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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. - PowerPoint PPT Presentation
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CONFIDENTIAL 1
Adding and Adding and SubtractingSubtracting
Real NumbersReal Numbers
CONFIDENTIAL 2
Warm UpWarm Up
1) x + y
2) x - y
3) y z
Evaluate each expression for x = 8, y = 4, and z = 2.
CONFIDENTIAL 3
Adding and Subtracting Real NumbersAdding 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
Add or subtract using a number line.
Adding and Subtracting Numbers on a Adding and Subtracting Numbers on a Number LineNumber 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 9units.
CONFIDENTIAL 6
Add or subtract using a number line.
Now you try!
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 NumbersAdding Real Numbers
CONFIDENTIAL 9
Adding Real NumbersAdding Real Numbers
A) -3 + (-16) = -3 + (-16) = 19
B) x + 7 for x = -13 x + 7 = (-13) + 7 = (-13) + 7 = -6
Add.
When the signs of the numbers are the same, findthe 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 differenceof the absolute values: 13 - 7 = 6.Use the sign of the number with the greaterabsolute value. The sum is negative.
CONFIDENTIAL 10
Add.
Now you try!
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 NumbersSubtracting Real Numbers
CONFIDENTIAL 13
Subtracting Real NumbersSubtracting Real Numbers
A) 7 - 107 - 10 = 7 + (-10) = -3
B) -3 - (-12)-3 - (-12) = -3 + 12 = -9
C) x - 22 for x = -11x - 22 = -11 - 22 = -11 + (-22) = -33
Subtract.
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 greaterabsolute 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 greaterabsolute 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
Subtract.
Now you try!
3a) 13 - 21
3b) -1 -(- 1) 2 2
3c) x - (-12) for x = -14
3
CONFIDENTIAL 15
Adding Real NumbersAdding Real Numbers
An emperor penguin stands on an iceberg thatextends 10 feet above the water. Then the penguindives to an elevation of -67 feet to catch a fish.What is the total length of the penguin’s dive?
To subtract -67, add 67.
Find the sum of the absolute values.
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
The total length of the penguin’s dive is 77 feet.
CONFIDENTIAL 16
4) The tallest known iceberg in the North Atlanticrose 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?
Now you try!
CONFIDENTIAL 17
Assessment
Add or subtract using a number line.
1) -4 + 7
2) -3.5 - 5 3) 5.6 - 9.2
4) 3 – (- 1) 4
6
CONFIDENTIAL 18
Add:
5) 91 + ( -11)
6) 3 + ( - 3) 4 4
7) 15.6 + x for x = -17.9
4 3
CONFIDENTIAL 19
Evaluate each expression for a = 3, b = 4, and c = 2.
8) 23 - 36
9) 4.3 - 8.4
10) x – 4 for x = 1 5 5
2 1
CONFIDENTIAL 20
Adding and Subtracting Real NumbersAdding 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.
Let’s review
CONFIDENTIAL 21
Add or subtract using a number line.
Adding and Subtracting Numbers on a Adding and Subtracting Numbers on a Number LineNumber 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 NumbersAdding Real Numbers
CONFIDENTIAL 24
Adding Real NumbersAdding Real Numbers
A) -3 + (-16) = -3 + (-16) = 19
B) x + 7 for x = -13 x + 7 = (-13) + 7 = (-13) + 7 = -6
Add.
When the signs of the numbers are the same, findthe 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 differenceof the absolute values: 13 - 7 = 6.Use the sign of the number with the greaterabsolute 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 NumbersSubtracting Real Numbers
CONFIDENTIAL 27
Subtracting Real NumbersSubtracting Real Numbers
A) 7 - 107 - 10 = 7 + (-10) = -3
B) -3 - (-12)-3 - (-12) = -3 + 12 = -9
C) x - 22 for x = -11x - 22 = -11 - 22 = -11 + (-22) = -33
Subtract.
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 greaterabsolute 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 greaterabsolute 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 NumbersAdding Real Numbers
An emperor penguin stands on an iceberg thatextends 10 feet above the water. Then the penguindives to an elevation of -67 feet to catch a fish.What is the total length of the penguin’s dive?
To subtract -67, add 67.
Find the sum of the absolute values.
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
The total length of the penguin’s dive is 77 feet.
CONFIDENTIAL 29
You did a great job You did a great job today!today!