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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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**Fractions that represent the same value are equivalent fractions**

Fractions that represent the same value are equivalent fractions. So are equivalent fractions. 1 2 2 4 4 8 = =

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**Additional Example 1: Finding Equivalent Fractions**

Find two equivalent fractions for . 10 ___ 12 10 12 ___ 15 18 ___ 5 6 __ = = The same area is shaded when the rectangle is divided into 12 parts, 18 parts, and 6 parts. 10 12 ___ 15 18 ___ 5 6 __ So , , and are all equivalent fractions.

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**Find two equivalent fractions for .**

Check It Out: Example 1 Find two equivalent fractions for . 4 __ 6 4 6 __ 8 12 ___ 2 3 __ = = The same area is shaded when the rectangle is divided into 6 parts, 12 parts, and 3 parts. 4 6 __ 8 12 ___ 2 3 __ So , , and are all equivalent fractions.

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**Find the missing number that makes the fractions equivalent.**

Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 3 5 __ ___ In the denominator, 5 is multiplied by 4 to get 20. = 20 3 5 ______ • 4 12 ____ Multiply the numerator, 3, by the same number, 4. = • 4 20 3 5 __ 12 20 ___ So is equivalent to 3 5 __ 12 20 ___ =

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**Find the missing number that makes the fractions equivalent.**

Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 4 5 __ ___ 80 = In the numerator, 4 is multiplied by 20 to get 80. 4 5 ______ • 20 80 ____ Multiply the denominator by the same number, 20. = • 20 100 4 5 __ 80 100 ___ So is equivalent to 4 5 __ 80 100 ___ =

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**Find the missing number that makes the fraction equivalent.**

Check It Out: Example 2A Find the missing number that makes the fraction equivalent. 3 9 __ ___ In the denominator, 9 is multiplied by 3 to get 27. = 27 3 9 ______ • 3 9 ____ Multiply the numerator, 3, by the same number, 3. = • 3 27 3 9 __ 9 27 ___ So is equivalent to 3 9 __ 9 27 ___ =

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**Find the missing number that makes the fraction equivalent.**

Check It Out: Example 2B Find the missing number that makes the fraction equivalent. 2 4 __ ___ 40 In the numerator, 2 is multiplied by 20 to get 40. = 2 4 ______ • 20 40 ____ Multiply the denominator by the same number, 20. = • 20 80 2 4 __ 40 80 ___ So is equivalent to 2 4 __ 40 80 ___ =

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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 ___ 48 20 48 ___ The GCF of 20 and 48 is 4, so is not in simplest form. Method 1: Use the GCF. 20 48 _______ ÷ 4 5 12 __ = Divide 20 and 48 by their GCF, 4. ÷ 4

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**So written in simplest form is .**

Additional Example 3A Continued Method 2: Use prime factorization. 20 48 ___ _________________ 2 • 2 • 5 5 12 ___ Write the prime factors of 20 and 48. Simplify. = = 2 • 2 • 2 • 2 • 3 20 48 ___ 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. 7 10 ___ 7 10 ___ The GCF of 7 and 10 is 1 so is already in simplest form.

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**Write each fraction in simplest form.**

Check It Out: Example 3A Write each fraction in simplest form. 12 ___ 16 12 16 ___ The GCF of 12 and 16 is 4, so is not in simplest form. Method 1: Use the GCF. 12 16 _______ ÷ 4 3 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. 12 16 ___ _____________ 2 • 2 • 3 3 4 ___ Write the prime factors of 12 and 16. Simplify. = = 2 • 2 • 2 • 2 12 16 ___ 3 4 ___ So written in simplest form is

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**Write the fraction in simplest form.**

Check It Out: Example 3B Write the fraction in simplest form. 3 10 ___ 3 10 ___ 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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**Find two equivalent fractions for each given fraction. 1. 2. **

Lesson Quiz Find two equivalent fractions for each given fraction. Find the missing number that makes the fractions equivalent. Write each fraction in simplest form. Possible answers: 4 10 ___ 8 20 ___ 2 5 , 7 14 ___ 1 2 ___ 14 28 , 2 7 __ 4 15 __ 20 ___ ___ = 6 = 75 21 4 8 __ 1 2 __ 7 49 ___ 1 7 ___

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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 C. 6 B D. 9

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**Lesson Quiz for Student Response Systems**

4. Identify the missing number that makes the given fractions equivalent. A C. 40 B D. 48

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**Lesson Quiz for Student Response Systems**

5. Identify the simplest form of the fraction A C. B D.

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