1. Adding and Subtracting Real Numbers
CONFIDENTIAL

2. 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

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)
Start at 0. Move left to -3.
To add 6, move right 6 units.
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5. B) -2 - (-9) Start at 0. Move left to -2. To subtract -9, move right 9
units.
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6. 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)
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7. 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

8. Adding Real Numbers
CONFIDENTIAL

9. 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

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
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
= 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

14. Now you try! Subtract. 3a) 13 - 21 3b) -1 -(- 1) 2 2 3
3c) x - (-12) for x = -14 3
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15. 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

16. 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

17. Add or subtract using a number line.
Assessment
Add or subtract using a number line. 1) 2)
3 – (- 1) 4 6
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18. 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
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19. Evaluate each expression for a = 3, b = 4, and c = 2.8) 9)
10) x – 4 for x = 1 2 1
CONFIDENTIAL

20. 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

21. 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

22. 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

23. Adding Real Numbers
CONFIDENTIAL

24. 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

25. 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

26. Subtracting Real Numbers
CONFIDENTIAL

27. 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

28. 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

29. You did a great job today!
CONFIDENTIAL