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Rational Numbers & Equations

Lesson 3. Rational Numbers & Equations. Adding and Subtracting Fractions. Warm-Up. Convert to an improper fraction. Convert to a mixed number. Write in simplest form. Write a fraction that is equivalent to. Adding and Subtracting Fractions. Target:

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Rational Numbers & Equations

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  1. Lesson 3 Rational Numbers & Equations Adding and Subtracting Fractions

  2. Warm-Up • Convert to an improper fraction. • Convert to a mixed number. • Write in simplest form. • Write a fraction that is equivalent to .

  3. Adding and Subtracting Fractions Target: Add or subtract fractions with like and unlike denominators.

  4. Vocabulary • Least Common Multiple: The smallest multiple that is common to two or more numbers. • Least Common Denominator: The least common multiple of two denominators.

  5. Example 1 Find the least common multiple of: 8 and 12 • List a few multiples and find the smallest number in both lists. • 8: 8, 16, 24, 32, 40, … • 12: 12, 24, 36, 48, … • The LCM is 24. 4 and 5 • List multiples of 5.5, 10, 15, 20, 25, … • Find the first multiple that 4 goes into evenly. • 5 - no, 10 - no, 15 - no, 20 - yes • The LCM is 20.

  6. Adding and Subtracting Fractions • If denominators are not equal, rewrite the fractions as equivalent fractions with common denominators using the least common denominator. • Add or subtract the numerators. • Write the sum or difference over the common denominator. • Write the fraction in simplest form.

  7. Example 2 Find the value of . • The fractions already have common denominators. • Add numerators. • Write in simplest form.

  8. Example 3 On Monday, the Portland International Airport reported inch of rain. On Tuesday it rained inch. What was the total rainfall for these two days? • The LCM is 16. Write with a denominator of 16. • Add the fractions. • Write as a mixed fraction. • It rained inches in Portland on Monday and Tuesday.

  9. Example 4 Find the value of . • The LCM of 3 and 4 is 12. • Rewrite fractions. • Subtract.

  10. Exit Problems Write each answer in simplest form.

  11. Communication Prompt What do you find to be the most difficult part about adding or subtracting fractions?

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