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Adding and Subtracting Real Numbers

Adding and Subtracting Real Numbers. Warm Up. Evaluate each expression for x = 8, y = 4, and z = 2. x + y x - y y z. Adding and Subtracting Real Numbers.

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Adding and Subtracting Real Numbers

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  1. Adding and SubtractingReal Numbers CONFIDENTIAL

  2. Warm Up Evaluate each expression for x = 8, y = 4, and z = 2. • x + y • x - y • y • z CONFIDENTIAL

  3. Adding and Subtracting Real Numbers 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. CONFIDENTIAL

  4. Adding and Subtracting Numbers on a Number Line Add or subtract using a number line. A) -3 + 6 Start at 0. Move left to -3. To add 6, move right 6 units. CONFIDENTIAL

  5. B) -2 - (-9) Start at 0. Move left to -2. To subtract -9, move right 9 units. CONFIDENTIAL

  6. Now you try! Add or subtract using a number line. 1a) -3 + 7 1b) -3 – 7 1c) -5 - (-6.5) CONFIDENTIAL

  7. The absolute value of a number is its distance from zero on a number line. The absolute value of 5 is written as |5|. CONFIDENTIAL

  8. Adding Real Numbers CONFIDENTIAL

  9. Adding Real Numbers Add. A) -3 + (-16) = -3 + (-16) = 19 B) x + 7 for x = -13 x + 7 = (-13) + 7 = (-13) + 7 = -6 When the signs of the numbers are the same, find the sum of their absolute values: 3 + 16 = 19. Both numbers are negative, so the sum is negative. First substitute -13 for x. When the signs are different, find the difference of the absolute values: 13 - 7 = 6. Use the sign of the number with the greater absolute value. The sum is negative. CONFIDENTIAL

  10. Now you try! Add. 2a) -5 + (-7) 2b) -13.5 + (-22.3) 2c) x + (-68) for x = 52 CONFIDENTIAL

  11. Two numbers are opposites if their sum is 0. A number and its opposite are the same distance from zero. They have the same absolute value. A number and its opposite are additive inverses . To subtract signed numbers, you can use additive inverses. Subtracting a number is the same as adding the opposite of the number. CONFIDENTIAL

  12. Subtracting Real Numbers CONFIDENTIAL

  13. Subtracting Real Numbers Subtract. A) 7 - 10 7 - 10 = 7 + (-10) = -3 B) -3 - (-12) -3 - (-12) = -3 + 12 = -9 C) x - 22 for x = -11 x - 22 = -11 - 22 =-11 + (-22) = -33 To subtract 10, add -10. When the signs of the numbers are different, subtract the absolute values: 10 - 7 = 3. Use the sign of the number with the greater absolute value. The sum is negative. To subtract -12, add 12. When the signs of the numbers are different, subtract the absolute values: 12 - 3 = 9. Use the sign of the number with the greater absolute value. The sum is positive. First substitute -11 for x. To subtract 22, add -22. When the signs of the numbers are the same, add the absolute values: 11 + 22 = 33. Both numbers are negative, so the sum is negative. CONFIDENTIAL

  14. Now you try! Subtract. 3a) 13 - 21 3b) -1 -(- 1) 2 2 3c) x - (-12) for x = -14 3 CONFIDENTIAL

  15. Adding Real Numbers An emperor penguin stands on an iceberg that extends 10 feet above the water. Then the penguin dives to an elevation of -67 feet to catch a fish. What is the total length of the penguin’s dive? Find the difference in the elevations of the iceberg and the fish. elevation of iceberg minus elevation of fish 10 - (-67) 10 - (-67) = 10 + 67 = 77 To subtract -67, add 67. Find the sum of the absolute values. The total length of the penguin’s dive is 77 feet. CONFIDENTIAL

  16. Now you try! 4) The tallest known iceberg in the North Atlantic rose 550 feet above the ocean’s 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? CONFIDENTIAL

  17. Assessment Add or subtract using a number line. • 1) -4 + 7 • 2) -3.5 - 5 • 5.6 - 9.2 • 3 – (- 1) • 4 6 CONFIDENTIAL

  18. Add: • 91 + ( -11) • 3 + ( - 3) • 4 4 • 7) 15.6 + x for x = -17.9 3 4 CONFIDENTIAL

  19. 8) 23 - 36 9) 4.3 - 8.4 10) x – 4 for x = 1 5 5 Evaluate each expression for a = 3, b = 4, and c = 2. 1 2 CONFIDENTIAL

  20. Let’s review Adding and Subtracting Real Numbers 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. CONFIDENTIAL

  21. Adding and Subtracting Numbers on a Number Line Add or subtract using a number line. A) -3 + 6 Start at 0. Move left to -3. To add 6, move right 6 units. CONFIDENTIAL

  22. The absolute value of a number is its distance from zero on a number line. The absolute value of 5 is written as |5|. CONFIDENTIAL

  23. Adding Real Numbers CONFIDENTIAL

  24. Adding Real Numbers Add. A) -3 + (-16) = -3 + (-16) = 19 B) x + 7 for x = -13 x + 7 = (-13) + 7 = (-13) + 7 = -6 When the signs of the numbers are the same, find the sum of their absolute values: 3 + 16 = 19. Both numbers are negative, so the sum is negative. First substitute -13 for x. When the signs are different, find the difference of the absolute values: 13 - 7 = 6. Use the sign of the number with the greater absolute value. The sum is negative. CONFIDENTIAL

  25. Two numbers are opposites if their sum is 0. A number and its opposite are the same distance from zero. They have the same absolute value. A number and its opposite are additive inverses . To subtract signed numbers, you can use additive inverses. Subtracting a number is the same as adding the opposite of the number. CONFIDENTIAL

  26. Subtracting Real Numbers CONFIDENTIAL

  27. Subtracting Real Numbers Subtract. A) 7 - 10 7 - 10 = 7 + (-10) = -3 B) -3 - (-12) -3 - (-12) = -3 + 12 = -9 C) x - 22 for x = -11 x - 22 = -11 - 22 =-11 + (-22) = -33 To subtract 10, add -10. When the signs of the numbers are different, subtract the absolute values: 10 - 7 = 3. Use the sign of the number with the greater absolute value. The sum is negative. To subtract -12, add 12. When the signs of the numbers are different, subtract the absolute values: 12 - 3 = 9. Use the sign of the number with the greater absolute value. The sum is positive. First substitute -11 for x. To subtract 22, add -22. When the signs of the numbers are the same, add the absolute values: 11 + 22 = 33. Both numbers are negative, so the sum is negative. CONFIDENTIAL

  28. Adding Real Numbers An emperor penguin stands on an iceberg that extends 10 feet above the water. Then the penguin dives to an elevation of -67 feet to catch a fish. What is the total length of the penguin’s dive? Find the difference in the elevations of the iceberg and the fish. elevation of iceberg minus elevation of fish 10 - (-67) 10 - (-67) = 10 + 67 = 77 To subtract -67, add 67. Find the sum of the absolute values. The total length of the penguin’s dive is 77 feet. CONFIDENTIAL

  29. You did a great job today! CONFIDENTIAL

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