2-2 Comparing and Ordering Rational Numbers AGENDA – August 11 th – 15 th Monday- 2-2 Comparing & Ordering Rational Numbers-NOTES – HW Practice B #’s 1-5

2-2 Comparing and Ordering Rational Numbers

AGENDA – August 11th – 15th

Monday- 2-2 Comparing & Ordering Rational Numbers-NOTES – HW Practice B #’s 1-5Tuesday – 2-2 Practice, Short QuizHW – Study for 2-1 & 2-2 TestWednesday – TEST 2-1 & 2-2Thursday – Integer Review NotesHW- Textbook page 57-58 #'s 28, 29, 32, 35, 36, 43, 46 (Write out the problems)Friday – 2-7 Solving Equations with Rational Numbers – HW p.98 #’s 1-12 EVEN


Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-2 Comparing and Ordering Rational NumbersWrite the question and show the work


Warm UpWrite each fraction as a decimal.

1. 1 3

0.3 2. 45

3. 4.

0.8

0.753 4

23

0.6


Problem of the Day

How much pie do you have if you take 2 of 5 total pieces?

0.4 pie


Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers.


least common denominator (LCD)

Vocabulary


To compare or order rational numbers, first write them in the same form. To compare fractions, find a common denominator. This could be the least common denominator (LCD), which is the least common multiple of the denominators.


Remember!

The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.


Additional Example 1A: Comparing Fractions by Finding a Common Denominator

Compare. Write <, >, or =.

Multiply 6 and 10 to find a common denominator.

5 6

7 10

Write the fractions with a common denominator.

Compare the fractions.

Method 1: Multiply to find a common denominator.

6 10 = 60

5 10 6 10

=5 6

10 10

= 50 60

7 6 10 6

=7 10

6 6

= 42 60

50 60

5 6

> 42 60

,so 7 10

>

>


Additional Example 1B: Comparing Fractions by Finding a Common Denominator


List multiples of 3 and 5. The LCM is 15.

2 3

4 5



Method 2: Find the least common denominator.

3; 3, 6, 9, 12, 15… 5; 5, 10, 15

2 5 3 5

=2 3

5 5

= 10 15

4 3 5

3

=4 5

3 3

= 12 15

10 15

2 3

< 12 15

,so 4 5

<

>


Check It Out: Example 1A


Multiply 2 and 5 to find a common denominator.

1 2

2 5



Method 1: Multiply to find a common denominator.

2 5 = 10

1 5 2 5

=1 2

5 5

= 5 10

2 2 5 2

=2 5

2 2

= 4 10

5 10

1 2

> 4 10

,so 2 5

>

>


Check It Out: Example 1B


List multiples of 3 and 4. The LCM is 12.

2 3

3 4



Method 2: Find the least common denominator.

3; 3, 6, 9, 12, … 4; 4, 8, 12…

2 4 3 4

=2 3

4 4

= 8 12

3 3 4

3

=3 4

3 3

= 9 12

8 12

2 3

< 9 12

,so 3 4

<

>


A. 5 5

Additional Example 2A: Comparing by Using Decimals


2 9 _ 2

7 _

Write the fractions as decimals.

5 = 5.2 and 5 = 5.285714… 2 9 _ 2

7 __

5.2 < 5.285714…, so 5 < 5 _ 2

9 _ 2

7 _ Compare the

decimals.

<


B. –0.44 –

Additional Example 2B & 2C: Comparing by Using Decimals

Compare. Write <, >, or =.2 5 _

– = –0.4 2 5 _

–0.44 < –0.4, so –0.44 < –2 5 _ Compare the

decimals.

<

Write - as decimal.2 5 _

C. 0.1 1 9 _

Compare the decimals.

Write as decimal.1 9 _

>

1 9 _ = 0.1

0.1 > 0.1, so > 0.11 9

_


A. 4 4

Check It Out: Example 2A


2 9 _ 3

5 _

Write the fractions as decimals.

4 = 4.2 and 4 = 4.6 2 9 _ 3

5 __


<

4.2 < 4.6, so 4 < 4 2 9 _ 3

5 _


B. –0.80 –

Check It Out: Example 2B & C

Compare. Write <, >, or =.4 5 _

– = –0.8 4 5 _

–0.80 = –0.8, so –0.80 = –4 5 _ Compare the

decimals.

=

Write – as decimal.4 5 _

C. 0.8 5 6 _


Write as decimal.5 6 _

>

0.83 > 0.8, so > 0.85 6

_ _

5 6 _ = 0.83


To order fractions and decimals, you can either write them all in the same form and then compare them, or place them on a number line.


Additional Example 3: Social Studies Application

The numbers , –3.4, 6.0, and –2.5

represent the percentage of change in populations for four states. List these numbers in order from least to greatest.

14 4__

–4 –3 –2 –1 0 1 2 3 4 5 6

6.0

Place the numbers on a number line and read them from left to right.

–2.5

–3.4

14 4__

14 4

The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0.__


Check It Out: Example 3

The numbers , 3.0, –2.2, and –3.9

represent the percentage of change in populations for four states. List these numbers in order from least to greatest.

7 2__

–5 –4 –3 –2 –1 0 1 2 3 4 5

–2.2

3.0

Place the numbers on a number line and read them from left to right.

–3.9

7 2__

The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and .7

2__


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizCompare. Write <, >, or =.

1.

2. – –0.29

4. Leeanne competed in a long-jump contest. Her

first jump was 3.75 m, her second jump was 3 m,

and her third jump was 3 m. Which jump was the longest?

3. –2 –2 >

>

<1 3

second jump

1 4

2 9

6 7

7 8

8 99

11


1. Identify the correct sign to compare.

A. <

B. =

C. >

D. ≤


1 5

1 7



– –0.498

A. <

B. >

C. =

D. ≤


3 7



–3 –3

A. <

B. ≥

C. >

D. =


5 8

4 9


4. Dalton competed in a shot put contest. His

first throw was 6 m, his second throw

was 6.78 m, his third throw was 6 m,

and his fourth throw was 6.59 m. Which was his longest throw?

A. first

B. second

C. third

D. fourth


4 9

8 9


Documents

2-2 Comparing and Ordering Rational Numbers AGENDA – August 11 th – 15 th Monday- 2-2 Comparing & Ordering Rational Numbers-NOTES – HW Practice B #’s 1-5