Add and Subtract Fractions with Unlike Denominators

1 GOOnlineAssessment Options: Soar to Success MathWITHTM Houghton Mifflin Harcourt Publishing CompanyChapter 6 241 Add and Subtract Fractions with Unlike Denominators Part of a Whole Write a fraction to name the shaded 2. Add and Subtract Fractions Write the sum or difference in simplest 3 __ 6 1 1 __ 6 5 _ 4. 4 ___ 10 1 1 ___ 10 5 _ 5. 7 __ 8 2 3 __ 8 5 _ 6. 9 ___ 12 2 2 ___ 12 5 _ Multiples Write the first six nonzero 5 ___ 8. 3 ___ 9. 7 ___NameCheck your understanding of important of shaded parts _number of total parts _fraction _number of shaded parts _number of total parts _fraction _There are 30 senators and 60 members of the House of Representatives in the Arizona Legislature.

2 Suppose 20 senators and 25 representatives came to a committee meeting. Be a math detective to write a fraction that compares the number of legislators that attended to the total number of legislators. eStudent Edition Multimedia eGlossaryGOOnlineVocabulary BuilderAdd and SubtractFractions with LikeAdd and SubtractFractions with Unlike 242 Houghton Mifflin Harcourt Publishing Company Visualize ItUse the 3 words to complete the H-diagram. Understand VocabularyDraw a line to match the word with its common multiple2. benchmark3. simplest form4. mixed number5. common denominator6. equivalent Fractions a number that is made up of a whole number and a fraction a number that is a multiple of two or more numbers a common multiple of two or more Denominators the form of a fraction in which the numerator and denominator have only 1 as their common factor a familiar number used as a point of reference Fractions that name the same amount or part Review Wordsbenchmark3common multiple3denominators3diff erence3equivalent Fractions mixed number3numerators3simplest form3sumPreview Words3 common denominatorInvestigateInvestigateMATHEMA TICAL PRACTICESMATHEMATICAL PRACTICESsumChapter 6

3 243 Houghton Mifflin Harcourt Publishing CompanyNameHilary is making a tote bag for her friend. She uses 1 _ 2 yard of blue fabric and 1 _ 4 yard of red fabric. How much fabric does Hilary use?Materials n fraction strips n MathBoardA. Find 1 _ 2 1 1 _ 4 . Place a 1 _ 2 strip and a 1 _ 4 strip under the 1-whole strip on your Find fraction strips, all with the same denominator, that are equivalent to 1 _ 2 and 1 _ 4 and fit exactly under the sum 1 _ 2 1 1 _ 4 . Record the addends, using like Denominators . C. Record the sum in simplest form. 1 __ 2 1 1 __ 4 5 _So, Hilary uses _ yard of with Unlike DenominatorsEssential Question How can you use models to add Fractions that have different Denominators ?

4 1 How can you tell if the sum of the Fractions is less than 1?Draw Conclusions N1. Describe how you would determine what fraction strips, all with the same denominator, would fit exactly under 1 _ 2 1 1 _ 3 . What are they?2. Explain the difference between finding fraction strips with the same denominator for 1 _ 2 1 1 _ 3 and 1 _ 2 1 1 _ 4 . MATHEMATICAL PRACTICESMATHEMATICAL PRACTICES244 Houghton Mifflin Harcourt Publishing CompanySTEP 2 Find fraction strips, all with the same denominator, that are equivalent to 3 _ 5 and 1 _ 2 . Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent 3 Add the Fractions with like Denominators .

5 Use the 1-whole strip to rename the sum in simplest : How many fraction strips with the same denominator are equal to 1 whole?STEP 1 Work with another student. Place three 1 _ 5 fraction strips under the 1-whole strip on your MathBoard. Then place a 1 _ 2 fraction strip beside the three 1 _ 5 Connections NSometimes, the sum of two Fractions is greater than 1. When adding Fractions with Unlike Denominators , you can use the 1-whole strip to help determine if a sum is greater than 1 or less than fraction strips to solve. 3 _ 5 1 1 _ 2 3 __ 5 + 1 __ 2 = _ + _= _ , or _ 3 __ 5 = _ 1 __ 2 = _ In what step did you find out that the answer is greater than 1?

