Use Properties of Addition. How can properties help you add fractions with unequal denominators? _ 8 )

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1 ? Name. Essential Question Use Properties of ddition How can properties help you add fractions with unequal denominators? Number and Operations..H MTHEMTIL PROESSES.1. onnect You can use properties of addition to help you add fractions with unequal denominators. ommutative Property: + _ = _ + ssociative Property: ( _ 9 + ) + _ = _ 9 + ( + _ ) Remember Parentheses ( ) tell which operation to do first. Unlock the Problem Jane and her family are driving to ig Lagoon State Park. On the first day, they travel of the total distance. On the second day, they travel of the total distance in the morning and then of the total distance in the afternoon. How much of the total distance has Jane s family driven by the end of the second day? Use the ssociative Property. ay 1 + ay 1 + ( ) = ( + ) + Write the number sentence to represent the problem. Use the ssociative Property to group fractions with equal denominators together. = + Use mental math to add the fractions with equal denominators. = + Write equivalent fractions with equal denominators. Then add. Houghton Mifflin Harcourt Publishing ompany = So, Jane s family has driven _ of the total distance by the end of the second day. Math Talk Mathematical Processes Explain Why grouping the fractions differently makes it easier to find the sum. Module

2 Example dd. ( + 1 ) + 1 _ Use the ommutative Property and the ssociative Property. ( ) 1 = ( + ) + = + ( + ) = + = + Use the ommutative Property to put fractions with equal denominators next to each other. Use the ssociative Property to group fractions with equal denominators together. Use mental math to add the fractions with equal denominators. Write equivalent fractions with equal denominators. Then add. = = Rename and simplify. Try This! Subtraction is not commutative or associative. When you subtract, perform operations in parentheses first. Then subtract from left to right. a. _ = _ = _ b. ( _ ) = _ = _ c. _ ( ) = _ _ = _ Explain how you can use your answers to conclude that subtraction is not associative. Share and Show Use the properties and mental math to solve. Write your answer in simplest form. 1. ( _ + _ ) ( 1 + _). ( + _ ) + 1 _ Houghton Mifflin Harcourt Publishing ompany

3 Name Problem Solving Use the properties and mental math to solve. Write your answer in simplest form.. ( _ + ) + _. ( + ) + _. ( + _ ) + _. Explain why grouping the fractions differently makes it easier to find the sum. Problem Solving Use the map to solve 9.. Multi-Step On one afternoon, Mario walks from his house to the library. That evening, Mario walks from the library to the mall, and then to Kyle s house. escribe how you can use the properties to find how far Mario walks. Sports omplex Park Library mile Mall School mile mile mile 1 1 miles Kyle s House Mario s House 1 miles Houghton Mifflin Harcourt Publishing ompany 9. Pose a Problem Write and solve a new problem that uses the distances between four locations. Module Lesson 9

4 aily ssessment Task Mathematical Processes Fill in the bubble completely to show your answer. 10. uring a scavenger hunt, en s team completed four tasks in the following times: hours, 1 hours, 1 hours, and 1 hours. How long did it take en s team to complete the scavenger hunt? hours hours hours hours 11. Use Symbols Elijah wants to add (_ + ) +. He rewrites the problem as ( + _ ) +. Then he uses the ssociative Property to rewrite the problem. Which shows his next step? + ( _ + ) ( )( _ + ) ( + _ + ) ( _ + )( ) 1. Multi-Step Glen finds the sum of ( 10 + ) + _ 10 and na finds the sum of ( + 10 ) + _ 10. What is the total sum of their answers? _ TEXS Test Prep 1. Use the properties and mental math to solve ( _ _ 1 ) Houghton Mifflin Harcourt Publishing ompany

