ALGEBRA 1ALGEBRA 12.1 Integers & Rational Numbers

VocabularyVocabularyWhole numbers: Counting

numbers starting with 0

Integers: positive and negative counting numbers and 0

Rational numbers: a number that can be written as a/b where a and b are both integers

Opposites: two numbers that are the same distance from 0 on a number line but on opposite sides

Absolute value: the distance between a number and 0 on the number line

VocabularyVocabulary

Graph and compare integersEXAMPLE 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

GUIDED PRACTICE

1. Graph 4 and 0 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

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

0 4

GUIDED PRACTICE

On the number line, 2 is to the right of –4. So, 2 > –5.

ANSWER

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

2–5

2. Graph 2 and -5 on a number line. Then tell which number is greater.

GUIDED PRACTICE

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

ANSWER

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

–1

–6

3. Graph -6 and -1 on a number line. Then tell which number is greater.

Classify numbers EXAMPLE 2

Tell whether each of the following numbers is a wholenumber, an integer, or a rational number: 5, 0.6, -2 and -24.

YesYesNo–24

YesNoNo

YesNoNo0.6

YesYesYes5

Rational number?

Integer?Whole number?

Number

23–2

3

2

GUIDED PRACTICE

1. Tell whether each of the following numbers is a wholenumber, an integer, or a rational number. Then order the numbers from least list to greatest.

Number Whole number?

Integer? Rational number?

3 Yes Yes Yes

–1.2 No No Yes

–2 No Yes Yes

0 Yes Yes Yes

3, –1.2, –2,0

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

GUIDED PRACTICE

4.5, – , – 2.1, 0.5

34

YesNoNo0.5

YesNoNo –2 .1

YesNoNo

YesNoNo4.5

Rational number?

Integer?Whole number?

Number

34

–

– 2.1, – ,0.5 ,– 2.1.(Order the numbers from least to greatest).

34

2. Tell whether each of the following numbers is a wholenumber, an integer, or a rational number. Then order the numbers from least list to greatest.

GUIDED PRACTICE

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

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

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

GUIDED PRACTICE

– , 0 , , 1.75. (Order the numbers from least to greatest).

23

16

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

Number Whole Number? Integer? Rational Number?1/6 No No Yes1.75 No No Yes-2/3 No No Yes

0 Yes Yes Yes

0,3

2,75.1,

6

1

Order rational numbers

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.

Star Rigel Arneb Denebola Shaula

Color index –0.03 0.21 0.09 – 0.22

SOLUTION

Begin by graphing the numbers on a number line.

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.

Order rational numbers

Find opposites of numbersEXAMPLE 4

a. If a = – 2.5, then – a = 2.5.

b. If a = , then – a = – . 34

34

Find absolute values of numbersEXAMPLE 5

23

23a. If a = – , then |a | = | | =

2-3

b. If a = 3.2, then |a| = |3.2| = 3.2.

GUIDED PRACTICE

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

1. a = 5.3

If a = 5.3, then –a = – 5.3 |a| = |5.3| = 5.3

2. a = -7

3. a = 9

4

If a = -7, then –a = 7 |a| = |-7| = 7

If a = -4/9, then –a = 4/9 |a| = |-4/9| = 4/9