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Adding and Subtracting Real Numbers. 1-2. Warm Up. Lesson Presentation. Lesson Quiz. Holt Algebra 1. Holt McDougal Algebra 1. 2. 2. 2. 2. 3. 5. Warm Up Simplify. 1. –4. –|4|. 2. |–3|. 3. Write an improper fraction to represent each mixed number. 6. 2. 14. 55. 3. 4.

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  1. Adding and Subtracting Real Numbers 1-2 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt McDougal Algebra 1

  2. 2 2 2 2 3 5 Warm Up Simplify. 1. –4 –|4| 2. |–3| 3 Write an improper fraction to represent each mixed number. 6 2 14 55 3. 4 4. 7 3 7 3 7 Write a mixed number to represent each improper fraction. 12 24 5. 6. 5 9

  3. Objectives Add real numbers. Subtract real numbers.

  4. Vocabulary real numbers absolute value opposites additive inverse

  5. All the numbers on a number line are called real numbers. You can use a number line to model addition and subtraction of real numbers. Addition To model addition of a positive number, move right. To model addition of a negative number move left. Subtraction To model subtraction of a positive number, move left. To model subtraction of a negative number, move right.

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

  7. - 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.

  8. 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.

  9. 1) (-4) + 8 = Examples: Use the number line if necessary. 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2

  10. 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

  11. 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?

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

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

  14. 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

  15. 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)

  16. 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

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

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

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

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

  21. A number and its opposite are additive inverses. To subtract signed numbers, you can use additive inverses. Subtracting 6 is the same as adding the inverse of 6. Additive inverses 11 – 6 = 5 11 + (–6) = 5 Subtracting a number is the same as adding the opposite of the number.

  22. 7 7 10 10 -100 100 5 - 8 -3= 3

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

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

  25. The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|. 5 units 5units - - - - - 6 5 - 1 0 1 2 3 4 5 6 4 3 2 |–5| = 5 |5| = 5

  26. Example 4: Oceanography Application An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg? Find the difference in the elevations of the top of the iceberg and the bottom of the iceberg. elevationat bottom of iceberg –247 elevation at top of iceberg 75 Minus – 75 – (–247) 75 – (–247) = 75 + 247 To subtract –247, add 247. Find the sum of the absolute values. = 322 The height of the iceberg is 322 feet.

  27. Check It Out! Example 4 What if…?The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? Minus elevationof the Titanic –12,468 elevation at top of iceberg 550 – 550 – (–12,468) To subtract –12,468, add 12,468. 550 – (–12,468) = 550 + 12,468 Find the sum of the absolute values. = 13,018 Distance from the iceberg to the Titanic is 13,018 feet.

  28. Lesson Quiz Add or subtract using a number line. –2 2. –5 – (–3) 1. –2 + 9 7 Add or subtract. 3. –23 + 42 19 4. 4.5 – (–3.7) 8.2 5. 6. The temperature at 6:00 A.M. was –23°F. At 3:00 P.M. it was 18°F. Find the difference in the temperatures. 41°F

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