrices are the same size by adding the corresponding elements.

20. Subtracting Numbers  To subtract a number, add its opposite.

21. Subtracting Real Numbers

22. Subtracting and Absolute Value

23. Evaluating Expressions

24. Subtracting Matrices

26. Multiplication Properties

27.  Multiplying Numbers with the Same Sign  The product of two positive numbers or two negative numbers is positive.  Multiplying Numbers with Different Signs  The product of a positive number and a negative number, or a negative number and a positive number, is negative.

28. Multiplying Numbers

29. Division Properties  Dividing Numbers with the Same Sign  The quotient of two positive numbers or two negative numbers is positive.  Dividing Numbers with Different Signs  The quotient of a positive number and a negative number, or a negative number and a positive number, is negative.

30. Dividing Numbers  Simplify each expression.  Your turn!

31. Inverse Property of Multiplication

32. Division Using a Reciprocal

33. The Distributive Property

35. Combining Like Terms

38. Multi-Step Equations

41. Steps for Solving a Multi-Step Equation

42. Variables on Both Sides

44. Practicing Identity and No Solution  Determine whether each equation is an identity or whether it has no solution.

45. Group Work Time!  Together at your table, figure out what the value of each variable is in both matrices below.

46. Let’s go over your homework!  We will be looking at the homework you turned in on Monday of this week!homework  If you have not turned it in yet, now is the time to do so!  Make sure that you work on MATH homework AT HOME or in time allotted in class—NOT in Mr. Suralik’s English class!!!!! (Yep—He saw you do it!)  I will pass your homework back out tomorrow (still going through them!)  Write down the answers on a sheet of paper (if you wish) so that you will know the correct answers to any you missed.  Today we will go over any questions you have!