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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 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 Additional Example 3A Continued 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 . 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.
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
