Comparing and Ordering Rational Numbers

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(No Transcript)
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Lesson 5-1 Warm-Up
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Comparing and Ordering Rational Numbers (5-1)

• What is the a multiple?
• What is the the least common multiple or LCM?
• How do you find the LCM?

• Multiple The multiple of a number is the product
  of that number and any nonzero number (when you
  count by a number, you are finding its multiples)
• Example Multiples of 4 are 4, 8, 12, 16, 20, 24,
  28, 32, 36,.
• Example Multiples of 6 are 6, 12, 18, 24, 30,
  36, 42, 48, 54,.
• Least Common Multiple (LCM) the smallest
  multiple shared by all of the numbers
• Example Common Multiples of 4 are 6 are 12, 24,
  and 36. The smallest multiple of both numbers ,
  or Least Common Multiple (LCM) is 12.
• To find the LCM 1. list the multiples of both
  numbers until you find the first one that they
  share in common, or 2. multiply the greatest
  power of the factors the numbers.
• Example Find the LCM of 18, 27, and 36.
• Method 1 List the multiples of each number until
  you find a common one.
• Multiples of 18 are 18, 36, 54, 72, 90, 108,.
  
• Multiples of 27 are 27, 54, 81, 108,
• Multiples of 36 are 36, 72, 108,.
• The LCM of 18, 27, and 36 is 108.

Find the multiple of each number. Stop when you
find a multiple the numbers share in common.
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Comparing and Ordering Rational Numbers (5-1)

• Method 2 Multiply the greatest power of all
  factors together.
• Example Find the LCM of 18, 27, and 36.
• 18 3 3 2 32 2
• 27 3 3 3 33
• 36 3 3 2 2 32 22
• 33 22 27 4 108
• Example Find the LCM of 6a2 and 18a3.
• LCM of 6a2 and 18a3 is 18a3.

Create a factor tree number to find the prime
factors of each number.
Write each number in prime factorization. form
Multiply the greatest powers of all factors
together.
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
Today, the schools baseball and soccer teams
had games. The baseball team plays every 7 days.
The soccer team plays every 3 days. When will the
teams have games on the same day again?
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
Find the LCM of 16 and 36.
The LCM of 16 and 36 is 144.
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
Find the LCM of 5a4 and 15a.
The LCM of 5a4 and 15a is 15a4.
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Comparing and Ordering Rational Numbers (5-1)

• How do you compare fractions?

• To compare fractions, you can 1. use a number
  line (numbers to the right are greater than
  numbers to the left), or 2. compare the
  numerators (number of parts) if the denominator
  (size of the parts) are equal. So, if the
  denominators arent the same, you need to change
  one or more of the fractions into equivalent
  fractions with a common denominator.
• Method 1 Use a number line.
• Example Compare and .
• is on the left of , so ? .
• Method 1 Compare the numerators.
• Example Compare and .
• 3 4 12 Multiply the denominators together
  to find a common denominator
• Write equivalent fractions with a denominator
  of 12 and compare the numerators (Hint Notice
  that you multiply the each fraction by the
  other fractions denominator)
• Since ? , then ? .

- 1 2
- 1 10
- 1 10
- 1 2
- 1 10
- 1 2
2 3
3 4
2 4 8_ 3 4 12
3 3 9_ 4 3 12
8 12
9 12
3 4
2 3
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
Graph and compare the fractions in each pair.
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Comparing and Ordering Rational Numbers (5-1)

• Least Common Denominator (LCD) the LCM of two
  or more denominators (in other words, the
  smallest common denominator)
• Example
• List the multiples of each denominator
  until you find a multiple that
  is shared by both numbers (LCM). LCM 36
• Rewrite the fractions into equivalent
  fractions with a denominator of 36 (The
  LCD is 36). Then, compare the numerators.
• Since ? , then ? .

• What is the least common denominator (LCD)?

16 36
15 36
4 9
5 12
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
The softball team won of its games and the
hockey team won of its games. Which team won
the greater fraction of its games?
The softball team won the greater fraction of its
games.
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Comparing and Ordering Rational Numbers
LESSON 5-1
Additional Examples
Order , , and from least to greatest.
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Comparing and Ordering Rational Numbers
LESSON 5-1
Lesson Quiz
Find the LCM of each pair of numbers. 1. 8,
6 2. 12, 16 3. Compare and order ,
, and from least to greatest.
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