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4-5 Equivalent Fractions Warm Up Problem of the Day

Course 1 Warm Up Problem of the Day Lesson Presentation

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4-5 Equivalent Fractions Warm Up List the factors of each number. 1. 8

Course 1 4-5 Equivalent Fractions 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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4-5 Equivalent Fractions Problem of the Day

Course 1 4-5 Equivalent Fractions 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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Course 1 4-5 Equivalent Fractions Learn to write equivalent fractions.

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Insert Lesson Title Here

Course 1 4-5 Equivalent Fractions Insert Lesson Title Here Vocabulary equivalent fractions simplest form

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4-5 Equivalent Fractions = =

Course 1 4-5 Equivalent Fractions Fractions that represent the same value are equivalent fractions. So , , and are equivalent fractions. 1 2 __ 2 4 __ 4 8 __ 12 24 48 = =

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Additional Example 1: Finding Equivalent Fractions

Course 1 4-5 Equivalent Fractions Additional Example 1: Finding Equivalent Fractions Find two equivalent fractions for . 10 ___ 12 10 12 ___ 15 18 ___ 5 6 __ = = 10 12 ___ 15 18 ___ 5 6 __ So , , and are all equivalent fractions.

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4-5 Equivalent Fractions Try This: Example 1

Course 1 4-5 Equivalent Fractions Try This: Example 1 Find two equivalent fractions for . 4 __ 6 4 6 __ 8 12 ___ 2 3 __ = = 4 6 __ 8 12 ___ 2 3 __ So , , and are all equivalent fractions.

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4-5 Equivalent Fractions

Course 1 4-5 Equivalent Fractions Additional Example 2A: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 3 5 __ A. ___ 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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4-5 Equivalent Fractions

Course 1 4-5 Equivalent Fractions Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. 4 5 __ 80 B. ___ = 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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4-5 Equivalent Fractions Try This: Example 2A

Course 1 4-5 Equivalent Fractions Try This: Example 2A Find the missing number that makes the fraction equivalent. 3 9 __ A. ___ 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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4-5 Equivalent Fractions Try This: Example 2B

Course 1 4-5 Equivalent Fractions Try This: Example 2B Find the missing number that makes the fraction equivalent. 2 4 __ ___ 40 B. 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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4-5 Equivalent Fractions

Course 1 4-5 Equivalent Fractions 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

Course 1 4-5 Equivalent Fractions Additional Example 3A: Writing Fractions in Simplest Form Write the fraction in simplest form. 20 ___ A. 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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Method 2: Use a ladder diagram. So written in simplest form is .

Course 1 4-5 Equivalent Fractions Additional Example 3A: Writing Fractions in Simplest Form Write the fraction in simplest form. Method 2: Use a ladder diagram. 2 20/48 Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore 2 10/24 5/12 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

Course 1 4-5 Equivalent Fractions Additional Example 3B: Writing Fractions in Simplest Form Write the fraction in simplest form. 7 10 ___ B. 7 10 ___ The GCF of 7 and 10 is 1 so is already in simplest form.

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4-5 Equivalent Fractions Try This: Example 3A

Course 1 4-5 Equivalent Fractions Try This: Example 3A Write the fraction in simplest form. 12 ___ A. 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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Method 2: Use a ladder diagram.

Course 1 4-5 Equivalent Fractions Try This: Example 3A Write the fraction in simplest form. Method 2: Use a ladder diagram. 2 12/16 Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore 2 6/8 3/4 12 16 ___ 3 4 So written in simplest form is

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4-5 Equivalent Fractions Try This: Example 3B

Course 1 4-5 Equivalent Fractions Try This: Example 3B Write the fraction in simplest form. 3 10 ___ B. 3 10 ___ The GCF of 3 and 10 is 1, so is already in simplest form.

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Insert Lesson Title Here

Course 1 4-5 Equivalent Fractions Insert Lesson Title Here Lesson Quiz Write 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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