5 Homework and Practice Name Number and Operations..H MTHEMTIL PROESSES.1.. Use Properties of ddition Use the properties and mental math to solve. Write your answer in simplest form. 1. ( + ) +. + ( _ + ) _. ( + _ ) +. ( + _ ) +. _ + ( _ + 1 _ ) _. ( _ + _ ) +. ( + 1 ) + 1_. + ( _ + 1 _ ) _ 9. ( _ + 1 ) Write a word problem for the addends 10,, and Explain how you solved your problem. Problem Solving 11. Last night, Hailey spent _ hour on math homework, hour on science homework, and _ hour on social studies homework. How long did Hailey spend on homework last night? 1. The rainfall totals at the airport for the last three months were inches, 1 _ inches, and 1 inches. What was the total rainfall for the last three months? Houghton Mifflin Harcourt Publishing ompany Module Lesson 1

6 Lesson heck TEXS Test Prep Fill in the bubble completely to show your answer. 1. Shelly volunteered at the pet shelter hours in June, 1 _ hours in July, and the same amount of hours in ugust as in June. How many hours did Shelly volunteer this summer? _ hours hours hours hours 1. Erica uses a recipe for cookies that calls for _ cups of flour and 1 cups of sugar. Erica doubles the recipe and adds the flour and sugar to a mixing bowl. Which is the amount of dry ingredients in the bowl? cups _ cups _ cups 9 _ cups 1. Stefan wants to add ( _ + 1 ) +. He uses the ommutative Property to rewrite the problem. Which shows this step? ( + 1 _ + _ ) + (1 _ + _ ) (1 _ + ) + _ ( _ + 1 _ ) + 1. Habib is making a frame for a rectangular picture that is feet by _ feet. How many feet of wood trim should Habib buy to make the frame? feet 10 _ feet 11 _ feet feet 1. Multi-Step Juliana used 10 yards of yarn to make three yarn dolls. She used yards of yarn for the first doll and yards for the second doll. How much yarn did Juliana use for the third doll? yards yards _ yards _ yards 1. Multi-Step Yuan finds the sum of 10 + ( ). Then he adds 1 1 to the sum. What is Yuan s final sum? Houghton Mifflin Harcourt Publishing ompany

7 Name Module ssessment Vocabulary hoose the best term from the box. 1. is a common multiple of two or more denominators. (p. 1) Vocabulary common denominator common multiple equivalent fraction oncepts and Skills Estimate the sum or difference. q TEKS... _ 9 + _. _ _. 1 _ + 11 Use the least common denominator to write an equivalent fraction for each fraction. q TEKS.. _, _ 10 least common denominator: _. _, _ least common denominator: _., _ least common denominator: Use models or strategies to find the sum or difference. Write your answer in simplest form. q TEKS..H,..K _ + _ 10. _ 10 Houghton Mifflin Harcourt Publishing ompany Use the properties and mental math to solve. Write your answer in simplest form. q TEKS..H 11. ( _ + _ ) _ + ( 0 + _ ) 1. _ 9 + (1 _ ) Module

8 Fill in the bubble completely to show your answer. 1. Samuel walks in the Labor ay parade. He walks miles along the parade route and _ miles home. How many miles does Samuel walk? q TEKS..K TEXS Test Prep 10 mile _ 1 miles miles 11 1 miles 1. Mrs. Michaels bakes a pie for her book club meeting. The shaded part of the diagram shows the amount of pie left after the meeting. That evening, Mr. Michaels eats of the whole pie. Which fraction represents the amount of pie remaining? q TEKS..H,..K _ 1. aron is practicing for a triathlon. On Sunday, he bikes 1 _ miles and swims _ miles. On Monday, he runs _ miles. How many total miles does aron cover on the two days? q TEKS..K miles 1 miles 1 miles _ miles 1. Mario is painting his walls. He needs a total of _ gallons of paint for the job. He has _ gallons of paint. How much more paint does he need? q TEKS..K _ gallons 9 _ 1 gallons _ 1 gallons gallons Houghton Mifflin Harcourt Publishing ompany