ObjectiveObjective

706.2.2 ~ compare and order rational 706.2.2 ~ compare and order rational numbers using appropriate inequality numbers using appropriate inequality

symbols.symbols.

Copy definitions in your journal Copy definitions in your journal glossary! glossary!

A A RATIONAL NUMBER RATIONAL NUMBER is a number that can be is a number that can be written as a fraction with an integer for its written as a fraction with an integer for its numerator and a nonzero integer for its numerator and a nonzero integer for its denominator.denominator.

2

1

5

3

1

12

4

31

5

2

““Rational Numbers”Rational Numbers”

Rational NumbersRational Numbers

IntegersIntegers

Whole NumbersWhole Numbers 0,1,2,3,4,5…0,1,2,3,4,5…

IntegersIntegers-3,-2,-1, 0,1,2,3…-3,-2,-1, 0,1,2,3…

Rational NumbersRational Numbers numbers that cannumbers that canrepresented as a represented as a ratio or fractionratio or fraction

0, bb

a

Whole NumbersWhole Numbers

““Comparison Property” Comparison Property”

If you are given any two numbers a and b, then there are three possible relationships between

them.

Either: a = b a  >  b a  <  b

We are comparing the two numbers,or putting them in order.

An inequality is a mathematical sentence using < or > to compare two expressions.

            Along with =, we can make any sentence true by Along with =, we can make any sentence true by using the appropriate symbol. using the appropriate symbol.

Symbol

Read as

< less than

> greater than

≤ less than or equal to

≥ greater than or equal to

≠ not equal to

We can use any of the following inequality symbols to compare numbers:

““Comparing Rational Numbers” Comparing Rational Numbers”

0.81

To compare Rational numbers, you must first make them all into decimals.To compare Rational numbers, you must first make them all into decimals. Then line up the decimal points and compare the digits from left to right until Then line up the decimal points and compare the digits from left to right until you find the place where the digits are different.you find the place where the digits are different.

0.84

0.81

0.84

4 is greater than 1, so 0.84 is greater than 0.81

Compare the fractions. Write < or >.

0.34 0.342

0.343

0.342

3 is greater than 2, so 0.34 is greater than 0.342

Compare the fractions. Write < or >.

>><<

Order the Numbers from Least to GreatestOrder the Numbers from Least to Greatest

0.7011, 0.7, 0.71, 0.70, 0.7 0.7011, 0.7, 0.71, 0.70, 0.7

0.70110.7011

0.70.7

0.710.71

0.700.70

0.70.7

Line up numbers by Line up numbers by the decimal pointthe decimal point

0.70110.7011

0.70.7000000

0.710.710000

0.700.707070

0.70.7777777

Write all decimals in Write all decimals in the same place valuethe same place value

Place numbers in Place numbers in order from least to order from least to

greatestgreatest

0.70110.7011

0.70.7

0.710.71

0.700.70

0.70.7

0 0.5 1

Plot the numbers on a number line. Then order them from least to greatest.

2

3,

8

5,67.0,2.0,

5

2

1.5

5.1,625.0,67.0,2.0,4.0

0.40.2 0.670.625 1.5

2

3,67.0,

8

5,

5

2,2.0

In order them from least to greatest.

Using a Number LineUsing a Number Line

Plot the numbers on a number line. Then order them from least to greatest.

,6.0,85.0,6.0,21.0,3.0

In order them from least to greatest.

Using a Number LineUsing a Number LineF DF D

3

2,85.0,

5

3,21.0,

3

1

85.0,3

2,

5

3,

3

1,21.0

0 0.5 1 1.50.30.21 0.6 0.6 0.85

Now, let’s practice!Now, let’s practice!

Study Assignment:Study Assignment:Textbook page 128 #1-38

Or706.2.2 Handout