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3-4 Equivalent Fractions and Mixed Numbers Preview Warm Up California Standards Lesson Presentation Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Warm Up Name a common factor for each pair. Possible answers: 1. 5 and 10 2. 9 and 12 5 3 3. 20 and 24 4 4. 10 and 14 2 5. 6 and 8 2 6. 8 and 15 1 Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers California Standards NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction). Also covered: NS1.1 Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Vocabulary equivalent fractions improper fraction mixed number Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Different fractions can name the same number. 3 5 Holt CA Course 1 = 6 10 = 15 25 3-4 Equivalent Fractions and Mixed Numbers In the diagram 3 = 6 = 15 . These are called 5 10 25 equivalent fractions because they are different expressions for the same nonzero number. To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 8 is an improper 5 fraction. Its numerator is greater than its denominator. Holt CA Course 1 3 is a mixed 5 number. It contains both a whole number and a fraction. 1 8 = 13 5 5 3-4 Equivalent Fractions and Mixed Numbers To determine if two fractions are equivalent, simplify the fractions. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Additional Example 1: Finding Equivalent Fractions Find two fractions equivalent to 5 7. 5 2 = 10 72 14 Multiply the numerator and denominator by 2. 53 73 Multiply the numerator and denominator by 3. = 15 21 Remember! A fraction with the same numerator and 2 denominator, such as is equal to 1. 2 Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 10 , and 15 are equivalent, The fractions 5 , 21 7 14 but only 5 is in simplest form. A fraction is in 7 simplest form when the greatest common divisor of its numerator and denominator is 1. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 4 and 28 6 42 Simplify both fractions and compare. 4 4÷2 2 = = 6 6÷2 3 28 = 28 ÷ 14 = 2 42 ÷ 14 3 42 4 and 28 are equivalent because both are equal to 2 . 6 42 3 Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 6 and 20 10 25 Simplify both fractions and compare. 6 = 6÷2 = 3 10 ÷ 2 10 5 20 = 20 ÷ 5 = 4 25 ÷ 5 25 5 6 and 20 are not equivalent because their simplest 10 25 forms are not equal. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Additional Example 4: Converting Between Improper Fractions and Mixed Numbers A. Write 13 as a mixed number. 5 First divide the numerator by the denominator. 13 = 2 3 5 5 Use the quotient and remainder to write the mixed number. B. Write 7 2 as an improper fraction. 3 First multiply the denominator and whole number, and then add the numerator. + 2 = 3 7 + 2 = 23 Use the result to write the improper 3 3 3 fraction. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 1 Find two fractions equivalent to 6 . 12 6 2 = 12 12 2 24 Multiply the numerator and denominator by 2. 6 ÷2 3 = 12 ÷ 2 6 Divide the numerator and denominator by 2. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 2 15 Write the fraction 45 in simplest form. Find the GCD of 15 and 45. 15 = 3 • 5 45 = 3 • 3 The GCD is 15 = 3 • 5. 5 15 = 15 ÷ 15 = 1 45 45 ÷ 15 3 Holt CA Course 1 • Divide the numerator and denominator by 15. 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 3A Determine whether the fractions in each pair are equivalent. 3 and 6 9 18 Simplify both fractions and compare. 3 3÷3 1 = = 9 9÷3 3 6 = 6 ÷6 = 1 18 ÷ 6 18 3 3 and 6 are equivalent because both are equal to 1 . 9 18 3 Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 4 A. Write 15 6 as a mixed number. First divide the numerator by the denominator. 15 = 2 3 = 2 1 2 6 6 Use the quotient and remainder to write the mixed number. B. Write 8 1 3 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to 3 8 + 1 1 25 = 83 = write the improper 3 3 fraction. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz 12 1 , 3 1. Write two fractions equivalent to 24 . 2 6 2. Determine if 5 and 4 are equivalent. no 12 10 3. Write the fraction 16 in simplest form. 1 48 3 4. Write 17 as a mixed number. 2 1 8 8 31 5. Write 4 3 as an improper fraction. 7 7 Holt CA Course 1