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Integers and Absolute Value

Integers and Absolute Value. Lesson 3-1. Integers can be graphed on a number line. To graph an integer on the number line, draw a dot on the line at its location. Identify and Graph Integers. Write an integer for each situation. a. An average temperature of 5 degrees below normal

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Integers and Absolute Value

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  1. Integers and Absolute Value Lesson 3-1

  2. Integers can be graphed on a number line. To graph an integer on the number line, draw a dot on the line at its location. Identify and Graph Integers

  3. Write an integer for each situation. a. An average temperature of 5 degrees below normal Because it represents below normal, the integer is -5 b. An average rainfall of 5 inches above normal. Becauseit represents above normal, the integer is +5 or 5. Example 1

  4. Write an integer for each situation. a. 6 degrees above normal +6 b. 2 inches below normal -2 Got it? 1

  5. Graph the set of integers {4, -6, 0} on a number line. Example 2

  6. Graph each set of integers on a number line. a. {-2, 8, -7} b. {-4, 10, -3, 7} Got it? 2

  7. On the number line in the box, notice that -5 and 5 are each 5 units from 0, even though they are on opposites sides of 0. Numbers that are the same distance from zero on the number line have the same absolute value. Absolute Value

  8. Evaluate each expression. a. -4 The graph of -4 is 4 units from 0. So, -4 = 4 b. -5 - 2 -5 - 2 5 – 2 3 Example 3

  9. Evaluate these expressions. a. 8 8 b. 2 + -3 5 c. -6 - 5 1 Got it? 3

  10. Nick climbs 30 feet up a rock wall and then climbs 22 feet down to a landing area. The number of feet Nick climbs can be represented using the expression 30 + -22. How many feet does Nick climb? 30 + -22 = 30 + -22 = 30 + 22 = 52 Example 4

  11. Add Integers Lesson 3-2

  12. Key Concept:

  13. a. Find -3 + (-2). Start at 0. Move 3 units down to show -3. From there, move 2 units down to show -2. Example 1

  14. b. Find -26 + (-17). -26 + (-17) = -43 Example 1

  15. a. -5 + (-7) -12 b. -10 + (-4) -14 c. -14 + (-16) -30 Got it? 1

  16. When you add integers with different signs, start at zero. Move right for positive integers. Move left for negative integers. So, the sum of p + q is located a distance q+ p. Key Concept:

  17. b. Find -3 + 2 So, -3 + 2 = -1 a. Find 5 + (-3) So, 5 + (-3) = 2 Example 2

  18. b. Find -15 + 19 4 a. Find 6 + (-7) -1 Got it? 2

  19. a. Find 7 + (-7) 7 + (-7) = 0 b. Find -8 + 3 -8 + 3 = -5 c. Find 2 + (-15) + (-2) 2 + (-2) + (-15) 0 + (-15) = -15 Example 3

  20. a. 10 + (-12) -2 b. -13 + 18 5 c. (-14) + (-6) + 6 -14 Got it? 3

  21. A roller coaster starts at point A. It goes up 20 feet, down 32 feet, and then up 16 feet to point B. Write an addition sentence to find the height at point B in relation to point A. Then find the sum and explain its meaning. 20 +(-32) + 16 = 20 + 16 + (-32) = 36 + (-32) = 4 Point B is 4 feet higher than point A. Example 4

  22. The temperature is -3. An hour later, it drops 6 and 2 hours later it rises 4. Write an addition expression to describe this situation. Then find the sum and explain its meaning. -3 + (-6) + 4 = -5 The new temperature is -5F. Got it? 4

  23. Subtract Integers Lesson 3-3

  24. Words: To subtract an integer, add its additive inverse. Symbols: p – q = p + (-q) Examples: 4 – 9 = 4 + (-9) 7 – (-10) = 7 + 10 Subtract Integers

  25. When you subtract 7, the result is the same as adding its additive inverse, -7.

  26. a. Find 8 – 13. 8 – 13 = 8 + (-13) = -5 b. Find -10 – 7. -10 – 7 = -10 + (-7) = -27 Example 1

