Lesson ( 1 = + ALGEBRA. Use Properties of Addition Essential Question How can properties help you add fractions with unlike denominators?

Transcription

1 Name Use Properties of Addition Essential Question How can properties help you add fractions with unlike denominators? connect You can use properties of addition to help you add fractions with unlike denominators. Commutative Property: + _ = _ + Associative Property: ( _ ) _ 8 = _ 8) 9 + ( 1 _ 8 + _ ALGEBRA Lesson 6.10 Number and Operations Fractions.NF.A.1 MATHEMATICAL PRACTICES MP, MP7, MP8 Parentheses ( ) tell which operation to do first. Unlock the Problem Jane and her family are driving to Big 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 6 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? Image Credits: (cr) Age Fotostock America, Inc. Use the Associative Property. Day 1 + Day 1 + ( ) = ( + ) + = So, Jane s family has driven _ of the total distance by the end of the second day. Write the number sentence to represent the problem. Use the Associative Property to group fractions with like denominators together. Use mental math to add the fractions with like denominators. Write equivalent fractions with like denominators. Then add. Math Talk MATHEMATICAL PRACTICES 8 Generalize Explain why grouping the fractions differently makes it easier to find the sum. Chapter 6 07

2 Example Add. ( ) + 1 _ 8 Use the Commutative Property and the Associative Property. ( ) 1 8 = ( + ) + ( + ) = = Use the Commutative Property to put fractions with like denominators next to each other. Use the Associative Property to group fractions with like denominators together. Use mental math to add the fractions with like denominators. Write equivalent fractions with like denominators. Then add. Rename and simplify. Try This! Use properties to solve. Show each step and name the property used. A + ( _ + 1 1) B ( 1 _ + 10) + _ 08

3 Name Share and Show MATH BOARD Use the properties and mental math to solve. Write your answer in simplest form. 1. ( _ 8 1 _ 1 1 6) ( 1 1 _ ). ( 1 _ 1 1 6) _ On Your Own Use the properties and mental math to solve. Write your answer in simplest form.. ( _ ) _. ( 1 1 ) _ Math Talk 6. ( 6 1 _ 7) 1 _ 7 MATHEMATICAL PRACTICES 7 Identify Relationships How is solving Exercise different from solving Exercise 1? 7. ( 1 1 ) ( 1 _ 9. 8) _ 9 1 ( 9 1 _ ) 10. DEEPER Tina 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 Tina use for the third doll? Chapter 6 Lesson 10 09

4 MATHEMATICAL PRACTICES M Use the map to solve DEEPER Julie rides her bike from the sports complex to the school. Then she rides from the school to the mall, and then on to the library. Kyle rides his bike from his house to the mall, and then to the library. Who rides farther? How many miles farther? 1. SMARTER 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. Describe how you can use the properties to find how far Mario walks. Sports Complex Park Library mile Mall School mile mile mile 1 1 miles 1 miles Kyle s House Mario s House 1. MATHEMATICAL PRACTICE Write an Expression Kyle is adding the distances between the school and the mall, the mall and the park, and the mall and his house. He writes _ + _ + _. Rewrite Kyle s expression using properties so the fractions are easier to add. 1. SMARTER For 1a 1c, tell whether the Commutative Property or the Associative Property can be used to show each equation is true without calculating. Choose the correct property of addition. 1a ( 10 + _ 6 ) = ( ) + _ 6 1b. ( _ + )+ = ( + _ ) + 1c. ( + 8 ) + 1 _ 8 = + ( _ 8 ) Associative Property Commutative Property Associative Property Commutative Property Associative Property Commutative Property 10

5 Name Use Properties of Addition Use the properties and mental math to solve. Write your answer in simplest form. 1. ( 1 _ + 1 _ ) + _ ) + _ = (1 _ + 1 _ = 1 _ + ( 1 _ + _ ) = 1 _ + 6 = 7 _. 8 1 _ + ( _ + 10 ) Practice and Homework Lesson 6.10 COMMON CORE STANDARD.NF.A.1 Use equivalent fractions as a strategy to add and subtract fractions.. ( _ _ ) + 7 _ 8. _ 10 + (1 _ ). 1 _ + ( 1 _ + 1 _ ) _ + ( _ + _ ) Problem Solving 7. Elizabeth rode her bike 6 miles from her house to the library and then another _ miles to her friend Milo s house. If Carson s house is miles beyond Milo s house, how far would she travel from her house to Carson s house? 8. Hassan made a vegetable salad with _ 8 pounds of tomatoes, 1 pounds of asparagus, and 7_ pounds of potatoes. How many pounds of 8 vegetables did he use altogether? 9. WRITE Math Write Commutative Property and Associative Property at the top of the page. Underneath the name of each property, write its definition and three examples of its use. Chapter 6 11

6 Lesson Check (.NF.A.1) 1. What is the sum of, _, and 6_?. Letitia has 7 yards of yellow ribbon, yards of 6 6 orange ribbon, and yards of brown ribbon. 6 How much ribbon does she have altogether? Spiral Review (.OA.A.1,.NBT.B.6,.NBT.B.7,.NF.A.1). Juanita wrote 7 as What property did she use to rewrite the expression?. What is the value of the expression? 18 ( 1 ). Evan spent $1.89 on 7 pounds of birdseed. How much did the birdseed cost per pound? 1 6. Cade rode 1 _ miles on Saturday and miles on Sunday. How far did he ride on the two days? FOR MORE PRACTICE GO TO THE Personal Math Trainer