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Adding and Subtracting Real Numbers | Number Line Examples

Learn how to graph sets of numbers on the number line and apply addition and subtraction rules with examples and karaoke fun. Understand additive inverses, absolute value, and practice problems.

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Adding and Subtracting Real Numbers | Number Line Examples

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  1. Section 2.2-2.3 Addition and Subtraction of Real Numbers

  2. The Number Line Integers = {…, -2, -1, 0, 1, 2, …} Whole Numbers = {0, 1, 2, …} Natural Numbers = {1, 2, 3, …} -5 0 5

  3. - 5 0 5 To GRAPH a set of numbers means to locate and mark the points on the number line. Graph {-1, 0, 2}. • • • Be sure to put the dots on the line - not above or below.

  4. Name the set of numbers graphed. {-2, -1, 0, . . . } The darkened arrow means that the graph keeps on going. When you see this, put 3 dots in your set.

  5. 1) (-4) + 8 = Examples: Use the number line if necessary. 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2

  6. Addition Rule 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = -6 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = 2 2 + (-4) = -2

  7. Karaoke Time! Addition Rule: Sung to the tune of “Row, row, row, your boat” Same signs add and keep,different signs subtract,keep the sign of the higher number,then it will be exact! Can your class do different rounds?

  8. Answer Now -1 + 3 = ? • -4 • -2 • 2 • 4

  9. Answer Now -6 + (-3) = ? • -9 • -3 • 3 • 9

  10. The additive inverses(or opposites) of two numbers add to equal zero. -3 Proof: 3 + (-3) = 0 We will use the additive inverses for subtraction problems. Example: The additive inverse of 3 is

  11. What’s the difference between7 - 3 and 7 + (-3) ? 7 - 3 = 4 and 7 + (-3) = 4 The only difference is that 7 - 3 is a subtraction problem and 7 + (-3) is an addition problem. “SUBTRACTING IS THE SAME AS ADDING THE OPPOSITE.” (Keep-change-change)

  12. When subtracting, change the subtraction to adding the opposite (keep-change-change) and then follow your addition rule. Example #1: - 4 - (-7) - 4+ (+7) Diff. Signs --> Subtract and use larger sign. 3 Example #2: - 3 - 7 - 3+ (-7) Same Signs --> Add and keep the sign. -10

  13. Okay, here’s one with a variable! Example #3: 11b - (-2b) 11b+ (+2b) Same Signs --> Add and keep the sign. 13b

  14. Answer Now Which is equivalent to-12 – (-3)? • 12 + 3 • -12 + 3 • -12 - 3 • 12 - 3

  15. Answer Now 7 – (-2) = ? • -9 • -5 • 5 • 9

  16. 1) If the problem is addition, follow your addition rule.2) If the problem is subtraction, change subtraction to adding the opposite (keep-change-change) and then follow the addition rule. Review

  17. Absolute Value of a number is the distance from zero. Distance can NEVER be negative! The symbol is |a|, where a is any number.

  18. Examples 7 = 7 10 = 10 -100 = 100 5 - 8 = -3= 3

  19. Answer Now |7| – |-2| = ? • -9 • -5 • 5 • 9

  20. Answer Now |-4 – (-3)| = ? • -1 • 1 • 7 • Purple

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