  27. a. 6 – 12 -6 b. -20 – 15 -35 c. -22 – 26 -48 Got it? 1

  28. a. Find 1 – (-2). 1 – (-2) = 1 + 2 = 3 b. Find -10 – (-7). -10 – (-7) = -10 + 7 = -3 Example 2

  29. a. 4 – (-12) 16 b. -15 – (-5) -10 c. 18 – (-6) 24 Got it? 2

  30. a. Evaluate x – y if x = -6 and y = -5 x – y = -6 – (-5) = -6 + 5 = -1 b. Evaluate m – n if m = -15 and n= 8 m – n = -15 – 8 = -15 + (-8) = -23 Example 3

  31. Evaluate each expression if a = 5, b = -8, and c = -9. a. b - 10 -18 b. a – b 13 c. c – a -14 Got it? 3

  32. The temperatures on the Moon vary from -173C to 127C. Find the difference between the maximum and minimum temperatures. Subtract the lower temperatures from the higher temperature. 127 – (-173) = 127 + 173 = 300. The difference between the two temperatures is 300C. Example 4

  33. Brenda had a balance of -$52 in her account. The bank charged her a fee of $10 for having a negative balance. What is her new balance? -$62 Got it? 4

  34. Multiply Integers Lesson 3-4

  35. Words: The product of two integers with different signs is negative. Examples: 6(-4) = -24 -5(7) = -35 Remember that multiplication is the same as repeated addition. 4(-3) = (-3) + (-3) + (-3) + (-3) = -12 Multiply Integers with Different Signs

  36. a. Find 3(-5). 3(-5) = -15 Different signs, negative b. Find -6(8). -6(8) = -48 Different signs, negative Example 1

  37. a. 9(-2) = -18 b. -7(4) = -28 Got it? 1

  38. Words: The product of two integers with same signs is positive. Examples: 2(6) = 12 -10(-6) = 60 The product of two positive integers is positive. You can use a pattern to find the sign of products of two negative integers. Start with (2)(-3) = -6 and (1)(-3) = -3. Multiply Integers with the Same Signs

  39. Each product is 3 more than the previous. This pattern can also be shown on a number line. If you extend the pattern, the next two products are (-3)(-3) = 9 and (-4)(-3) = 12. Multiply Integers with the Same Signs

  40. a. Find -11(-9) -11(-9) = 99 Same signs, positive b. Find (-4)2 (-4)(-4) = 16 Same signs, positive c. Find -3(-4)(-2) -3(-4) = 12 Same signs, positive 12(-2) = -24 Different signs, negative Example 2

  41. a. -12(-4) 48 b. (-5)2 25 c. -7(-5)(-3) -105 Got it? 2

  42. A submersible is diving from the surface of the water at a rate of 90 feet per minute. What is the depth of the submersible after 7 minutes. The submersible descends 90 feet per minute. After 7 minutes, the vessel will be at 7(-90) or -630 feet. The submersible will be 630 feet below sea level. Example 3

  43. Mr. Simon’s bank automatically deducts a $4 monthly maintenance fee from his savings account. Write a multiplication expression to represent the maintenance fees for one year. Then find the product and explain its meaning. 12(-4) = -48 Mr. Simon will have $48 deducted from his account at the end of the year. Got it? 3

  44. Divide Integers Lesson 3-5

  45. Words: The quotient of two integers with different signs is negative. Examples: 33  (-11) = 3 -64  8 = -8 Divide Integers with Different Signs

  46. a. Find 80  (-10). 80  (-10) = -8 Different signs, negative b. Find . -55  11 = -5 Different signs, negative Example 1

  47. Use the table to find the constant rate of change in centimeters per hour. The height of the candle decreases by 2 centimeters each hour. So the constant rate of change is -2 centimeters per hour. Example 2

  48. a. 20  (-4) = -5 b. = -9 c. -45  9 = -5 Got it? 1 & 2

  49. Words: The quotient of two integers with the same signs is positive. Examples: 15  5 = 3 -64  (-8) = 8 Divide Integers with the Same Signs

  50. a. Find -14  (-7). -14  (-7) = 2 Same signs, positive b. Find . -27  -3 = 9 Same signs, positive Example 3

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