Transcript Slide 1

Do Now 12/7/09
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Take out HW from last night.
– Text page 190, #16-36 evens
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Copy HW in your planner.
– Text page 190, #40-68 evens
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Be ready to copy POTW #4
Homework
Text page 190, #16-36 evens
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16)
18)
20)
22)
24)
26)
28)
36
16
42
165
12
420
80a³
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30)
32)
34)
36)
51b³
120s4
200a²
24 figures
Objective
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SWBAT find the least common multiple
of two numbers.
Section 4.4 “Least Common Multiple”
A multiple of a number is the
product of the number and any other
number greater than zero.
What are the multiples of 5?
Think of counting by fives…
5: ,5 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 …
Least Common Multiple
Of all the common multiples of two
numbers, the smallest is the least
common multiple.
Least Common Multiple
Find the LCM of 180 and 378.
When the numbers are too large to list the multiples
of the two numbers, find the prime factorization of each
number. The LCM is the product of the common prime
factors and the factors that are not common.
180: 2 · 2 · 3 · 3 · 5
Common
Factors
2·3·3
378: 2 · 3 · 3 · 3 · 7
Not Common
Factors
2·5
3·7
From the list you can see that 2, 3, and 3 are common prime
Factors, and the factors that are not common are 2, 3, 5, and 7.
The LCM is then 2 · 3 · 3 · 2 · 5 · 3 · 7 which is 3780.
Least Common Multiple
Find the LCM of 15, 30, and 50.
When you have three or more numbers,
the common prime factors may only be shared
by two of the numbers. The LCM is the product of the
common prime factors and the factors that are not common.
15:
3·5
30: 2 · 3 · 5
Common
Factors
2·3·5
Not Common
Factors
5
50: 2 · 5 · 5
From the list you can see that 2, 3, and 5 are common prime
factors, and the factor that is not common is 5.
The LCM is then 2 · 3 · 5 · 5 which is 150.
Least Common Multiple
Find the LCM of 10ab and 6b.
The LCM is the product of the common prime
factors and the factors that are not common.
10ab: 2 · 5 · a · b
Common
Factors
2·b
6b: 2 · 3 · b
Not Common
Factors
5·a
3
From the list you can see that 2 and b are common prime
factors, and the factors that are not common are 3, 5, and a.
The LCM is then 2 · b · 5 · a · 3 which is 30ab.
Least Common Multiple
Find the LCM of 2a³b and 3ab.5
The LCM is the product of the common prime
factors and the factors that are not common.
Common Factors
2a³b : 2 · a · a · a · b
5
3ab : 3 · a · b · b · b · b · b
a·b
Not Common Factors
2·a·a
3·b·b·b·b
From the list you can see that a and b are common prime
factors, and the factors that are not common are 2, 3, a, a, b,
b, b, and b. The LCM is then a · b · 2 · a · a · 3 · b · b · b · b
5
which is 6a³b.
Least Common Denominator
– The LCD of two or more fractions is the least
common multiple of the denominators. Use
the LCD to compare and order fractions.
“Using the LCD”
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Compare the fractions
3
4
and
2
3
.
List the equivalent fractions and find two with the same
denominator. Then compare.
3
6
9
4 = 8 = 12
2
4
6
8
=
=
=
3
6
9
12
same denominator,
now compare
Therefore, 3/4 is
greater than 2/3.
Compare the Following Fractions
1
4
2
7
1 7

4 28
2 8

7 28
1
4
5
12
1
3
5
5 1 4

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12 12 3 12
5
12
2
6
3
4
2 4

6 12
3 9

4 12
2
6
<
2
7
>
1
3
<
3
4
Order the fractions from
least to greatest.
Find the LCD for 4, 9, & 15.
3 4 7
, ,
4 9 15
LCD = 180
Rewrite equivalent fractions using the LCD.
3 135

4 180
4 80

9 180
4 7 3
, ,
9 15 4
7
84

15 180
Order the fractions from
least to greatest.
Find the LCD for 6, 9, & 3.
7 1 11
,1 ,
6 3 9
LCD = 18
Rewrite equivalent fractions using the LCD.
7 21

6 18
1 4 24
1  
3 3 18
7 11 1
, ,1
6 9 3
11 22

9 18
Rewrite the variable
expressions with a
common denominator.
Find the LCD for 5b and 4ab².
2a 3
,
2
5b 4ab
LCD = 20ab²
Rewrite equivalent fractions using the LCD.
2a
?

2
5b 20 ab
2a 2a  4ab 8a b
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
2
5b 5b  4ab 20ab
3
?
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2
2
4ab
20 ab
3
35
15
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2
2
2
4ab
4ab  5 20 ab
2
Rewrite the variable
expressions with a
common denominator.
Find the LCD for 5xy and 4y².
3x 2
,
2
4 y 5 xy
LCD = 20xy²
Rewrite equivalent fractions using the LCD.
3x
?

2
2
4y
20xy
3x
3x  5 x
15x
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2
2
2
4y
4 y  5x 20xy
2
?
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2
5 xy 20xy
2
24y
8y

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2
5 xy 5 xy  4 y 20xy
2
Rewrite the variable
expressions with a
common denominator.
5
18s
2 2 4
63r s t
3
2
2s 5r t
, 2
2 4
7r t 9s
4 5
35r t
2 2 4
63r s t
Homework
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Text page 190, #40-68 evens