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!