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Integers and Absolute Values

Objective: Graph integers on a

number line and find absolute value.

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Example 1.

Study the pattern of the following subtraction sentences.

51 = 4

52 = 353 = 2

54 = 1

55 = 0

5

6 = ?

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Example 1.

Study the pattern of the following subtraction sentences.

51 = 4

52 = 353 = 2

54 = 1

55 = 0

5

6 = -1

This is an example of a negative number. A

negative number is less than zero.

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Integers

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IntegersNumbers to the left of zero

are less than zero.

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IntegersNumbers to the left of zero

are less than zero.

Numbers to the right of

zero are more than zero.

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IntegersNumbers to the left of zero

are less than zero.

Numbers to the right of

zero are more than zero.

The numbers1, -2, -3,

are called negative

integers. The number

negative 3 is written3.

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IntegersNumbers to the left of zero

are less than zero.

Numbers to the right of

zero are more than zero.

The numbers1, -2, -3,

are called negative

integers. The number

negative 3 is written3.

The numbers 1, 2, 3, are

called positive integers.

The number positive 4 is

written +4 or 4.

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IntegersNumbers to the left of zero

are less than zero.

Numbers to the right of

zero are more than zero.

The numbers1, -2, -3,

are called negative

integers. The number

negative 3 is written3.

The numbers 1, 2, 3, are

called positive integers.

The number positive 4 is

written +4 or 4.

Zero is neither negative nor

positive.

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Example 2a: Name the coordinates of D, E, and B

A E C B D

-6 -5 -4 -3 -2 -1 0 1 62 3 4 5

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Example 2b: Graph points F, U, and N on a number line if F has

coordinate 1, U has coordinate3, and N has coordinate 4.

-6 -5 -4 -3 -2 -1 0 1 62 3 4 5

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Absolute Value

Absolute Value

In words: The absolute value of a number is the distance the

number is from the zero point on the number line.

In symbols:|4| = 4 and |-4| = 4

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Example 3: Simplify

a. |9| + |-9|

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Example 3: Simplify

a. |9| + |-9|

|9| + |-9| = 9 + 9

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Example 3: Simplify

a. |9| + |-9||

|9| + |-9| = 9 + 9

= 18

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Example 3: Simplify

a. |9| + |-9||

|9| + |-9| = 9 + 9

= 18

b. |13| - |-2|

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Example 3: Simplify

a. |9| + |-9||

|9| + |-9| = 9 + 9

= 18

b. |13| - |-2|

|13| - |-2| = 132

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Example 3: Simplify

a. |9| + |-9||

|9| + |-9| = 9 + 9

= 18

b. |13| - |-2|

|13| - |-2| = 132

= 11

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Example 4: Evaluate the expression

|x| - 7 if x = - 13

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Example 4: Evaluate the expression

|x| - 7 if x = - 13

|x| - 7 = |-13| - 7

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Example 4: Evaluate the expression

|x| - 7 if x = - 13

|x| - 7 = |-13| - 7

= 137

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Example 4: Evaluate the expression

|x| - 7 if x = - 13

|x| - 7 = |-13| - 7

= 137

= 6

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Assignment: 1846 even, 4760 all