6 And ShowUse fraction strips to find the sum. Write your answer in simplest 2. 1 __ 2 1 3 __ 8 5 _ 1 _ 5 _ 1 __ 2 1 2 __ 5 5 _ 1 _ 5 _Chapter 6 Lesson 1 245 Houghton Mifflin Harcourt Publishing CompanyName 14. Explain how using fraction strips with like Denominators makes it possible to add Fractions with Unlike Denominators . 5. 2 __ 5 1 3 ___ 10 5 _6. 1 __ 4 1 1 ___ 12 5 _ 7. 1 __ 2 1 3 ___ 10 5 _8. 2 __ 3 1 1 __ 6 5 _9. 5 __ 8 1 1 __ 4 5 _10. 1 __ 2 1 1 __ 5 5 _Use fraction strips to find the sum. Write your answer in simplest 4. 3 __ 8 1 1 __ 4 5 _ 1 _ 5 _ 3 __ 4 1 1 __ 3 5 _ 1 _ 5 _11.

7 3 __ 4 1 1 __ 6 5 _12. 1 __ 2 1 2 __ 3 5 _13. 7 __ 8 1 1 __ 4 5 _Use fraction strips to find the sum. Write your answer in simplest Reason Make SenseMATHEMATICALPRACTICES246 Houghton Mifflin Harcourt Publishing CompanyProblem SolvingNPose a Problem15. Maya makes trail mix by combining 1 _ 3 cup of mixed nuts and 1 _ 4 cup of dried fruit. What is the total amount of ingredients in her trail mix? Write a new problem using different amounts for each ingredient. Each amount should be a fraction with a denominator of 2, 3, or 4. Then use fraction strips to solve your problem. 1 __ 3 1 1 __ 4 5 7 ___ 12 Maya uses 7 __ 12 cup of a your problem.

8 Draw a picture of the fraction strips you use to solve the problem. Explain why you chose the amounts you did for your problem. FOR MORE PRACTICE:Standards Practice Book, pp. P121 P122 InvestigateInvestigatedifferenceMATHEMAT ICAL PRACTICESMATHEMATICAL PRACTICESC hapter 6 247 Houghton Mifflin Harcourt Publishing CompanyNameMario fills a hummingbird feeder with 3 _ 4 cup of sugar water on Friday. On Monday, Mario sees that 1 _ 8 cup of sugar water is left. How much sugar water did the hummingbirds drink?Materials n fraction strips n MathBoardA. Find 3 _ 4 2 1 _ 8 . Place three 1 _ 4 strips under the 1-whole strip on your MathBoard.

9 Then place a 1 _ 8 strip under the 1 _ 4 Find fraction strips all with the same denominator that fit exactly under the difference 3 _ 4 2 1 _ 8 . C. Record the difference. 3 __ 4 2 1 __ 8 5 _So, the hummingbirds drank _ cup of sugar water. Subtraction with Unlike DenominatorsEssential Question How can you use models to Subtract Fractions that have different Denominators ?Lesson Conclusions 1. Describe how you determined what fraction strips, all with the same denominator, would fit exactly under the difference. What are they?2. Explain whether you could have used fraction strips with any other denominator to find the difference.

10 If so, what is the denominator? How can you tell if the difference of the Fractions is less than 1? PRACTICESMATHEMATICAL PRACTICES??248 Houghton Mifflin Harcourt Publishing CompanyMake ConnectionsNSometimes you can use different sets of same-denominator fraction strips to find the difference. All of the answers will be 2 _ 3 2 1 _ 6 B Find another set of fraction strips, all with the same denominator, that fit exactly under the difference 2 _ 3 2 1 _ 6 . Draw the fraction strips you used. 2 _ 3 2 1 _ 6 5 _C Find other fraction strips, all with the same denominator, that fit exactly under the difference 2 _ 3 2 1 _ 6.