2.1

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Use Integers and Rational Numbers

2.1 Warm-Up

Complete the statement using <, >, or =.

1. 1.3 ? 1.03

ANSWER >

ANSWER <

2. ?58

69

2.1 Warm-Up

Complete the statement using <, >, or =.

3. Order from least to greatest: , 0.04, , 0.4512

37

ANSWER 316

-inch strip

ANSWER0.04, , 0.45,37

12

A hobby store has balsa wood strips in three

thicknesses (in inches): , , and .

Which strip is the thickest?

316

532

18

4.

2.1 Example 1

Graph – 3 and – 4 on a number line. Then tell which number is greater.

On the number line, –3 is to the right of – 4. So, –3 > – 4.

ANSWER

2.1 Guided Practice

Graph the numbers on a number line. Then tell which number is greater.

On the number line, 4 is to the right of 0. So, 4 > 0.

ANSWER

1. 4 and 0

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

0 4

2.1 Guided Practice

On the number line, 2 is to the right of –5. So, 2 > –5.

ANSWER

2. 2 and –5

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

2–5

2.1 Guided Practice

On the number line, –1 is to the right of –6. So, –1 > –6.

ANSWER

3. –1 and –6

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

–1–6

2.1 Example 2

Tell whether each of the following numbers is a wholenumber, an integer, or a rational number: 5, 0.6,–2 , and –24.2

3

2.1 Example 3

A star’s color index is a measure of the temperature of the star. The greater the color index, the cooler the star. Order the stars in the table from hottest to coolest.

SOLUTION

Begin by graphing the numbers on a number line.

ASTRONOMY

2.1 Example 3

Read the numbers from left to right: – 0.22, – 0.03, 0.09, 0.21.

ANSWER

From hottest to coolest, the stars are Shaula, Rigel, Denebola, and Arneb.

2.1 Guided Practice

Tell whether each number in the list is a whole number, an integer, or a rational number. Then order the numbers from least to greatest.

YesYesYes0

YesYesNo –2

YesNoNo–1.2

YesYesYes3

Rational number?

Integer?Whole number?

Number

4. 3, –1.2, –2,0

ANSWER

–2, –1.2, 0, 3(Ordered the numbers from least to greatest).

2.1 Guided Practice

5. 4.5, – , – 2.1, 0.5 34

YesNoNo0.5

YesNoNo –2 .1

YesNoNo

YesNoNo4.5

Rational number?

Integer?Whole number?

Number

34

–

ANSWER

– 2.1, – , 0.5 , – 2.1.(Ordered the numbers from least to

greatest).

34

2.1 Guided Practice

6. 3.6, –1.5, –0.31, – 2.8

YesNoNo–2.8

YesNoNo –0.31

YesNoNo

YesNoNo3.6

Rational number?

Integer?Whole number?

Number

–1.5

ANSWER

–2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest).

2.1 Guided Practice

16

7. , 1.75, – , 023

ANSWER

– , 0 , , 1.75. (Ordered the numbers from least to

greatest).

23

16

16

YesYesYes0

YesNoNo

YesNoNo

YesNoNo

Rational number?

Integer?Whole number?

Number

1.75

23

–

2.1

Example 4

a. If a = – 2.5,

b. If a = , 34

For the given value of a, find –a.

then – a = –(– 2.5) = 2.5.

34

then – a = – .

2.1 Example 5

23

a. If a = – ,

b. If a = 3.2,

For the given value of a, find | a | .

then |a| = |3.2| = 3.2.

23

23

23

then | a | = |– | = – (– ) = .

2.1 Guided Practice

For the given value of a, find –a and |a|.

8. a = 5.3

– 5.3, 5.3

ANSWER

9. a = – 7

10. a = 49

–

7, 7

ANSWER

ANSWER

49

49

,

2.1 Example 6

Identify the hypothesis and the conclusion of the statement “If a number is a rational number, then the number is an integer.” Tell whether the statement is true or false. If it is false, give a counterexample.

Hypothesis: a number is a rational number

Conclusion: the number is an integer

The statement is false. The number 0.5 is a counterexample, because 0.5 is a rational number but not an integer.

SOLUTION

2.1 Guided Practice

Identify the hypothesis and the conclusion of the statement. Tell whether the statement is true or false. If it is the false, give a counterexample. 11. If a number is a rational number, then the number is positive

Conclusion: the number is positive – false

The number –1 is a counterexample, because –1 is a rational number but not positive.

Hypothesis: a number is a rational number

ANSWER

2.1 Guided Practice

Conclusion: the number is positive – false

The number –2 is a counterexample, because the absolute value of –2 is 2, but –2 is negative.

If the absolute value of a number is a positive, then the number is positive.

12.

Hypothesis: the absolute value of a number is positive

ANSWER

2.1 Lesson Quiz

1. Graph – 3 and –5 on a number line.Then tell which number is greater.

ANSWER –3 > –5

2. Tell whether each number is a whole number, an integer, or a rational number: –2.24, 6, , –16. 3 1

4

ANSWER

–2.24 :rational number; 6: whole number, integer, rational number ; :rational number; –16 : integer, rational number

3 14

2.1 Lesson Quiz

3. The table shows the boiling-point temperature of some elements. Order the elements from lowest boiling-point temperature to highest.

ANSWER

Hydrogen, Nitrogen, Oxygen, Mercury

Element Temperature

Hydrogen – 2593°C

Mercury 357°C

Nitrogen – 196°C

Oxygen – 183°C