Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to write equivalent fractions.

Vocabulary equivalent fractions simplest form

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 = =

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.

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.

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 ___ =

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 ___ =

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 ___ =

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 ___ =

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.

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

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.

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.

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

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 .

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.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Find two equivalent fractions for each given fraction. 1. 2. Lesson Quiz Find two equivalent fractions for each given fraction. 1. 2. Find the missing number that makes the fractions equivalent. 3. 4. Write each fraction in simplest form. 5. 6. 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 ___

Lesson Quiz for Student Response Systems 1. Identify two equivalent fractions for . A. C. B. D.

Lesson Quiz for Student Response Systems 2. Identify two equivalent fractions for . A. C. B. D.

Lesson Quiz for Student Response Systems 3. Identify the missing number that makes the given fractions equivalent. A. 3 C. 6 B. 4 D. 9

Lesson Quiz for Student Response Systems 4. Identify the missing number that makes the given fractions equivalent. A. 24 C. 40 B. 32 D. 48

Lesson Quiz for Student Response Systems 5. Identify the simplest form of the fraction A. C. B. D.