Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Name a common factor for each pair. 1. 5 and 10 2. 9 and 12 3. 20 and 24 4. 10 and 14 5. 6 and 8 6. 8 and 15 Possible answers: 5 3 4 2 2 1

Find a number less than 100 for which all three statements are true: Problem of the Day Find a number less than 100 for which all three statements are true: • Divide by 3. Remainder of 2. • Divide by 4. Remainder of 3. • Divide by 5. Remainder of 4. 59

Learn to identify, write, and convert between equivalent fractions and mixed numbers.

2-9 Vocabulary equivalent fractions relatively prime

Different fractions can name the same number. In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful. Different fractions can name the same number. 3 5 6 10 15 25 = =

In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number. 3 5 6 10 15 25 = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number.

Additional Example 1: Finding Equivalent Fractions 5 7 Find two fractions equivalent to . 5 · 2 10 14 = Multiply numerator and denominator by 2. 7 · 2 5 · 3 15 21 Multiply numerator and denominator by 3. = 7 · 3

Check It Out: Example 1 6 12 Find two fractions equivalent to . 6 · 2 12 24 = Multiply numerator and denominator by 2. 12 · 2 6 ÷ 2 12 ÷ 2 3 6 Divide numerator and denominator by 2. =

A fraction is in simplest form when the numerat or and denominator are relatively prime. Relatively prime numbers have no common factors other than 1.

Additional Example 2: Writing Fractions in Simplest Form 18 24 Write the fraction in simplest form. Find the GCF of 18 and 24. 18 = 2 • 3 • 3 The GCF is 6 = 2 • 3. 24 = 2 • 2 • 2 • 3 18 24 18 ÷ 6 24 ÷ 6 3 4 Divide the numerator and denominator by 6. = =

Check It Out: Example 2 15 45 Write the fraction in simplest form. Find the GCF of 15 and 45. 15 = 3 • 5 The GCF is 15 = 3 • 5. 45 = 3 • 3 • 5 15 45 15 ÷ 15 45 ÷ 15 1 3 Divide the numerator and denominator by 15. = =

Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 4 6 28 42 and Both fractions can be written with a denominator of 3. 4 6 4 ÷ 2 6 ÷ 2 2 3 = = 28 42 28 ÷ 14 42 ÷ 14 2 3 = = The numerators are equal, so the fractions are equivalent.

Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 6 10 20 25 and Both fractions can be written with a denominator of 50. 6 10 6 · 5 10 · 5 30 50 = = 20 25 20 · 2 25 · 2 40 50 = = The numerators are not equal, so the fractions are not equivalent.

8 5 3 5 is an improper 1 is a mixed fraction. Its numerator is greater than its denominator. number. It contains both a whole number and a fraction. 8 5 3 5 = 1 An improper fraction is a fraction where the numerator is than or equal to the denominator. Remember!

Additional Example 4: Converting Between Improper Fractions and Mixed Numbers 13 5 A. Write as a mixed number. First divide the numerator by the denominator. 13 5 3 5 Use the quotient and remainder to write a mixed number. = 2 2 3 B. Write 7 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to write the improper fraction. 2 3 3 · 7 + 2 23 3 = = 7 3 

8  Check It Out: Example 4 A. Write as a mixed number. 15 6 A. Write as a mixed number. First divide the numerator by the denominator. 15 6 3 6 1 2 = 2 Use the quotient and remainder to write a mixed number. = 2 1 3 B. Write 8 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to write the improper fraction. 1 3 3 · 8 + 1 25 3 8 = = 3 

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

1. Write two fractions equivalent to . Lesson Quiz 12 24 1 2, 3 6 1. Write two fractions equivalent to . 2. Determine if and are equivalent. 3. Write the fraction in simplest form. 4. Write as a mixed number. 5. Write 4 as an improper fraction. 5 12 4 10 no 16 48 1 3 17 8 1 8 2 31 7 3 7

Lesson Quiz for Student Response Systems 12 60 1. Identify two fractions equivalent to . A. Possible answer: , B. Possible answer: , C. Possible answer: , D. Possible answer: , 1 5 3 15 1 5 3 5 1 6 3 18 1 10 3 30

Lesson Quiz for Student Response Systems 2. Identify the fractions that are not equivalent. A. , C. , B. , D. , 3 16 6 32 7 10 14 20 3 16 7 10 3 7 15 35

Lesson Quiz for Student Response Systems 3. Which of the following represents the fraction in simplest form? A. C. B. D. 15 30 1 5 1 3 1 4 1 2

Lesson Quiz for Student Response Systems 4. Which of the following represents as a mixed number? A. 5 C. 3 B. 4 D. 2 19 6 1 6 1 6 1 6 1 6

Lesson Quiz for Student Response Systems 5. Which of the following represents the fraction 4 as an improper fraction? A. C. B. D. 5 6 29 6 27 6 28 6 25 6