Lesson 3 Rational Numbers Equations Adding and Subtracting

Lesson 3 Rational Numbers & Equations Adding and Subtracting Fractions

Warm-Up 1. Convert to an improper fraction. 2. Convert 3. Write 4. Write a fraction that is equivalent to to a mixed number. in simplest form. .

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

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.

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, … 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. The LCM is 24.

Adding and Subtracting Fractions 1. If denominators are not equal, rewrite the fractions as equivalent fractions with common denominators using the least common denominator. 2. Add or subtract the numerators. 3. Write the sum or difference over the common denominator. 4. Write the fraction in simplest form.

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

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 � It as a mixed fraction. rained inches in Portland on Monday and Tuesday.

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

Exit Problems Write each answer in simplest form. 1. 2. 3. 4.

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