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Rational Numbers & Equations

Lesson 1. Rational Numbers & Equations. Simplifying Fractions. Warm-Up. List the factors of 21. List the factors of 12. What fraction is represented by the model? Write two fractions that are equivalent to. Simplifying Fractions. Targets: Write fractions in simplest form. Vocabulary.

daniel-harrell
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Rational Numbers & Equations

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  1. Lesson 1 Rational Numbers & Equations Simplifying Fractions

  2. Warm-Up • List the factors of 21. • List the factors of 12. • What fraction is represented by the model? • Write two fractions that are equivalent to .

  3. Simplifying Fractions Targets: Write fractions in simplest form.

  4. Vocabulary • Fraction: A number that represents a part of a whole number. • Equivalent Fractions: Fractions that represent the same number but have different numerators and denominators. • Greatest Common Factor: Greatest factor that is common to two or more numbers. • Simplest Form: When a numerator and denominator’s only common factor is 1.

  5. Writing Fractions in Simplest Form • Divide the numerator and denominator by the greatest common factor (GCF). - OR - • Divide the numerator and denominator by common factors until the only common factor is 1.

  6. Example 1 Find two fractions that are equivalent to . • Multiply the top and bottom by the same number. • Divide the top and bottom by the same number.

  7. Example 2a Find the GCF of 10 and 15. • Prime factorizations: • 10 = 2 · 5 • 15 = 3 · 5 • The only common factor is 5. GCF = 5.

  8. Example 2b Find the GCF of 24 and 36. • Prime factorizations: • 24 = 2 · 2 · 2 · 3 • 36 = 2 · 2 · 3 · 3 • Common factors: 2 · 2 · 3 = 12. GCF = 12.

  9. Example 3a Write the fraction in simplest form: • Find GCF of 20 and 50. • Prime factorization: • 20 = 2 · 2 · 5 • 50 = 2 · 5 · 5 • Greatest Common Factor: 2 · 5 = 10 • Divide the numerator and denominator by the GCF.

  10. Example 3b Write the fraction in simplest form: • One common factor is 5. • A remaining common factor of 9 and 12 is 3. • One is the only remaining common factor. is in simplest form.

  11. Exit Problems • Find two fractions that are equivalent to . • Find the GCF of 32 and 48. • Write each fraction in simplest form. a. b.

  12. Communication Prompt Describe a situation where you might see a fraction that is not in simplest form.

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