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4-5. Equivalent Fractions. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 4-5. Equivalent Fractions. Course 1. 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.

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4-5

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4-5

Equivalent Fractions

Course 1

Warm Up

Problem of the Day

Lesson Presentation

4-5

Equivalent Fractions

Course 1

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

4-5

Equivalent Fractions

Course 1

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

4-5

Equivalent Fractions

Course 1

Learn to write equivalent fractions.

4-5

Equivalent Fractions

Course 1

Insert Lesson Title Here

Vocabulary

equivalent fractions

simplest form

4-5

Equivalent Fractions

1

4

2

__

__

__

4

8

2

12

48

24

Course 1

Fractions that represent the same value are equivalent fractions. So , , and are equivalent fractions.

=

=

4-5

Equivalent Fractions

5

5

__

__

6

6

15

10

10

15

___

___

___

___

18

12

12

18

Course 1

Additional Example 1: Finding Equivalent Fractions

Find two equivalent fractions for .

10

___

12

=

=

The same area is shaded when the rectangle is divided into 10 parts, 15 parts, and 5 parts.

So , , and are all equivalent fractions.

4-5

Equivalent Fractions

2

2

__

__

3

3

8

4

4

8

__

___

___

__

12

6

6

12

Course 1

Check It Out: Example 1

Find two equivalent fractions for .

4

__

6

=

=

The same area is shaded when the rectangle is divided into 4 parts, 8 parts, and 2 parts.

So , , and are all equivalent fractions.

4-5

Equivalent Fractions

3

______

5

12

3

3

3

___

__

__

__

20

5

5

5

12

___

20

Course 1

Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions

Find the missing number that makes the fractions equivalent.

___

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 .

=

4-5

Equivalent Fractions

4

______

5

80

4

4

4

___

__

__

__

100

5

5

5

80

___

100

Course 1

Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions

Find the missing number that makes the fractions equivalent.

80

___

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 .

=

4-5

Equivalent Fractions

3

______

9

9

3

3

3

___

__

__

__

27

9

9

9

9

___

27

Course 1

Check It Out: Example 2A

Find the missing number that makes the fraction equivalent.

___

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 .

=

4-5

Equivalent Fractions

2

______

4

40

2

2

2

___

__

__

__

80

4

4

4

40

___

80

Course 1

Check It Out: Example 2B

Find the missing number that makes the fraction equivalent.

40

___

In the numerator, 2 is multiplied by 20 to get 40.

=

• 20

40

____

Multiply the denominator by the same number, 20.

=

• 20

80

So is equivalent to .

=

4-5

Equivalent Fractions

Course 1

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.

4-5

Equivalent Fractions

20

_______

5

20

___

__

48

12

48

Course 1

Additional Example 3A: Writing Fractions in Simplest Form

Write each fraction in simplest form.

20

___

48

The GCF of 20 and 48 is 4, so is not in simplest form.

Method 1: Use the GCF.

÷ 4

Divide 20 and 48 by their GCF, 4.

=

÷ 4

4-5

Equivalent Fractions

2 • 2•5

5

20

5

20

___

___

___

___

48

12

12

48

Course 1

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 .

Method 2 is useful when you know that the numerator and denominator have common factors, but you are not sure what the GCF is.

4-5

Equivalent Fractions

7

7

___

___

10

10

Course 1

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.

4-5

Equivalent Fractions

12

_______

3

12

___

__

16

4

16

Course 1

Check It Out: Example 3A

Write each fraction in simplest form.

12

___

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

4-5

Equivalent Fractions

2 • 2 • 3

3

12

12

3

___

___

___

___

16

16

4

4

Course 1

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 .

4-5

Equivalent Fractions

3

3

___

___

10

10

Course 1

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.

4-5

Equivalent Fractions

,

,

7

4

4

2

4

7

1

1

14

8

2

1

___

__

__

___

__

___

___

___

___

__

___

___

8

14

15

49

7

10

28

5

20

2

2

7

Course 1

Insert Lesson Title Here

Lesson Quiz

Find two equivalent fractions for each given fraction. Possible Answers:

1. 2.

Find the missing number that makes the fractions equivalent.

3. 4.

Write each fraction in simplest form.

5.6.

20

___

___

75

=

=

6

21