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**Adding and Subtracting Real Numbers**

CONFIDENTIAL

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**Evaluate each expression for x = 8, y = 4, and z = 2.**

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

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**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

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**Adding and Subtracting Numbers on a Number Line**

Add or subtract using a number line. A) Start at 0. Move left to -3. To add 6, move right 6 units. CONFIDENTIAL

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

units. CONFIDENTIAL

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**Add or subtract using a number line.**

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

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**absolute value of 5 is written as |5|.**

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

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Adding Real Numbers CONFIDENTIAL

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**Adding Real Numbers A) -3 + (-16) B) x + 7 for x = -13 Add.**

= -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: = 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: = 6. Use the sign of the number with the greater absolute value. The sum is negative. CONFIDENTIAL

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**Now you try! Add. 2a) -5 + (-7) 2b) -13.5 + (-22.3)**

2c) x + (-68) for x = 52 CONFIDENTIAL

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**Two numbers are opposites if their sum is 0**

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

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**Subtracting Real Numbers**

CONFIDENTIAL

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**Subtracting Real Numbers**

= 7 + (-10) = -3 B) -3 - (-12) -3 - (-12) = = -9 C) x - 22 for x = -11 x - 22 = = (-22) = -33 To subtract 10, add -10. When the signs of the numbers are different, subtract the absolute values: = 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: = 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: = 33. Both numbers are negative, so the sum is negative. CONFIDENTIAL

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**Now you try! Subtract. 3a) 13 - 21 3b) -1 -(- 1) 2 2 3**

3c) x - (-12) for x = -14 3 CONFIDENTIAL

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**The total length of the penguin’s dive is 77 feet.**

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) = = 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

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**4) The tallest known iceberg in the North Atlantic**

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

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**Add or subtract using a number line.**

Assessment Add or subtract using a number line. 1) 2) 3 – (- 1) 4 6 CONFIDENTIAL

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**Add: 91 + ( -11) 3 + ( - 3) 4 4 3 7) 15.6 + x for x = -17.9 4**

3 + ( - 3) 7) x for x = -17.9 4 3 CONFIDENTIAL

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**Evaluate each expression for a = 3, b = 4, and c = 2.**

8) 9) 10) x – 4 for x = 1 2 1 CONFIDENTIAL

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**Adding and Subtracting Real Numbers**

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

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**Adding and Subtracting Numbers on a Number Line**

Add or subtract using a number line. A) Start at 0. Move left to -3. To add 6, move right 6 units. CONFIDENTIAL

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**absolute value of 5 is written as |5|.**

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

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Adding Real Numbers CONFIDENTIAL

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**Adding Real Numbers A) -3 + (-16) B) x + 7 for x = -13 Add.**

= -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: = 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: = 6. Use the sign of the number with the greater absolute value. The sum is negative. CONFIDENTIAL

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**Two numbers are opposites if their sum is 0**

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

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**Subtracting Real Numbers**

CONFIDENTIAL

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**Subtracting Real Numbers**

= 7 + (-10) = -3 B) -3 - (-12) -3 - (-12) = = -9 C) x - 22 for x = -11 x - 22 = = (-22) = -33 To subtract 10, add -10. When the signs of the numbers are different, subtract the absolute values: = 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: = 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: = 33. Both numbers are negative, so the sum is negative. CONFIDENTIAL

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**The total length of the penguin’s dive is 77 feet.**

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) = = 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

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**You did a great job today!**

CONFIDENTIAL

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Adding Integers. Zero Pair 1 + -1 = 0 Why it works… __________ Property says you can add or subtract zero without changing the value of an expression.

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