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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.
<
>
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.
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
Compare the decimals. Write < or >.
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
2-11 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
Additional Example 2B: Comparing Decimals
0.73 0.734
0.733…
0.734
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
3
4
3 < 4.
Course 2
2-11 Comparing and Ordering Rational Numbers
0.73 =_
Since 0.03 is < 0.04, 0.73 < 0.734._
Compare the decimals. Write < or >.
Check It Out: Example 2B
0.334
0.3333…
0.334
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
3
4
3 < 4.
Course 2
2-11 Comparing and Ordering Rational Numbers
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
11/17/10 Compare and Order Rational Numbers
Learning Target:
-I can convert, compare, and order fractions and decimals.
Learn to compare and order fractions and decimals.
Course 2
2-11 Comparing and Ordering Rational Numbers
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
2-11 Comparing and Ordering Rational Numbers
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
2-11 Comparing and Ordering Rational Numbers
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
2-11 Comparing and Ordering Rational Numbers
Compare the numbers.
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >.
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
2-11 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
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
2-11 Comparing and Ordering Rational Numbers
Compare the numerators.
Compare the fractions. Write < or >.
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
2-11 Comparing and Ordering Rational Numbers
Course 2
2-11 Comparing and Ordering Rational Numbers
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
2-11 Comparing and Ordering Rational Numbers
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
2-11 Comparing and Ordering Rational Numbers
0.60 < 0.70 < 0.84 Compare the decimals in order.
35
From least to greatest, the numbers are , 0.7, 0.84.
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.
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.
Today’s Plan:-Mental math with decimals-Multiply decimals-Add and Subtract Decimals
11/17/10 Decimals
Learning Target:
-I can solve problems containing decimals and determine if my answer is reasonable.
Multiply Decimals Worksheet
Conversion Practice
Today’s Plan:-Mental math with decimals-Multiply decimals-Add and Subtract Decimals
11/17/10 Decimals
Learning Target:
-I can solve problems containing decimals and determine if my answer is reasonable.
Today’s Plan:-Mental math with decimals-Multiply decimals-Add and Subtract Decimals
11/17/10 Decimals
Learning Target:
-I can solve problems containing decimals and determine if my answer is reasonable.
Add and subtract decimals
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