Using Equivalent Fractions to Solve Problems

Transcription

1 Using Equivalent Fractions to Solve Problems Home Link -1 1 Fill in the equivalent fractions in the table below. Multi ply Both the Numerator and Denominator by: Fraction 6 1 _ 6_ 6_ _ 1 6_ 1 _ 1 16, 11 1 Estim ate. Then solve by finding fractions with a common denominator. Write a number sentence to show which fractions you used. Example: 1 _ + 7 _ 1 =? close to 1, because _ 1 is less than _ 1, and _ 7 1 is a little more than _ 1 Common denominator: 1 Answer: _ 11 1 Number sentence: _ _ 1 =? 6_ - 1 _ =? Common denominator: Number sentence: An swer: 1_ 6 + _ =? Common denominator: Number sentence: Answer: Estimate. Then solve using U.S. traditional multiplication. Show your work on the back of this page. 7 9 = 1,0 7 = 16

2 Using a Common Denominator Home Link - 1 For each pair of fractions in the table, find a common denominator. Then rewrite the two fractions as equivalent fractions with a common denominator. Write > or < in the space provided to create a true number sentence. 177, 190 Remember the three strategies you have learned: List equivalent fractions. Check to see if one denominator is a multiple of the other denominator. Multiply denominators to get a quick common denominator. a. b. c. d. e. Original Common Equivalent Fractions > or < Fractions Denominator _ 7 _ 7 _ 9 _ 9 1_ 1_ 10 7_ _ 1 _ 1 _ Use the table to help you rewrite the problems with common denominators. Then solve. _ - _ 7 = - = 1_ + _ 10 = + = _ 9 + _ = + = Solve. Show your work on the back of the page. 10 _ 6 _,

3 Adding Fractions and Mixed Numbers Home Link - Estimate and then solve. Show your work. Use your estimates to check your answers. Remember: Before adding fractions and mixed numbers with different denominators, you must rename one or both fractions so both fractions have a common denominator. 11, 17, Example: _ + _ =? Find a common denominator for the fraction parts. The quick common denominator for _ and _ is the product of the denominators,, or 1. Use the multiplication rule for equivalent fractions to rename each fraction so both fractions have the common denominator. _ + _ Add. Rename the sum. 6 _ 19 1 = 6 + _ _ 1 = _ 1 = 7 + _ 1 = 7 _ 1 _ _ _ _ + 6 _ 1 = 6 6 _ 1 + _ 1 = 6 _ + _ 7 = 1 Write each decimal using numerals. three and six hundred twenty-four thousandths 6 fourteen and twelve thousandths Write each decimal using words. 1 _ _ =

4 Home Link - Marathon Training Katie is training to run a marathon. She keeps track of how many miles she runs each day. Use the information in the table to answer the questions. 1 How many more miles did Katie run on Day 1 than on Day? Show your work: Answer: miles How many miles did Katie run on Day and Day combined? Show your work: Training Day 17, 1, Number of Miles _ 1 _ 9 1 _ Answer: miles Katie set a goal to run _ 1 miles on Day. How much farther than her goal did she run? Show your work: Answer: miles , ,9.6. Choose from the list above. Write the number that has: a 7 in the hundredths place. a in the thousandths place. 6 a that is worth

5 Fraction-Of Problems Home Link - Solve each fraction-of problem. Include a unit in your answer. Then write a multiplication number model for each problem Suri made 6 gallons of lemonade to sell at her lemonade stand. In one day she sold _ of the lemonade. How much lemonade did she sell? