3-8 Equivalent Fractions and Mixed Numbers Warm Up Course 2 3-8 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

Course 2 3-8 Equivalent Fractions and Mixed Numbers Learn to identify, write, and convert between equivalent fractions and mixed numbers.

Insert Lesson Title Here Course 2 3-8 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Vocabulary equivalent fractions improper fractions mixed number

3-8 Equivalent Fractions and Mixed Numbers Course 2 3-8 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 = =

3-8 Equivalent Fractions and Mixed Numbers Course 2 3-8 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. 3 5 3 · 2 5 · 2 6 10 15 25 15 ÷ 5 25 ÷ 5 3 5 = = = =

3-8 Equivalent Fractions and Mixed Numbers Remember! 3 Course 2 3-8 Equivalent Fractions and Mixed Numbers Remember! is in simplest form because the greatest common factor of 3 and 5 is 1. 3 5

Additional Example 1: Finding Equivalent Fractions Course 2 3-8 Equivalent Fractions and Mixed Numbers Additional Example 1: Finding Equivalent Fractions Find a fraction equivalent to the given fraction. 5 7 A. 5 7 5 · 3 15 21 = Multiply numerator and denominator by 3. = 7 · 3 18 24 B. Divide numerator and denominator by 2. 18 24 18 ÷ 2 24 ÷ 2 9 12 = =

Insert Lesson Title Here Course 2 3-8 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Try This: Example 1 Find a fraction equivalent to the given fraction. 3 8 A. 3 8 3 · 2 6 16 = Multiply numerator and denominator by 2. = 8 · 2 6 12 B. 6 12 6 ÷ 3 12 ÷ 3 Divide numerator and denominator by 3. 2 4 = =

3-8 Equivalent Fractions and Mixed Numbers Course 2 3-8 Equivalent Fractions and Mixed Numbers To determine if two fractions are equivalent, find a common denominator and compare the numerators. You can also put both fractions into simplest form and see if they are equal.

Additional Example 2A: Determining Whether Fractions are Equivalent Course 2 3-8 Equivalent Fractions and Mixed Numbers Additional Example 2A: Determining Whether Fractions are Equivalent Write the fractions with a common denominator. Then determine if they are equivalent. 4 6 28 42 A. 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 2B: Determining Whether Fractions are Equivalent Course 2 3-8 Equivalent Fractions and Mixed Numbers Additional Example 2B: Determining Whether Fractions are Equivalent Write the fractions with a common denominator. Then determine if they are equivalent. 6 10 20 25 B. 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 3-8 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Try This: Example 2A Write the fractions with a common denominator. Then determine if they are equivalent. A. 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 3-8 Equivalent Fractions and Mixed Numbers Insert Lesson Title Here Try This: Example 2B Write the fractions with a common denominator. Then determine if they are equivalent. 4 12 9 48 B. 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.

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

3-8 Equivalent Fractions and Mixed Numbers  Course 2 3-8 Equivalent Fractions and Mixed Numbers Additional Example 3: 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 

3-8 Equivalent Fractions and Mixed Numbers  Try This: Example 3 Course 2 3-8 Equivalent Fractions and Mixed Numbers Try This: Example 3 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 