Lesson 2.1

Use Integers and Rational

Numbers

Essential Question: How do you compare positive and negative

numbers?

Before we start…

South Bend, Indiana + 725

Valdes Peninsula, Argentina

- 131

Fresno, California + 296

Laredo, Texas + 414

Cambridge, Massachusetts + 30

Lake Eyre, South Australia - 52

Dead Sea, Israel-Jordan - 1312

The elevation of several places on Earth is given below. Can you order them from highest to lowest?

South Bend, Indiana + 725

Valdes Peninsula, Argentina - 131

Fresno, California + 296

Laredo, Texas + 414

Cambridge, Massachusetts + 30

Lake Eyre, South Australia - 52

Dead Sea, Israel-Jordon - 1312

How do you display numbers?

• All numbers can be displayed using a number line.

• Remember the number line shows every number in order from least to greatest, from negative to positive.

The Sets of NumbersReal Numbers

Rational Numbers

Integers

Whole Numbers

• Whole numbers are the counting numbers 0, 1, 2, 3, …

• Integers are the numbers -3, -2, -1, 0, 1, 2, …– Positive integers are integers that are greater than

0– Negative integers are integers that are less than 0– 0 is neither positive or negative.

What are the rational numbers?

• The integers belong to the set of rational numbers.

• A rational number can be written as a fraction,

where and are integers and 0a

a b bb

• Since a rational number can be written as a fraction, it can also be written as a decimal.

• In decimal form, a rational number either terminates or repeats.

• Rational numbers belong to the set of real numbers.

Classify the numbers

Number Whole Number?

Integer? Rational Number?

5

0.6

- 24

22

3

Classify the numbers

Number Whole Number?

Integer? Rational Number?

Order the numbers from least to greatest and then classify.

Order the numbers from least to greatest and then classify.

Order the numbers from least to greatest and then classify.

Astronomy 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

Astronomy The apparent magnitude of a star is its brightness as observed from Earth. The greater the magnitude, the dimmer the star. Order the stars from brightest to dimmest.

Star Arcturus

Sirius Vega

Magnitude -0.06 -1.47 0.03

Geography The map shows various locations in Imperial County, California, and their elevations above or below sea level. Order the locations from lowest elevation to highest elevation.

Sports In golf, the goal is to have the least score among all the players. Which golf score, or , is the better score?

What are opposites?

• Two numbers that are the same distance from 0 on a number line but are on opposite sides of 0.

• 4 and – 4 are opposites because they are both 4 units from 0 and on opposite sides of 0.

Find the opposites of the given numbers

If 2.5, then

3If , then

4

If 8, then

a a

a a

a a

What is absolute value?

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

• The symbol represents the absolute value of a.

a

Absolute Value of a Number

If is a positive number, then .

If is 0, then 0.

If is a negative number, then .

a a a

a a

a a a

2 2

0 0

2 2 2

Find the absolute value of the numbers

2

3

3.2

9

#23. 6

#24. 3

a

a

#25. 18

#26. 0

a

a

What is a conditional statement?

• A conditional statement has a hypothesis and a conclusion.

• An if-then statement is a form of a conditional statement.– The if part contains the hypothesis.– The then part contains the conclusion.

If is a positive number, then .a a a

conditional statement

hypothesis conclusion

What do you do with an if-then statement?

• In mathematics, if-then statements are either true or false. – An if-then statement is true if the conclusion is

always true when the hypothesis is satisfied.– An if-then statement is false if for just one

example, counterexample, the conclusion is false when the hypothesis is satisfied.

Tell whether the statement is true or false

• If a number is a rational number, then the number is an integer.

• If a number is a rational number, then the number is positive.

Tell whether the statement is true or false

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

• If a number is an integer, then the number is either positive or negative.

• If a number is a positive integer, then the number is a whole number.

• If a number is negative, then its absolute value is negative.

• How do you compare positive and negative numbers?

Ticket Out the Door

• Order the elements in the table from the lowest boiling-point temperature to highest. Place your name on the paper and place it in the basket.

Element Hydrogen Mercury

Nitrogen

Oxygen

Temperature - 2593°C 357°C -196°C -183°C