Rational Numbers

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Rational Numbers Equations
Lesson 1

• Simplifying Fractions

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Warm-Up

1. List the factors of 21.
2. List the factors of 12.
3. What fraction is represented by the model?
   
4. Write two fractions that are equivalent to .

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Simplifying Fractions

• Targets Write fractions in simplest form.

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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 denominators
  only common factor is 1.

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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.

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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.

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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.

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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.

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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.

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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.

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Exit Problems

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

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Communication Prompt

• Describe a situation where you might see a
  fraction that
• is not in simplest form.