2-2 comparing and ordering rational numbers agenda – august 11 th – 15 th monday- 2-2 comparing...
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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
2-2 Comparing and Ordering Rational Numbers
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
2-2 Comparing and Ordering Rational Numbers
Warm UpWrite each fraction as a decimal.
1. 1 3
0.3 2. 45
3. 4.
0.8
0.753 4
23
0.6
2-2 Comparing and Ordering Rational Numbers
Problem of the Day
How much pie do you have if you take 2 of 5 total pieces?
0.4 pie
2-2 Comparing and Ordering Rational Numbers
Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers.
2-2 Comparing and Ordering Rational Numbers
least common denominator (LCD)
Vocabulary
2-2 Comparing and Ordering Rational Numbers
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.
2-2 Comparing and Ordering Rational Numbers
Remember!
The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.
2-2 Comparing and Ordering Rational 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
>
>
2-2 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions by Finding a Common Denominator
Compare. Write <, >, or =.
List multiples of 3 and 5. The LCM is 15.
2 3
4 5
Write the fractions with a common denominator.
Compare the fractions.
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
<
>
2-2 Comparing and Ordering Rational Numbers
Check It Out: Example 1A
Compare. Write <, >, or =.
Multiply 2 and 5 to find a common denominator.
1 2
2 5
Write the fractions with a common denominator.
Compare the fractions.
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
>
>
2-2 Comparing and Ordering Rational Numbers
Check It Out: Example 1B
Compare. Write <, >, or =.
List multiples of 3 and 4. The LCM is 12.
2 3
3 4
Write the fractions with a common denominator.
Compare the fractions.
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
<
>
2-2 Comparing and Ordering Rational Numbers
A. 5 5
Additional Example 2A: Comparing by Using Decimals
Compare. Write <, >, or =.
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.
<
2-2 Comparing and Ordering Rational Numbers
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
_
2-2 Comparing and Ordering Rational Numbers
A. 4 4
Check It Out: Example 2A
Compare. Write <, >, or =.
2 9 _ 3
5 _
Write the fractions as decimals.
4 = 4.2 and 4 = 4.6 2 9 _ 3
5 __
Compare the decimals.
<
4.2 < 4.6, so 4 < 4 2 9 _ 3
5 _
2-2 Comparing and Ordering Rational Numbers
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 _
Compare the decimals.
Write as decimal.5 6 _
>
0.83 > 0.8, so > 0.85 6
_ _
5 6 _ = 0.83
2-2 Comparing and Ordering Rational Numbers
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.
2-2 Comparing and Ordering Rational Numbers
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.__
2-2 Comparing and Ordering Rational Numbers
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__
2-2 Comparing and Ordering Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-2 Comparing and Ordering Rational Numbers
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
2-2 Comparing and Ordering Rational Numbers
1. Identify the correct sign to compare.
A. <
B. =
C. >
D. ≤
Lesson Quiz for Student Response Systems
1 5
1 7
2-2 Comparing and Ordering Rational Numbers
2. Identify the correct sign to compare.
– –0.498
A. <
B. >
C. =
D. ≤
Lesson Quiz for Student Response Systems
3 7
2-2 Comparing and Ordering Rational Numbers
3. Identify the correct sign to compare.
–3 –3
A. <
B. ≥
C. >
D. =
Lesson Quiz for Student Response Systems
5 8
4 9
2-2 Comparing and Ordering Rational Numbers
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
Lesson Quiz for Student Response Systems
4 9
8 9
2-2 Comparing and Ordering Rational Numbers