Transcript Compare & Order Rational Numbers

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Objective:
Compare and order
Rational numbers
Vocabulary:
Rational Numbers
Irrational Number
• Common Denominator
Least Common Denominator
•
•
•
What is a rational number???
Rational Number:
any number that can be
expressed as a fraction
Ex. Fractions, decimals, %’s, and
integers (whole #’s that are + and -)
Examples of Rational Numbers
20%
-5
Rational Numbers
Integers
-35
-27
Whole Numbers
1
0.8
-3
5
2.22
-1.444…
35
3
6
1
2
1.3
Irrational Number:
a number that does
not terminate AND
does not repeat
Pi (π) is an irrational
number…
3.1415926535897932384626433832795028841971693993751
05820974944592307816406286208998628034825342117067
98214808651328230664709384460955058223172535940812
84811174502841027019385211055596446229489549303819
64428810975665933446128475648233786783165271201909
14564856692346034861045432664821339360726024914127
37245870066063155881748815209209628292540917153643
67892590360011330530548820466521384146951941511609
43305727036575959195309218611738193261179310511854
80744623799627495673518857527248912279381830119491
Common Denominator:
A common number that
both denominators fit
into
Examples
Comparing Rational Numbers
Which is greater, or ?
7
9
2
9
When two fractions have the same
denominator, just compare the
numerators.
7 2
>
because
7
>
2.
9 9
Least Common Denominator (LCD):
the smallest number
that both
denominators will fit
into.
Examples
Which is greater, or ?
3
4
4
5
When two fractions have
different denominators,
find the LCD, then
compare.
Which is greater, 34 or 45 ?
What’s the LCD of both fractions?
The LCD of the denominators 4 and 5 is 20.
Answer:
Compare the Following Fractions
1
4
2
7
1
7

4 28
2
8

7
28
1
4
5
12
1
3
5
5

12 12
1
4

3 12
5
12
2
6
3
4
2
4

6 12
3
9

4 12
2
6
<
2
7
>
1
3
<
3
4
Comparing and Ordering
2-11 Rational Numbers
Additional Example 1A: Comparing Fractions
Compare the fractions. Write < or >.
7
5
9
8
The LCM of the denominators 9 and 8 is 72.
7 =
9
5 =
8
56 >
72
Course 2
7 · 8 = 56
9·8
72
5 · 9 = 45
8·9
72
45 , and so
72
7 .> 5
9
8
Write equivalent
fractions with 72 as the
denominator.
Compare the numbers.
Ordering Rational Numbers
To put decimals in order,
line up the decimal points
and compare using place
value.
Ordering Rational Numbers
Compare the decimals
0.427
> 0.425
0.427
0.425
Compare the numbers
that are different… 7 > 5
so…
Comparing and Ordering
2-11 Rational Numbers
Additional Example 3: Ordering Fractions and
Decimals
Order 4 , 0.93, and 0.9 from least to greatest.
5
Write as decimals with the same number of places.
4 = 0.80
0.93 = 0.93
0.9 = 0.90
5
Graph the numbers on a number line.
0.93
0
0.2
0.4
0.80 < 0.90 < 0.93
0.6
0.8
1
Compare the decimals in order.
From least to greatest, the numbers are 0.9, 0.93, 4 .
5
Course 2
Comparing and Ordering
2-11 Rational
Insert Lesson
Title Here
Numbers
Lesson Practice
Compare the fractions. Write > or <.
3 or 4
>
2. 5 or 2
8
3
10
7
Compare the decimals. Write < or >.
1.
3. 0.32 and 0.312
<
>
5 , 0.8, 0.826 from least to greatest.
6
5
0.8, 0.826,
6
4. Order
Course 2
Converting Fractions to Decimals
• To convert a Fraction to a Decimal manually, follow these
steps:
• Step 1: Find a number you can multiply by the bottom of the
fraction to make it 10, or 100, or 1000, or any 1 followed by
0s.
• Step 2: Multiply both top and bottom by that number.
•
Step 3. Then write down just the top number, putting the
decimal place in the correct spot (one space from the right for
every zero in the bottom number)
Method #1: Converting with
Proportions
• Example # 1: Express 3/4 as a Decimal
• Step 1: We can multiply 4 by 25 to become
100
• Step 2: Multiply top and bottom by 25
3
4
= 75
100
Example # 1 continued….
• Step 3: Write down 75 with the decimal place
2 spaces from the right (because 100 has 2
zeros);
• Answer = 0.75
• Can you explain what we just did?
• Try to express ¼ as a decimal using method #
1.
Try to express ¼ as a decimal using
method # 1.
Method #2: Convert by Dividing
 Example #1: to write 5/8 as a decimal, we
need to calculate 5 ÷ 8:
0.625
8 √ 5.000
So = 0.625 as a decimal.
 Try this example: write 4/5 as a decimal using
division (method #2).
write 4/5 as a decimal using
division (method #2)
Write 3/8 as a decimal using
division (method 2)
Write 2/7 as a decimal using
division (method 2)
Convert decimals to Percents
• To convert a decimal to a percent
Step 1:Multiply the decimal
by 100.
Step 2: Move the decimal
to the right two places.
0.45
Convert decimals to Percents
1.
2.
3.
4.
5.
0.38
0.235
0.005
1.05
0.023