Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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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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Insert Lesson Title Here
Vocabulary
equivalent fractions simplest form
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Fractions that represent the same value are
equivalent fractions. So , , and are
equivalent fractions.


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Additional Example 1 Finding Equivalent
Fractions Find two equivalent fractions for .
10
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So , , and are all equivalent
fractions.
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Try This Example 1 Find two equivalent fractions
for .
4
__
6


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.
A.

20
4
12
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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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B.
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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Try This 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.
A.

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

3
27
So is equivalent to .

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Try This Example 2B Find the missing number that
makes the fraction equivalent.
40
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B.
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 the fraction in simplest form.
20
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A.
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 Writing Fractions in
Simplest Form Write the fraction in simplest form.
Method 2 Use a ladder diagram.
Use a ladder. Divide 20 and 48 by any common
factor (except 1) until you cannot divide anymore
2
20/48
2
10/24
5/12
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.
B.
The GCF of 7 and 10 is 1 so is already in
simplest form.
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Try This Example 3A Write the fraction in
simplest form.
12
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A.
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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Try This Example 3A Write the fraction in
simplest form.
Method 2 Use a ladder diagram.
Use a ladder. Divide 20 and 48 by any common
factor (except 1) until you cannot divide anymore
2
12/16
2
6/8
3/4
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Try This Example 3B Write the fraction in
simplest form.
B.
The GCF of 3 and 10 is 1, so is already in
simplest form.
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Insert Lesson Title Here
Lesson Quiz
Write 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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