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Understanding Mixed Numbers and Improper Fractions: Conversion and Simplification

In this lesson, we explore the process of converting mixed numbers to improper fractions and vice versa. We will define mixed numbers as the sum of a whole number and a proper fraction, and improper fractions as those with a numerator equal to or greater than the denominator. Step-by-step examples will guide you through rewriting mixed numbers as improper fractions by multiplying, adding, and keeping the denominator. Additionally, we will look at how to convert improper fractions back to mixed numbers by dividing. Master these conversions to enhance your understanding of rational numbers.

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Understanding Mixed Numbers and Improper Fractions: Conversion and Simplification

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  1. Lesson 2 Rational Numbers & Equations Mixed Numbers and Improper Fractions

  2. Warm-Up Write each fraction in simplest form.

  3. Mixed Numbers and Improper Fractions Targets: Write mixed numbers as improper fractions.Write improper fractions as mixed numbers.

  4. Vocabulary • Mixed Number: The sum of a whole number and a fraction less than 1. • Improper Fraction: A fraction with a numerator that is greater than or equal to its denominator.

  5. Rewriting Mixed Numbers as Improper Fractions • Multiply the whole number by the denominator. • Add the numerator to the product. • Write this number as the numerator and keep the original denominator as the denominator of the improper fraction.

  6. Rewriting Improper Fractions as Mixed Numbers • Divide the numerator by the denominator. The quotient is the whole number in the mixed number. • Write the remainder as the numerator over the original denominator. This is the fraction in the mixed number.

  7. Example 1 Write as an improper fraction. • Multiply the whole number by the denominator.5(6) = 30 • Add the numerator to the product.1 + 30 = 31 • Put the total over the original denominator:

  8. Example 2 Write as a mixed number. • Divide the numerator by the denominator. • Write the mixed number:

  9. Exit Problems Write each mixed number as an improper fraction. Write each improper fraction as a mixed number.

  10. Communication Prompt What is the process for converting a mixed number to an improper fraction?

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