# Integers and Absolute Value - · PDF file Integers and Absolute Value • The absolute value of a number is the distance between 0 and the number on a number line. • Remember that

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• Integers and Absolute Value Unit 1 Lesson 5

• Integers and Absolute Value

Students will be able to:

Understand integers and absolute value

Key Vocabulary:

An integer

Positive number

Negative number

Absolute value

Opposite

• Integers and Absolute Value

Integers

• An integer is a positive or negative whole number.

• A positive number is a number greater than zero.

• A negative number is a number less than zero.

• Integers and Absolute Value

This number line shows integers.

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

Negative integers Positive integers

Zero is neither positive nor negative

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

a. 𝟐𝟐 𝒇𝒕 below sea level

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

a. 𝟐𝟐 𝒇𝒕 below sea level

−𝟐𝟐

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

b. a bonus of \$𝟏𝟓𝟎

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

b. a bonus of \$𝟏𝟓𝟎

+𝟏𝟓𝟎

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

c. 𝟕 points lost

• Integers and Absolute Value

Sample Problem 1: Write an integer to represent each situation.

c. 𝟕 points lost

−𝟕

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

a. −𝟒

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

a. −𝟒

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

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

b. −𝟑, 𝟎, 𝟑

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

b. −𝟑, 𝟎, 𝟑

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

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

c. −𝟐,−𝟏, 𝟒, 𝟔

• Integers and Absolute Value

Sample Problem 2: Graph each integer or set of integers on a number line.

c. −𝟐,−𝟏, 𝟒, 𝟔

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

• Integers and Absolute Value

• Every integer has an opposite integer.

• A number and its opposite are the same distance from 0.

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

a. −𝟑𝟒

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

a. −𝟑𝟒

+𝟑𝟒

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

b. +𝟏𝟎𝟎

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

b. +𝟏𝟎𝟎

−𝟏𝟎𝟎

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

c. 𝟎

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

c. 𝟎

None opposite

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

a. −𝟔

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

a.

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

−𝟔

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

b. 𝟓

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

b.

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

𝟓

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

c. −𝟏

• Integers and Absolute Value

Sample Problem 4: Graph each integer and its opposite on a number line.

c. −𝟏

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

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

a. 𝟏𝟐 _____ − 𝟏𝟐𝟓

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

a. 𝟏𝟐 > −𝟏𝟐𝟓

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

b. 𝟐𝟓_______ − 𝟏𝟓

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

b. 𝟐𝟓 > −𝟏𝟓

• Integers and Absolute Value

• The absolute value of a number is the distance between 0 and the number on a number line.

• Remember that distance is always a positive quantity (or zero).

• Two vertical bars are used to represent absolute value. The symbol for absolute value of 𝟑 is 𝟑 .

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

a. −𝟏𝟑 =

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

a. −𝟏𝟑 =

−𝟏𝟑 = 𝟏𝟑

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

b. +𝟒𝟒 =

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

b. +𝟒𝟒 =

+𝟒𝟒 = 𝟒𝟒

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

c. −𝟏, 𝟗𝟗𝟗 =

• Integers and Absolute Value

Sample Problem 6: Find the absolute value of the following numbers.

c. −𝟏, 𝟗𝟗𝟗 =

−𝟏, 𝟗𝟗𝟗 = 𝟏, 𝟗𝟗𝟗

• Integers and Absolute Value

Sample Problem 7: Order the values from least to greatest.

a. −𝟏𝟓 , 𝟏𝟏,−𝟐, −𝟒

• Integers and Absolute Value

Sample Problem 7: Order the values from least to greatest.

a. −𝟏𝟓 , 𝟏𝟏,−𝟐, −𝟒

−𝟏𝟓 = 𝟏𝟓 −𝟒 = 𝟒

𝟏𝟓, 𝟏𝟏, −𝟐, 𝟒

−𝟐, 𝟒, 𝟏𝟏, 𝟏𝟓

−𝟐, −𝟒 , 𝟏𝟏, −𝟏𝟓

• Integers and Absolute Value

Sample Problem 7: Order the values from least to greatest.

b. 𝟒, +𝟒𝟒 , −𝟖 ,−𝟏, −𝟑𝟐

• Integers and Absolute Value

Sample Problem 7: Order the values from least to greatest.

b. 𝟒, +𝟒𝟒 , −𝟖 ,−𝟏, −𝟑𝟐

+𝟒𝟒 = 𝟒𝟒 −𝟖 = 𝟖 −𝟑𝟐 = 𝟑𝟐

𝟒, 𝟒𝟒, 𝟖, −𝟏, 𝟑𝟐

−𝟏, 𝟒, 𝟖, 𝟑𝟐, 𝟒𝟒

−𝟏, 𝟒, −𝟖 , −𝟑𝟐 , +𝟒𝟒

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

a. −𝟏𝟑 + 𝟏𝟑 − 𝟏𝟒 =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

a. −𝟏𝟑 + 𝟏𝟑 − 𝟏𝟒 =

= 𝟏𝟑 + 𝟏𝟑 − 𝟏𝟒 =

= 𝟐𝟔 − 𝟏𝟒 =

= 𝟏𝟐

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

b. 𝟓𝟒 − +𝟒𝟒 − −𝟖 =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

b. 𝟓𝟒 − +𝟒𝟒 − −𝟖 =

= 𝟓𝟒 − 𝟒𝟒 − 𝟖 =

= 𝟏𝟎 − 𝟖 =

= 𝟐

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

c. 𝟏𝟐𝟖 + −𝟗 ∗ 𝟏𝟎 ∗ −𝟒 =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

c. 𝟏𝟐𝟖 + −𝟗 ∗ 𝟏𝟎 ∗ −𝟒 =

= 𝟏𝟐𝟖 + 𝟗 ∗ 𝟏𝟎 ∗ 𝟒 =

= 𝟏𝟐𝟖 + 𝟗𝟎 ∗ 𝟒 =

= 𝟏𝟐𝟖 + 𝟑𝟔𝟎 =

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