Factor Trees
Objective To provide experiences with finding the greatest
common factor and the least common multiple of two numbers.
c
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Identify the prime factorization for
a number. [Number and Numeration Goal 3]
• Use greatest common factors and least
common multiples to rename fractions. [Number and Numeration Goal 5]
• Use multiplication facts to find
factor strings. [Operations and Computation Goal 2]
• Find greatest common factors and least
common multiples using factor strings. [Number and Numeration Goal 3]
Key Activities
Students use factor trees to find all the prime
factors of a number and write the prime
factorization. They use prime factorizations
to simplify fractions.
Family
Letters
1 2
4 3
Playing Factor Captor
Student Reference Book, p. 306
Math Masters, p. 455
calculator paper and pencil per partnership: 70 counters
Students practice finding factors
of larger numbers and recognizing
prime factors.
Math Boxes 12 1
Math Journal 2, p. 397
Students practice and maintain skills
through Math Box problems.
Study Link 12 1
Math Masters, p. 348
Students practice and maintain skills
through Study Link activities.
Use journal page 394. [Number and Numeration Goal 3]
Key Vocabulary
prime factorization factor tree common
factor greatest common factor least
common multiple
Materials
Math Journal 2, pp. 393 –396
Student Reference Book Glossary
Class Data Pad
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 79–82
Unit 12
Probability, Ratios, and Rates
Common
Core State
Standards
Ongoing Learning & Practice
Ongoing Assessment:
Recognizing Student Achievement
914
Assessment
Management
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Making Factor Rainbows
Students factor numbers by making
factor rainbows.
ENRICHMENT
Using a Division Method for Prime
Factorizations
Math Masters, p. 349
Students use division to find prime
factorizations.
EXTRA PRACTICE
Using Factor Trees to Find Common
Denominators
Math Masters, p. 350
Students identify common denominators
by using factor trees.
ELL SUPPORT
Making a Factor Tree Poster
per group: chart paper, markers
Students make a display to reference
concepts related to factor trees.
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, SMP8
Content Standards
Getting Started
5.NF.7a, 5.NF.7b, 5.NF.7c
Mental Math and Reflexes
Math Message
Have students compute each quotient and explain their answer using the
relationship between multiplication and division.
Solve Problems 1 and 2
on journal page 393.
1
1
_
5 ÷ (_
2 ) = 10 because 10 ∗ ( 2 ) = 5.
1
1
1
1
(_
)÷2=_
because (_
)∗2=_
.
4
8
8
4
1
1
_
5 ÷ (_
3 ) = 15 because 15 ∗ ( 3 ) = 5.
1
1
1
1
(_
)÷3=_
because (_
)∗3=_
.
5
15
15
5
1
1
1
1
_
_
_
(_
2 ) ÷ 4 = 8 because ( 8 ) ∗ 4 = 2 .
1
1
6 ÷ (_
) = 24 because 24 ∗ (_
) = 6.
4
4
1 Teaching the Lesson
▶ Math Message Follow-Up
(Math Journal 2, p. 393; Student Reference Book Glossary)
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
DISCUSSION
Have students read the definitions for factor, factor pair, composite
number, prime number, and factor string in the Student Reference
Book Glossary. Read and discuss how the terms relate. Discussion
should include the following points:
A factor of a number can be any type of number, but the other
terms only refer to whole numbers.
Numbers can be defined by their factors. For example, a prime
number has only two whole-number factors, 1 and itself.
A composite number has more than two whole-number factors.
A square number has an odd number of factors.
Each factor in the longest factor string of a number is prime.
The longest factor string is called its prime factorization.
Ask: What device can be used to find all the factor pairs for a number?
Factor rainbow Have students make factor rainbows for 48 and
share their solutions using the Class Data Pad. A factor tree is a
device that can be used to find the prime factorization of a number.
Draw one for 48 on the Class Data Pad. Ask: What is the prime
factorization for 48? 2 ∗ 2 ∗ 2 ∗ 2 ∗ 3 Have students refer to the
factor tree examples for 45 on Math Journal 2, page 393. Note that
each factor tree begins with two different factors for 45 but the
prime factorizations are the same. Ask students to make factor
trees for 36. Ask: What do you notice about the longest factor string
you recorded for Problem 2 and the result of your factor tree for 36?
