# 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

β’ An integer is a positive or negative whole number.

β’ A positive number is a number greater than zero.

β’ 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. ππ ππ below sea level

• Integers and Absolute Value

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

a. ππ ππ below sea level

βππ

• Integers and Absolute Value

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

b. a bonus of \$πππ

• Integers and Absolute Value

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

b. a bonus of \$πππ

+πππ

• Integers and Absolute Value

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

c. π points lost

• Integers and Absolute Value

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

c. π points lost

βπ

• Integers and Absolute Value

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

a. βπ

• Integers and Absolute Value

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

a. βπ

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. βπ, π, π

• Integers and Absolute Value

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

b. βπ, π, π

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. βπ,βπ, π, π

• Integers and Absolute Value

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

c. βπ,βπ, π, π

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

• Integers and Absolute Value

β’ Every integer has an opposite integer.

β’ 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. βππ

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

a. βππ

+ππ

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

b. +πππ

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

b. +πππ

βπππ

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

c. π

• Integers and Absolute Value

Sample Problem 3: Find the opposite of each integer.

c. π

None opposite

• Integers and Absolute Value

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

a. βπ

• 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

βπ

• Integers and Absolute Value

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

b. π

• 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

π

• Integers and Absolute Value

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

c. βπ

• Integers and Absolute Value

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

c. βπ

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. ππ _____ β πππ

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

a. ππ > βπππ

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

b. ππ_______ β ππ

• Integers and Absolute Value

Sample Problem 5: Compare the following integers. Write .

b. ππ > βππ

• Integers and Absolute Value

β’ The absolute value of a number is the distance between 0 and the number on a number line.

β’ Remember that distance is always a positive quantity (or zero).

β’ Two vertical bars are used to represent absolute value. The symbol for absolute value of π is π .

• Integers and Absolute Value

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

a. βππ =

• Integers and Absolute Value

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

a. βππ =

βππ = ππ

• Integers and Absolute Value

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

b. +ππ =

• Integers and Absolute Value

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

b. +ππ =

+ππ = ππ

• Integers and Absolute Value

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

c. βπ, πππ =

• Integers and Absolute Value

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

c. βπ, πππ =

βπ, πππ = π, πππ

• Integers and Absolute Value

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

a. βππ , ππ,βπ, βπ

• Integers and Absolute Value

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

a. βππ , ππ,βπ, βπ

βππ = ππ βπ = π

ππ, ππ, βπ, π

βπ, π, ππ, ππ

βπ, βπ , ππ, βππ

• Integers and Absolute Value

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

b. π, +ππ , βπ ,βπ, βππ

• Integers and Absolute Value

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

b. π, +ππ , βπ ,βπ, βππ

+ππ = ππ βπ = π βππ = ππ

π, ππ, π, βπ, ππ

βπ, π, π, ππ, ππ

βπ, π, βπ , βππ , +ππ

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

a. βππ + ππ β ππ =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

a. βππ + ππ β ππ =

= ππ + ππ β ππ =

= ππ β ππ =

= ππ

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

b. ππ β +ππ β βπ =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

b. ππ β +ππ β βπ =

= ππ β ππ β π =

= ππ β π =

= π

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

c. πππ + βπ β ππ β βπ =

• Integers and Absolute Value

Sample Problem 8: Evaluate each of the following expressions.

c. πππ + βπ β ππ β βπ =

= πππ + π β ππ β π =

= πππ + ππ β π =

= πππ + πππ =

= πππ

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