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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Vocabulary equivalent fractions improper fraction mixed number

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Different fractions can name the same number. 3535 = = 15 25 6 10

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number. In the diagram =. These are called equivalent fractions because they are different expressions for the same nonzero number. 3535 6 10 15 25

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Find two fractions equivalent to. Additional Example 1: Finding Equivalent Fractions 5757 5 2 7 2 = 10 14 Multiply the numerator and denominator by 2. 5 3 7 3 = 15 21 Multiply the numerator and denominator by 3. Remember! A fraction with the same numerator and denominator, such as is equal to 1. 2

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 5757 The fractions,, and are equivalent, but only is in simplest form. A fraction is in simplest form when the greatest common divisor of its numerator and denominator is 1. 5757 10 14 15 21

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 1 Find two fractions equivalent to. 6 2 12 2 = 12 24 Multiply the numerator and denominator by 2. 6 ÷ 2 12 ÷ 2 = 3636 Divide the numerator and denominator by 2. 6 12

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Write the fraction in simplest form. Additional Example 2: Writing Fractions in Simplest Form 18 24 Find the GCD of 18 and 24. The GCD is 6 = 2 3. = 18 24 Divide the numerator and denominator by 6. 18 = 2 3 3 24 = 2 2 2 3 18 ÷ 6 24 ÷ 6 = 3 4

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Write the fraction in simplest form. Check It Out! Example 2 15 45 Find the GCD of 15 and 45. The GCD is 15 = 3 5. = 15 45 Divide the numerator and denominator by 15. 15 = 3 5 45 = 3 3 5 15 ÷ 15 45 ÷ 15 = 1 3

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers To determine if two fractions are equivalent, simplify the fractions.

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Determine whether the fractions in each pair are equivalent. Additional Example 3A: Determining Whether Fractions are Equivalent and 4646 28 42 Simplify both fractions and compare. 4646 = 4 ÷ 2 6 ÷ 2 = 2323 28 42 = 28 ÷ 14 42 ÷ 14 = 2323 are equivalent because both are equal to.and 4646 28 42 2323

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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. and 6 10 20 25 Simplify both fractions and compare. = 6 ÷ 2 10 ÷ 2 = 3535 20 25 = 20 ÷ 5 25 ÷ 5 = 4545 6 10 are not equivalent because their simplestand 20 25 6 10 forms are not equal.

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 3A Simplify both fractions and compare. 3939 = 3 ÷ 3 9 ÷ 3 = 1313 = 6 ÷ 6 18 ÷ 6 = 1313 and 3939 6 18 6 18 Determine whether the fractions in each pair are equivalent. are equivalent because both are equal to.and 3939 6 18 1313

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Check It Out! Example 3B and 4 12 9 48 Simplify both fractions and compare. = 4 ÷ 4 12 ÷ 4 = 1313 9 48 = 9 ÷ 3 48 ÷ 3 = 3 16 4 12 Determine whether the fractions in each pair are equivalent. are not equivalent because their simplestand 9 48 4 12 forms are not equal.

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Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz 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. 12 24 16 48 3737 31 7 1818 2 17 8 1313 no 1212 3636, 5 12 4 10

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