They are the same: 2 ∗ 2 ∗ 3 ∗ 3.
Student Page
Date
Time
LESSON
12 1
䉬
Factors
Math Message
1.
Write all the pairs of factors whose product is 48. One pair has been done for you.
48 ⫽ 6 ⴱ 8,
2.
1 ⴱ 48; 2 ⴱ 24; 3 ⴱ 16; 4 ⴱ 12
One way to write 36 as a product of factors is 2 ⴱ 18. Another way is 2 ⴱ 2 ⴱ 9. Write 36
as the product of the longest possible string of factors. Do not include 1 as a factor.
2ⴱ2ⴱ3ⴱ3
Factor Trees and Greatest Common Factors
One way to find all the prime factors of a number is to make a factor tree. First write
the number. Underneath the number write any two factors whose product is that number.
Then write factors of each of these factors. Continue until all the factors are prime
numbers. Below are two factor trees for 45.
45
45
3 ⴱ 15
9 ⴱ 5
3 ⴱ 3 ⴱ 5
3 ⴱ 3 ⴱ 5
The greatest common factor of two whole numbers is the largest number that is a
factor of both numbers.
Example: Find the greatest common factor of 24 and 60.
Step 1 List all the factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.
Step 2 List all the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
▶ Finding Greatest
Common Factors
WHOLE-CLASS
ACTIVITY
Step 3 1, 2, 3, 4, 6, and 12 are on both lists. They are common factors. 12 is the
largest number, so it is the greatest common factor of 24 and 60.
3.
Find the greatest common factor of 18 and 27.
1, 2, 3, 6, 9, 18
1, 3, 9, 27
Factors of 27:
9
Greatest common factor:
Factors of 18:
SOLVING
(Math Journal 2, pp. 393–395)
Write the numbers 18 and 30 on the board. Ask students to name
all the factors of each number while you list them.
Math Journal 2, p. 393
Lesson 12 1
915
Student Page
Date
Time
LESSON
Factors of 18: 1, 2, 3, 6, 9, and 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30
Factor Trees and Greatest Common Factors
12 1
䉬
Another way to find the greatest common factor of two numbers is to use
prime factorization.
Circle 1, 2, 3, and 6 on both lists. Explain that because 1, 2, 3, and 6
are factors of both 18 and 30, they are called common factors.
Example: Find the greatest common factor of 24 and 60.
Step 1 Make factor trees and write the prime factorization of each number.
24 ⫽ 2 ⴱ 2 ⴱ 2 ⴱ 3
24
The largest of these common factors is called the greatest
common factor. The greatest common factor of 18 and 30 is 6.
2 ⴱ 12
2 ⴱ 2 ⴱ 6
2 ⴱ 2 ⴱ 2 ⴱ 3
60 ⫽ 2 ⴱ 2 ⴱ 3 ⴱ 5
60
2 ⴱ 30
There are two ways to find the greatest common factor of
two numbers:
2 ⴱ 2 ⴱ 15
2 ⴱ 2 ⴱ 3 ⴱ 5
Step 2 Circle pairs of common factors.
List all the factors of each number and identify the largest
common factor.
24 ⫽ 2 º 2 º 2 º 3
60 ⫽ 2 º 2 º 3 º 5
Step 3 Multiply one factor in each pair of circled factors.
The greatest common factor of 24 and 60 is 2 ⴱ 2 ⴱ 3, or 12.
夹
4.
Use factor trees to write the prime factorization of each
number. Identify the prime factors that these two numbers
have in common, and multiply them.
Make a factor tree for each number below, and write the prime factorization.
10
a.
75
b.
90
c.
3 ⴱ 30
3 ⴱ 25
2ⴱ5
3 ⴱ 3 ⴱ 10
3ⴱ5ⴱ5
3 ⴱ 3ⴱ2ⴱ5
2ⴱ5
10 ⫽
75 ⫽
3ⴱ5ⴱ5
Ask students to make factor trees for 18 and 30, and have
volunteers draw these two factor trees on the board.
