Lesson Presentation

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Multiply. Write each answer in simplest
form. 1. 2 2 2. 1 3 3. 3
3 4. 2 1
5
or 5
10
or 2
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Problem of the Day Rachel is building a
doghouse. She needs to cut a 12-foot-long board
into lengths of 65 in. How many lengths can she
cut, and will there be any wood left? If so, how
much?
2 cuts yes, 14 in.
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Learn to divide fractions and mixed numbers.
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Vocabulary
reciprocal
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Reciprocals can help you divide by fractions. Two
numbers are reciprocals if their product is 1.
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Additional Example 1A Finding Reciprocals Find
the reciprocal.
of is 1.
The reciprocal of is 9.
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Additional Example 1B Finding Reciprocals Find
the reciprocal.
Think of what number is 1?
of is 1.
1
The reciprocal of is .
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Additional Example 1C Finding Reciprocals Find
the reciprocal.
Write 3 as .
1
of is 1.
1
The reciprocal of is .
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Check It Out Example 1A Find the reciprocal.
of is 1.
The reciprocal of is 4.
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Check It Out Example 1B Find the reciprocal.
Think of what number is 1?
of is 1.
1
The reciprocal of is .
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Check It Out Example 1C Find the reciprocal.
Write 4 as .
1
of is 1.
1
The reciprocal of is .
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Look at the relationship between the fractions
and . If you switch the numerator and
denominator of a fraction, you will find its
reciprocal. Dividing by a number is the same as
multiplying by its reciprocal.
24 4 6
24 6
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Additional Example 2A Using Reciprocals to
Divide Fractions and Mixed Numbers Divide. Write
each answer in simplest form.
7
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Multiply by the reciprocal.

The answer is in simplest form.
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Additional Example 2B Using Reciprocals to
Divide Fractions and Mixed Numbers

Rewrite as multiplication using the reciprocal of
, .

1

Simplify before multiplying.
2
Multiply.

You can write the answer as a mixed number.
1
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Additional Example 2C Using Reciprocals to
Divide Fractions and Mixed Numbers
2 1
Write the mixed numbers as improper fractions. 2
and 1
2 1
Rewrite as multiplication.


3

Simplify before multiplying.
1
Multiply.

You can write the answer as a mixed number.
2
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Check It Out Example 2A Divide. Write each
answer in simplest form.
3
3

Multiply by the reciprocal.

The answer is in simplest form.
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Check It Out Example 2B

Rewrite as multiplication using the reciprocal of
, .

1

Simplify before multiplying.
2
Multiply.

You can write the answer as a mixed number.
3
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Check It Out Example 2C
3 1
Write the mixed numbers as improper fractions. 3
and 1 .
3 1
Rewrite as multiplication.


3

Simplify before multiplying.
1
Multiply.

You can write the answer as a mixed number.
3
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Lesson Quiz
Find the reciprocal. 1. 2. Divide. Write
each answer in simplest form. 3. 20 4. 3
2 5. Rhonda put 2 pounds of pecans into
a -pound bag. How many bags did Rhonda
fill?
, or 1
11 bags