2-9 Equivalent Fractions and Mixed Numbers Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

2-9 Equivalent Fractions and Mixed Numbers Warm Up Course 2 2-9 Equivalent Fractions and Mixed Numbers 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

2-9 Equivalent Fractions and Mixed Numbers Problem of the Day Course 2 2-9 Equivalent Fractions and Mixed Numbers 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

Course 2 2-9 Equivalent Fractions and Mixed Numbers Learn to identify, write, and convert between equivalent fractions and mixed numbers.

Insert Lesson Title Here Course 2 2-9 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Vocabulary equivalent fractions improper fractions mixed number

2-9 Equivalent Fractions and Mixed Numbers Course 2 2-9 Equivalent Fractions and Mixed Numbers 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 = =

2-9 Equivalent Fractions and Mixed Numbers Course 2 2-9 Equivalent Fractions and Mixed Numbers 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 Course 2 2-9 Equivalent Fractions and Mixed Numbers 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

Insert Lesson Title Here Course 2 2-9 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here 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. =

Additional Example 2: Writing Fractions in Simplest Form Course 2 2-9 Equivalent Fractions and Mixed Numbers 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. = =

2-9 Equivalent Fractions and Mixed Numbers Check It Out: Example 2 15 Course 2 2-9 Equivalent Fractions and Mixed Numbers 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 Course 2 2-9 Equivalent Fractions and Mixed Numbers 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 Course 2 2-9 Equivalent Fractions and Mixed Numbers 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.

Insert Lesson Title Here Course 2 2-9 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Check It Out: Example 2A Determine whether the fractions in each pair are equivalent. and 3 9 6 18 Both fractions can be written with a denominator of 3. 3 9 3 ÷ 3 9 ÷ 3 1 3 = = 6 18 6 ÷ 6 18 ÷ 6 1 3 = = The numerators are equal, so the fractions are equivalent.

Insert Lesson Title Here Course 2 2-9 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Check It Out: Example 2B Determine whether the fractions in each pair are equivalent. 4 12 9 48 and Both fractions can be written with a denominator of 96. 4 12 4 · 8 12 · 8 32 96 = = 9 48 9 · 2 48 · 2 18 96 = = The numerators are not equal, so the fractions are not equivalent.

2-9 Equivalent Fractions and Mixed Numbers 8 5 3 5 = 1 8 5 3 5 Course 2 2-9 Equivalent Fractions and Mixed Numbers 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

2-9 Equivalent Fractions and Mixed Numbers  Course 2 2-9 Equivalent Fractions and Mixed Numbers 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 

2-9 Equivalent Fractions and Mixed Numbers 8  Check It Out: Example 4 Course 2 2-9 Equivalent Fractions and Mixed Numbers Check It Out: Example 4 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 

Insert Lesson Title Here Course 2 2-9 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here 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