3ⴱ3ⴱ2ⴱ5
90 ⫽
30
18
Math Journal 2, p. 394
2
6
º
3
º
3
º
10 º 3
3
2
º
5
º
3
Write the prime factorizations for 18 and 30 as shown below (one
above the other) on the board or a transparency. Ask: What prime
factors do these two numbers have in common? 2 and 3 Circle the
pairs of common factors in the prime factorizations for 18 and 30.
Explain that since 2 ∗ 3 = 6, the greatest common factor is 6. It is
the greatest number by which both 18 and 30 are divisible.
∗3∗3
30 = 2 ∗ 3 ∗ 5
GCF = 2 ∗ 3
18 = 2
Student Page
Date
Factor Trees and Greatest Common Factors
12 1
䉬
5. a.
b.
6. a.
b.
7. a.
b.
8.
9.
Have students make factor trees for 24 and 50, and have
volunteers add these two trees to the display on the board.
Ask: What is the greatest common factor of 24 and 50? 2 How do
the factor trees confirm that 2 is the greatest common factor of 24
and 50? They show that 2 is the only common prime factor.
5
3 and 5
15
2 and 5
10
What is the greatest common factor of 10 and 75?
Which prime factor(s) do 75 and 90 have in common?
What is the greatest common factor of 75 and 90?
Which prime factor(s) do 10 and 90 have in common?
What is the greatest common factor of 10 and 90?
Have students refer back to the factor trees for 24 and 36. Ask:
What is the greatest common factor of 24 and 36? 2 ∗ 2 ∗ 3,
or 12 Write the prime factorizations for 24 and 36, circling the
pairs of common factors. Point out that 2, 2, and 3 are the
common prime factors. Therefore, the greatest common factor is
2 ∗ 2 ∗ 3, or 12.
Use the factor trees in Problem 4 to help you write each fraction below in simplest
form. Divide the numerator and denominator by their greatest common factor.
10
a. ᎏᎏ
75
⫽
10
c. ᎏᎏ
90
⫽
⫼
⫼
10
ᎏᎏ
75
10
ᎏᎏ
90
5
ᎏᎏ
5
10
ᎏᎏ
10
⫽ ᎏ12ᎏ5
⫽ ᎏ19ᎏ
75
b. ᎏᎏ
90
What is the greatest common factor of 20 and 25?
20
ᎏᎏ
20
25
Write the fraction ᎏᎏ in simplest form.
⫼
Use the space below to draw factor trees. What
is the greatest common factor of 1,260 and 1,350?
⫽
75
ᎏᎏ
90
5
ᎏᎏ
5
5
⫽ ᎏ45ᎏ
⫼
ⴱ
2
2
⫽
15
ᎏᎏ
15
5
ᎏᎏ
6
2 ⴱ 32 ⴱ 5 ⫽ 90
1,260
2
cont.
5
Which prime factor(s) do 10 and 75 have in common?
25
10.
Greatest Common Factor = 6
Time
LESSON
1,350
ⴱ
2
630
2
ⴱ
2
ⴱ
315
ⴱ
2
ⴱ
3
ⴱ
105
2
ⴱ
2
ⴱ
3
ⴱ
3
ⴱ
35
ⴱ
2
ⴱ
3
ⴱ
3
ⴱ
5
ⴱ
2
7
2
675
2
ⴱ
3
ⴱ
225
ⴱ
3
ⴱ
3
ⴱ
75
2
ⴱ
3
ⴱ
3
ⴱ
3
ⴱ
25
ⴱ
3
ⴱ
3
ⴱ
3
ⴱ
5
ⴱ
5
Math Journal 2, p. 395
916
Unit 12
Probability, Ratios, and Rates
Tell students that the greatest common factor can be used to
simplify fractions. Ask students how they might use the greatest
24 .
common factor and the division rule to simplify the fraction _
36
The factor trees for 24 and 36 show their greatest common factor
to be 12. Divide the numerator and the denominator by the
24÷12
2.
2 . The simplified fraction is _
greatest common factor, _
=_
36÷12
3
3
Have students complete journal pages 393–395.
