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5.3 Adding and Subtracting Unlike Fractions Skill Check Lesson Presentation Lesson Quiz 5.3 Adding and Subtracting Unlike Fractions Skill Check Write the mixed number as an improper fraction. 1. 2. 3. 4. 5.3 Adding and Subtracting Unlike Fractions Hiking You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the 1 campsites is 10 miles. You 5 have already hiked 5 3 4 miles. How many more miles do you have to hike? 5.3 Adding and Subtracting Unlike Fractions To add or subtract fractions with different denominators, begin by using the LCD of the fractions to write equivalent fractions that have the same denominator. 5.3 Adding and Subtracting Unlike Fractions EXAMPLE 1 Adding and Subtracting Fractions 5 1 5 4 + = + 12 3 12 12 5+4 = 12 = 9 12 3 = 4 Write 1 using LCD. 3 Write sum of numerators over denominator. Add. Simplify. 5.3 Adding and Subtracting Unlike Fractions EXAMPLE 5 1 Adding and Subtracting Fractions 7 –15 14 – 6 – 9 = 18 – 18 Write fractions using LCD. = –15 – 14 Write difference of numerators over denominator. = –29 Subtract. 18 18 11 = –1 18 Write fraction as a mixed number. 5.3 EXAMPLE –4 Adding and Subtracting Unlike Fractions 2 Adding Mixed Numbers 2 6 –22 –28 + + = –2 5 11 5 11 Write mixed numbers as improper fractions. = –242 –140 + 55 55 Write fractions using LCD. = –242 + (–140) 55 Write sum of numerators over denominator. = –382 52 = –6 55 55 Add. Then write fraction as a mixed number. 5.3 Adding and Subtracting Unlike Fractions EXAMPLE 3 Subtracting Mixed Numbers You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the 1 3 campsites is You have already hiked miles. 10miles. 5 5 4 How many more miles do you have to hike? SOLUTION 10 To find the remaining distance, subtract. 1 3 51 23 – – 5 = 5 4 5 4 Write mixed numbers as improper fractions. = 204 115 – 20 20 Write fractions using LCD. = 204 – 115 20 Write difference of numerators over denominator. 5.3 EXAMPLE Adding and Subtracting Unlike Fractions 3 Subtracting Mixed Numbers You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the 1 3 campsites is You have already hiked miles. 10miles. 5 5 4 How many more miles do you have to hike? SOLUTION To find the remaining distance, subtract. = 204 – 115 20 89 9 = 20 = 4 20 ANSWER Subtract. Then write fraction as a mixed number. 9 1 You need to hike 4 20 miles, or about 4 2 miles. 5.3 Adding and Subtracting Unlike Fractions EXAMPLE 4 Simplifying an Expression a a Simplify the expression 2 – 6 . a a – 2 6 a 3 a = 2•3 – 6 3a a = 6 – 6 = 3a – a 6 2a = 6 a Write 2 using LCD. Multiply. Write difference of numerators over denominator. Subtract. 1 2a = 6 3 a = 3 Divide out common factor. Simplify. 5.3 Adding and Subtracting Unlike Fractions Lesson Quiz Find the sum or difference. 1. 2. 3. 4. 6. Challenge Find a value of y so that the sum is equal to 2. 2