Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up List the factors of each number. 1.
8 2. 10 3. 16 4. 20 5. 30
1, 2, 4, 8
1, 2, 5, 10
1, 2, 4, 8, 16
1, 2, 4, 5, 10, 20
1, 2, 3, 5, 6, 10, 15, 30
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Problem of the Day John has 3 coins, 2 of which
are the same. Ellen has 1 fewer coin than John,
and Anna has 2 more coins than John. Each girl
has only 1 kind of coin. Who has coins that could
equal the value of a half dollar?
Ellen and Anna
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Learn to write equivalent fractions.
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Vocabulary
equivalent fractions simplest form
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Additional Example 1 Finding Equivalent
Fractions Find two equivalent fractions for .
10
___
12


The same area is shaded when the rectangle is
divided into 12 parts, 18 parts, and 6 parts.
So , , and are all equivalent
fractions.
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Check It Out Example 1 Find two equivalent
fractions for .
4
__
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The same area is shaded when the rectangle is
divided into 6 parts, 12 parts, and 3 parts.
So , , and are all equivalent
fractions.
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Additional Example 2A Multiplying and Dividing
to Find Equivalent Fractions Find the missing
number that makes the fractions equivalent.
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In the denominator, 5 is multiplied by 4 to get
20.

20
4
12
____
Multiply the numerator, 3, by the same number, 4.

4
20
So is equivalent to .

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Additional Example 2B Multiplying and Dividing
to Find Equivalent Fractions Find the missing
number that makes the fractions equivalent.
80
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In the numerator, 4 is multiplied by 20 to get 80.

20
80
Multiply the denominator by the same number, 20.
____

20
100
So is equivalent to .

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Check It Out Example 2A Find the missing number
that makes the fraction equivalent.
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In the denominator, 9 is multiplied by 3 to get
27.

27
3
9
____
Multiply the numerator, 3, by the same number, 3.

3
27
So is equivalent to .

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Check It Out Example 2B Find the missing number
that makes the fraction equivalent.
40
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In the numerator, 2 is multiplied by 20 to get 40.

20
40
Multiply the denominator by the same number, 20.
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20
80
So is equivalent to .

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Every fraction has one equivalent fraction that
is called the simplest form of the fraction. A
fraction is in simplest form when the GCF of the
numerator and the denominator is 1.
Example 3 shows two methods for writing a
fraction in simplest form.
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Additional Example 3A Writing Fractions in
Simplest Form Write each fraction in simplest
form.
20
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48
The GCF of 20 and 48 is 4, so is not in
simplest form.
Method 1 Use the GCF.
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Divide 20 and 48 by their GCF, 4.

4
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Additional Example 3A Continued
Method 2 Use prime factorization.
Write the prime factors of 20 and 48. Simplify.
_________________


2 2 2 2 3
So written in simplest form is .
Helpful Hint
Method 2 is useful when you know that the
numerator and denominator have common factors,
but you are not sure what the GCF is.
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Additional Example 3B Writing Fractions in
Simplest Form Write the fraction in simplest form.
The GCF of 7 and 10 is 1 so is already in
simplest form.
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Check It Out Example 3A Write each fraction
in simplest form.
12
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16
The GCF of 12 and 16 is 4, so is not in
simplest form.
Method 1 Use the GCF.
4
Divide 12 and 16 by their GCF, 4.

4
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Check It Out Example 3A Continued
Method 2 Use prime factorization.
Write the prime factors of 12 and 16. Simplify.
_____________


2 2 2 2
So written in simplest form is .
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Check It Out Example 3B Write the fraction in
simplest form.
The GCF of 3 and 10 is 1, so is already in
simplest form.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz

• Find two equivalent fractions for each given
  fraction.
• 1. 2.
• Find the missing number that makes the fractions
  equivalent.
• 3. 4.
• Write each fraction in simplest form.
• 5. 6.

Possible answers
20
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75
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Lesson Quiz for Student Response Systems
1. Identify two equivalent fractions for .
A. C. B. D.
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Lesson Quiz for Student Response Systems
2. Identify two equivalent fractions for .
A. C. B. D.
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Lesson Quiz for Student Response Systems
3. Identify the missing number that makes the
given fractions equivalent. A. 3 C.
6 B. 4 D. 9
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Lesson Quiz for Student Response Systems
4. Identify the missing number that makes the
given fractions equivalent. A. 24 C.
40 B. 32 D. 48
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Lesson Quiz for Student Response Systems
5. Identify the simplest form of the fraction
A. C. B. D.