Student Page
Date
Time
LESSON
12 1
䉬
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 394
Problem 4
Factor Trees and Least Common Multiples
The least common multiple of two numbers is the smallest number that is a
multiple of both numbers.
Example: Find the least common multiple of 8 and 12.
Step 1 List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, and so on.
Step 2 List the multiples of 12: 12, 24, 36, 48, 60, and so on.
Use journal page 394, Problem 4 to assess students’ ability to factor numbers
and identify the prime factorizations. Students are making adequate progress if
they correctly form the factor pairs in each factor tree and write the correct
prime factorizations.
[Number and Numeration Goal 3]
Step 3 24 and 48 are in both lists. They are common multiples.
24 is the smallest number. It is the least common multiple for 8 and 12.
24 is also the smallest number that can be divided by both 8 and 12.
Another way to find the least common multiple for two numbers is to use
prime factorization.
Example: Find the least common multiple of 8 and 12.
Step 1 Write the prime factorization of each number:
8⫽2º2º2
12 ⫽ 2 º 2 º 3
Step 2 Circle pairs of common factors. Then cross out one factor in each
pair as shown below.
8⫽2º2º2
▶ Finding Least Common Multiples
(Math Journal 2, p. 396; Student Reference Book Glossary)
PARTNER
ACTIVITY
PROBLEM
PRO
PR
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VIN
ING
Have students locate the term least common multiple in the
Student Reference Book Glossary and read the entry. Ask: What is a
common multiple? A number that is a multiple of two or more given
numbers The quick common denominator is an example of a
common multiple. The smallest number that is a multiple of two
or more numbers is the least common multiple.
12 ⫽ 2 º 2 º 3
Step 3 Multiply the factors that are not crossed out. The least common multiple
of 8 and 12 is 2 º 2 º 2 º 3, or 24.
1.
Make factor trees and write the prime factorizations for each number.
15
a.
9
b.
3 ⴱ5
15 ⫽
2.
30
c.
2 ⴱ 15
3ⴱ3
3ⴱ5
3ⴱ3
9⫽
30 ⫽
2ⴱ 3 ⴱ 5
2ⴱ3ⴱ5
What is the least common multiple of …
a.
9 and 15?
45
b.
15 and 30?
30
c.
90
9 and 30?
Math Journal 2, p. 396
Have students list the first seven multiples of 6 and 9. Ask: What
numbers are in both lists? The common multiples are 18 and 36.
What is the least common multiple of 6 and 9? 18
Tell students that factor trees also can be used to find the least
common multiple of two numbers. This procedure is similar to
finding the greatest common factor.
Step 1: Refer to the prime factorizations for 18 and 30 from the
previous activity, circling the pairs of common factors.
Step 2: Draw a line through one factor in each of the pairs of
common factors.
∗3∗3
30 = 2 ∗ 3 ∗ 5
Game Master
18 = 2
Least common multiple: 2
Name
∗ 3 ∗ 3 ∗ 5 = 90
Date
Time
1 2
4 3
Factor
Lesson Captor
Title 1–110 Grid
Step 3: Write the remaining factors in a multiplication expression,
2 ∗ 3 ∗ 3 ∗ 5 = 90. The least common multiple of 18 and 30 is 90.
11 12 13 14 15 16 17 18 19 20
Have partners complete journal page 396. Circulate and assist.
21 22 23 24 25 26 27 28 29 30
1
2
3
4
5
6
7
8
9
10
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
2 Ongoing Learning & Practice
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
▶ Playing Factor Captor
(Student Reference Book, p. 306;
Math Masters, p. 455)
Students practice finding factors of larger numbers and
recognizing prime factors by playing Factor Captor on the
1–110 Grid.
PARTNER
ACTIVITY
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101
10
101 102
102 103
103 104
104 105
105 106
106 107
107 108
108 109
109 1110
Math Masters, p. 455
Lesson 12 1
917
Student Page
Date
▶ Math Boxes 12 1
Time
LESSON
12 1
(Math Journal 2, p. 397)
Solve.
1.
3
5
25 marbles
200 pennies
a.
If 15 marbles are ᎏᎏ of the marbles in a bag, how many are in the bag?
b.
If 14 pennies are 7% of a pile of pennies, how many are in the pile?
c.
75 students are absent today. This is 10% of the students enrolled at the school.
750
How many students are enrolled at the school?
3
Tyesha paid $90 for a new radio. It was on sale for ᎏ4ᎏ of
the regular price. What is the regular price of the radio?
d.
INDEPENDENT
ACTIVITY
Math Boxes
䉬
students
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 12-3.
$120.00
75
A scooter is on sale for 30% of the list
price. The sale price is $84. What is the
list price?
2.
3.
$280.00
Writing/Reasoning Have students write a response to the
following: Explain your solution strategy for Math Boxes,
Problem 2. Since $84.00 represents 30%, I divided 84 by
3 to find 10% of the list price. Then I multiplied that result by 10
to find the total list price; 84 ÷ 3 ∗ 10 = $280.00.
Write ⬎ or ⬍.
a.
0.75
b.
0.2
⬍
⬎
⬍
⬍ 0.9
⬍
8
ᎏᎏ
9
1
ᎏᎏ
6
3
c. ᎏᎏ
7
4
ᎏᎏ
8
5
d. ᎏᎏ
9
6
e. ᎏᎏ
11
7
ᎏᎏ
12
9
52
89
90
Solve.
4.
▶ Study Link 12 1
a.
One orange
weighs as much as
4
One cube
weighs as much as
Xs.
2
INDEPENDENT
ACTIVITY
8X
(Math Masters, p. 348)
Xs.
b.
4X
6X
One triangle
weighs as much as
1
One paper clip
weighs as much as
X.
1
ᎏᎏ
6
228 229
X.
Math Journal 2, p. 397
Home Connection Students work with factor trees.
They use these to write prime factorizations and to write
fractions in simplest form.
3 Differentiation Options
SMALL-GROUP
ACTIVITY
READINESS
▶ Making Factor Rainbows
To provide experience finding all the factors of a number, have
students make factor rainbows. For example, to make a factor
rainbow for the number 48, list all the factors of 48 in ascending
order. Then connect factor pairs. Every factor should be paired with
another factor. If there is an odd number of factors, the middle
factor is paired with itself. The product of each pair of factors
should be 48.
Study Link Master
Name
Date
STUDY LINK
Time
Factor Trees
12 1
䉬
1.
Make factor trees and find the prime factorization for the following numbers.
Example: 20
4
2
66
a.
12
20 ⫽ 2 ⴱ 2 ⴱ 5
20
º 5
º 2 º 5
66
b.
72
72
2 º 33
2 º 2 º 18
2 º 2 º 3 º6
2º 2º 3 º 2º3
2.
3.
2 ⴱ 3 ⴱ 11
⫽
10
ᎏᎏ
33
66
b. ᎏᎏ
72
⫽
Find the prime factorization for 250.
4. a.
11
ᎏᎏ
12
20
c. ᎏᎏ
72
⫽
5
ᎏᎏ
18
250 ⫽ 5 ⴱ 5 ⴱ 5 ⴱ 2
32
Simplify the fraction to the right.
150
ᎏᎏ
225
⫽
3
4
6
8
12
16
24
48
Have students make factor rainbows for given numbers.
Suggestions: 25, 32, 40, 49, 80, 100
ENRICHMENT
▶ Using a Division Method for
49
Prime Factorizations
2
ᎏᎏ
3
(Math Masters, p. 349)
49
Which has the fewest prime factors?
2
2ⴱ2ⴱ3ⴱ2ⴱ3
Circle the number that has the most prime factors.
63
b.
5.
72 ⫽
Write each fraction in simplest form. Use factor trees to help you. Show your work.
20
a. ᎏᎏ
66
1
2 º 36
2 º 3 º 11
66 ⫽
5–15 Min
100
PARTNER
ACTIVITY
5–15 Min
Practice
1
6. ᎏᎏ
4
ⴱ 36 ⫽
1
8. ᎏᎏ
3
ⴱ 90 ⫽
9
30
7.
0.25 ⴱ 360 ⫽
9.
33ᎏᎏ% of 90 ⫽
1
3
90
30
Math Masters, p. 348
918
Unit 12
Probability, Ratios, and Rates
To apply students’ understanding of factors, have them
use a division method to find prime factorizations. When
students have finished, discuss any questions or curiosities
they encountered.
Teaching Master
Name
INDEPENDENT
ACTIVITY
EXTRA PRACTICE
▶ Using Factor Trees to Find
Date
LESSON
Time
The Division Method for Prime Factorization
12 1
䉬
Use the method below to find the prime factorization of the following numbers.
5–15 Min
Example: Find the prime factorization for 732.
Step 1 Divide, using the smallest prime factor of the number as the divisor.
Common Denominators
Step 2 The quotient becomes the dividend. Use the smallest prime factor as the divisor,
and continue dividing until the quotient is a prime number.
2 732
(Math Masters, p. 350)
Divide: 732 ⫼ 2 ⫽ 366
Divide: 366 ⫼ 2 ⫽ 183
2 366
2 is not a factor of 183.
The next smallest prime factor is 3.
Students practice making factor trees to find prime factorizations.
They use factor trees to find common denominators, identify the
least common multiple of the denominators, and use the least
common multiple as a common denominator.
3 183
Divide: 183 ⫼ 3 ⫽ 61
61 61 is a prime number.
The prime factorization of 732 is
2 º 2 º 3 º 61
Step 3 Write the divisors as a multiplication expression.
732 = 2 º 2 º 3 º 61
This is the prime factorization of 732.
Use the division method to find the prime factorizations. Show your work.
SMALL-GROUP
ACTIVITY
ELL SUPPORT
▶ Making a Factor Tree Poster
15–30 Min
To provide language support for factors, guide students to make a
poster showing important vocabulary words related to factor trees.
Display the poster during lessons in this unit.
1.
1,056
2.
25 ⴱ 3 ⴱ 11
3,190
3.
24,598
2 ⴱ 72 ⴱ 251
2 ⴱ 5 ⴱ 11 ⴱ 29
2 1,056
2 3,190
2 528
5 1,595
2 264
29 319
2 132
11
2 66
3 33
11
2 24,598
7 12,299
7 1,757
251
Math Masters, p. 349
Factors
12
Factors: 1, 2, 3, 4, 6, 12
Factor
Tree:
20
1, 2, 4, 5, 10, 20
12
20
3 º4
4 º5
3 º2 º2
2 º2º5
Greatest Common Factor for 12 and 20 is 4
Least Common Multiple for 12 and 20 is 60
(3 º 22 ºº 22 º 5
)
3 º 2 º 2 º 5 = 60
Teaching Master
Name
Date
LESSON
Factor Trees and Adding Fractions
12 1
䉬
1.
Time
Make factor trees and write the prime factorization for each number below.
a.
b.
12
c.
42
32
6º2
7º6
2 º 16
2 º 3 º 2
7 º 2 º 3
2 º 2 º 8
2 º 2 º 2 º 4
2 º 2 º 2 º 2 º 2
12 ⫽
2.
a.
3.
2º3º2
42 ⫽
7º2º3
32 ⫽
2º2º2º2º2
Add the following fractions. Use the factor trees above to help you find the
least common multiple of the denominators. Use this least common multiple
as a common denominator.
40
96
21
7
—
ᎏ
ᎏ
⫽
⫹ 32
96
61
96
5
ᎏᎏ
12
⫽
b.
—
82
84
7
1
—
ᎏ
ᎏ
⫽
⫹ 12
84
89
, or 1ᎏ854ᎏ
84
41
ᎏᎏ
42
⫽
—
Use factor trees or some other method to find a common denominator for
the fraction pairs below. If you do not use factor trees, explain how you found
the least common denominators.
2
21
42
16
36
36
21
64
192
5
a. ᎏᎏ
14
and ᎏᎏ
7
b. ᎏᎏ
18
and ᎏᎏ
9
c. ᎏᎏ
24
and ᎏᎏ
Math Masters, p. 350
Lesson 12 1
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