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Course 2, Lesson 3-1

Lesson 1: Integers and Absolute Value

The Number System

Chapter 3

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Course 2, Lesson 3-1

WHAT happens when you add,

subtract, multiply, and divide integers?

The Number System

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  • To identify and graph integers
  • To find absolute value

Course 2, Lesson 3-1

The Number System

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  • integer
  • negative integer
  • positive integer
  • graph
  • absolute value

Course 2, Lesson 3-1

The Number System

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1

Need Another Example?

Step-by-Step Example

Write an integer for the situation.

1.

an average temperature of 5 degrees below normal

Because it represents below normal, the integer is –5.

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Answer

Need Another Example?

a loss of 12 yards

−12

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1

Need Another Example?

Step-by-Step Example

2.

Write an integer for the situation.

an average rainfall of 5 inches above normal

Because it represents above normal, the integer is +5 or 5.

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Answer

Need Another Example?

a snowfall of 4 inches above normal

+4

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1

Need Another Example?

Step-by-Step Example

3.

Graph the set of integers {4, –6, 0} on a number line.

Draw a number line. Then draw a

dot at the location of each integer

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Answer

Need Another Example?

Graph the set of integers {–1, 3, –2} on a number line.

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Course 2, Lesson 3-1

Absolute Value

The Number System

Words The absolute value of a number is the distance between

the number and zero on a number line.

Examples

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1

Need Another Example?

2

3

Step-by-Step Example

4.

Evaluate the expression.

| –4 |

The graph of –4 is 4 units from 0.

4 Units

So, | –4 | = 4.

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Answer

Need Another Example?

Evaluate | –5 |.

5

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| –5 | – | 2 |

Need Another Example?

2

Step-by-Step Example

5.

Evaluate the expression.

| –5 | – | 2 | = 5 – 2

| –5 | = 5, | 2 | = 2

So, | –5 | – | 2 | = 3.

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Answer

Need Another Example?

Evaluate | –4 | – | –3 |.

1

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1

Need Another Example?

2

3

Step-by-Step Example

6.

Nick climbs 30 feet up a rock wall and then climbs

22 feet down to a landing area. The number of feet Nick climbs can be represented using the expression | 30 | + | –22 |. How many feet does Nick climb?

| 30 | + | –22 | = 30 + | –22 |

The absolute value of 30 is 30.

The absolute value of –22 is 22. Simplify.

= 30 + 22 or 52

So, Nick climbs 52 feet.

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Answer

Need Another Example?

Megan’s dog gained weight and then lost weight. The number of pounds her dog gained and then lost is represented by the expression | 6 | + | –3 |. How many pounds did Megan’s dog gain and lose?

9 pounds

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How did what you learned

today help you answer the

WHAT happens when you add,

subtract, multiply, and divide integers?

Course 2, Lesson 3-1

The Number System

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How did what you learned

today help you answer the

WHAT happens when you add,

subtract, multiply, and divide integers?

Course 2, Lesson 3-1

The Number System

Sample answers:

  • Integers can be used to represent real-world situations.
  • You can evaluate absolute value expressions involving integers.

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Describe a�real-world situation�that uses integers.

Course 2, Lesson 3-1

Ratios and Proportional Relationships

The Number System