Download Comparing and Ordering Fractions and Mixed Numbers

Comparing and
Ordering Fractions
and Mixed Numbers
Topic 9-5
Pgs. 230-231
How can you compare
fractions?
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Problem: Shawna and Tom walked two
different paths in Trout park. Shawna
walked 5/6 mile. Tom walked ¾ mile.
Which is greater, 5/6 or ¾?
Which is greater 5/6 or ¾?
One Way
To compare fractions, find
a common denominator
by writing the multiples
of each denominator
4: 4, 8, 12, 16, 20…
6: 6, 12, 16, 18, 24…
Use 12 as the common
denominator
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Multiply your fractions
by the number it takes
to get 12 as a
denominator

5 x 2 = 10
6
2
12
3 x 3 = 9
4
3
12
10/12 > 9/12 so,
5/6 > 3/4
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Which is greater 5/6 or ¾?
Another Way:
You can multiply the
denominators to find a
common denominator.
Compare ¾ and 5/6
Multiply denominators:
4 x 6= 24
Use 24 as the common
denominator

Multiply your fractions by
the number it takes to
get 24 as the
denominator
5 x 4 = 20
6
4
24
3 x 6 = 18
4 x 6
24
20/24 > 18/24 so
5/6 > 3/4
How can you order fractions
and mixed numbers?
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Write 2 5/12, 11/12, 3 1/6, 2 1/3 in order from least to greatest
You know that 11/12 < 1 and all the mixed numbers are greater
than 1. So 11/12 is the least number
When comparing mixed numbers, look at the whole number
parts. Since 3>2, you know that 3 1/6 is greater than both 2
1/3 and 2 5/12
Next, compare 2 1/3 and 2 5/12. Since the whole numbers are
the same, compare the fractions.
Compare 1/3 and 5/12. Change 1/3 to 4/12
4/12 < 5/12 so 2 1/3 < 2 5/12
From greatest to least, the numbers are 3 1/6, 2 5/12, 2 1/3,
11/12
Let’s Try it Together
Compare the
following fractions
1. 3
4
5
5
<, >, or =?
2. 1
2
4
3

Order from least to
greatest
1) 2
1
9
3 , 4 , 10
Answer: ¼, 2/3, 9/10
2) 1 2 2 1 1 9
3 10
4
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Answers: 1 2/3, 1 9/10, 2 1/4
Independent Practice #7-12
Use your notes to determine the correct
answer for #7-12.
 We will review the answers in 10
minutes
 Good Luck!

Common Factors
and Greatest
Common Factors
9-6
Pgs. 232- 233
Vocabulary
If a number is a factor of two numbers,
it is called a common factor
 The greatest common factor (GCF) of
two numbers is the greatest number
that is a factor of both numbers

How can you find the greatest
common factor of 20 and 30?
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Problem: A pet store has
goldfish and angelfish that
have to be put into the
fewest number of glass
containers. Each container
must contain the same
number of fish, and each
must contain all goldfish or
all angelfish.
Find the GCF of 20 and 30
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One Way:
To find the greatest common
factor of 20 and 30, you can
list all the factors of each
and circle the numbers they
have in common
20: 1, 2, 4, 5, 10, 20
30: 1, 2, 3, 5, 6, 10, 15, 30
Of all the numbers they have in
the common what is the
largest number?
10 so the GCF of 20 and 30=10
How can you find the greatest
common factor of 20 and 30?
Another way is to use prime factorization to find the GCF
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Find GCF of 24 and 18 (pg. 232)
1.
Find the prime factors of each number
2.
List the prime factors of each number
24= 2 x 2 x 2 x 3
18= 2 x 3 x 3
3. Circle the prime factors that both numbers share which are 2
and 3
4. Multiply the common factors: 2 x 3=6
So, the GCF of 18 and 24 is 6
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Let’s Try it Together!

1)
2)
3)
4)
5)
Find the GCF of each
pair of numbers
9 and 12
20 and 45
7 and 28
18 and 32
If two numbers are
prime, what is their
GCF?
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1.
2.
3.
4.
Answers:
3
5
7
2
Independent Practice
Complete #7-14 and we will review
them as a class
 Good Luck
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