Today’s Plan: -Compare and order decimals -Human Number Line -Compare and order fractions 11/17/10 Compare and Order Rational Numbers Learning Target:

$Page 1: Today’s Plan: -Compare and order decimals -Human Number Line -Compare and order fractions 11/17/10 Compare and Order Rational Numbers Learning Target:$
Today’s Plan:-Compare and order decimals-Human Number Line-Compare and order fractions

11/17/10 Compare and Order Rational Numbers

Learning Target:

-I can convert, compare, and order fractions and decimals.

Entry Task

Compare the decimals. Write < or >.

1. 1.2 1.03 3.5 3.51

3. 0.32 and 0.312

2.>

56

0.8, 0.826, 56

4. Order , 0.8, 0.826 from least to greatest.

<

>



Learning Target:


Correct Homework

To compare decimals, line up the decimal points and compare digits from left to right until you find the place where the digits are different.

Course 2

2-11 Comparing and Ordering Rational Numbers


Additional Example 2A: Comparing Decimals

0.427 0.425

0.427

0.425

Since 0.007 > 0.005, 0.427 > 0.425.

Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:

7

5

7 > 5.

Course 2



Additional Example 2B: Comparing Decimals

0.73 0.734

0.733…

0.734


3

4

3 < 4.

Course 2


0.73 =_

Since 0.03 is < 0.04, 0.73 < 0.734._


Check It Out: Example 2B

0.334

0.3333…

0.334


3

4

3 < 4.

Course 2


0.33 =__

Since 0.003 is < 0.004, 0.33 < 0.334. __

0.3

Human Number Line: Order Decimals

Today’s Plan:-Mental math with decimals-Multiply decimals-Add and Subtract Decimals


Learning Target:


Learn to compare and order fractions and decimals.

Course 2


Vocabulary

rational number

A rational number is a number that can be written as a fraction with integers for its numerator and denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.

Course 2


Which is greater, or ?79

29

When two fractions have the same denominator, just compare the numerators.

79 > 2

9 because 7 > 2.

= 79

=29

Course 2


Compare the fractions. Write < or >.

Additional Example 1A: Comparing Fractions

79

58

79 = 7 · 8

9 · 8 = 5672

58 = 5 · 9

8 · 9 = 4572

5672 > 45

72 , and so . 79 > 5

8

Write equivalent fractions with 72 as the denominator.

Course 2


Compare the numbers.

Additional Example 1B: Comparing Fractions


25

37

– –

25– = –2 · 7

5 · 7= –14

3537– = –3 · 5

7 · 5=

–15 35

– 1435 > – 15

35 , and so – > .25

– 37

Write equivalent fractions with 35 as the denominator.Put the negative signs in the numerators.

Both fractions can be written with a denominator of 35.

Course 2



56

78

The LCM of the denominators 6 and 8 is 48.

56 = 5 · 8

6 · 8 = 4048

78 = 7 · 6

8 · 6 = 4248

4048 < 42

48 , and so . 56 < 7

8

Write equivalent fractions with 48 as the denominator.

Check It Out: Example 1A

Course 2


Compare the numerators.


68

57

– –

68– = –6 · 7

8 · 7= –42

5657– = –5 · 8

7 · 8=

–40 56

– 4256 < – 40

56 , and so – < .68

– 57

Write equivalent fractions with common denominators.Put the negative signs in the numerators.

Check It Out: Example 1B

Both fractions can be written with a denominator of 56.

Course 2


Course 2


The values on a number line increase as you move from left to right.

Remember!

Order

Additional Example 3: Ordering Fractions and Decimals

45

0.93, and 0.9 from least to greatest.,

45 = 0.80

Graph the numbers on a number line.

0 0.2 0.4 0.6 0.8 1

0.93

Write as decimals with the same number of places.

0.93 = 0.93 0.9 = 0.90

Course 2


0.80 < 0.90 < 0.93 Compare the decimals in order.

45From least to greatest, the numbers are , 0.9, 0.93.

Order , 0.84, and 0.7 from least to greatest.

Check It Out: Example 3

35

35 = 0.60

Graph the numbers on a number line.

0 0.2 0.4 0.6 0.8 1

0.84

Write as decimals with the same number of places.

0.84 = 0.84 0.7 = 0.70

Course 2


0.60 < 0.70 < 0.84 Compare the decimals in order.

35

From least to greatest, the numbers are , 0.7, 0.84.



Learning Target:


Assignment: Page 176 #

Course 2

4-3 Multiplying Decimals

You can use decimal grids to model multiplication of decimals. Each large square represents 1. Each row and column represents 0.1. Each small square represents 0.01. The area where the shading overlaps shows the product of the two decimals.

0.7

0.8

=

0.56

Course 2

4-3 Multiplying Decimals

To multiply decimals, multiply as you would with integers. To place the decimal point in the product, count the number of decimal places in each factor. The product should have the same number of decimal places in the factors.

7 856 56

0.7 0.8

1 decimal place

1 decimal place

2 decimal places

+

Same digits

0.


11/17/10 Decimals

Learning Target:

-I can solve problems containing decimals and determine if my answer is reasonable.

Multiply Decimals Worksheet

Conversion Practice


11/17/10 Decimals

Learning Target:



11/17/10 Decimals

Learning Target:


Add and subtract decimals

Documents

Today’s Plan: -Compare and order decimals -Human Number Line -Compare and order fractions 11/17/10 Compare and Order Rational Numbers Learning Target: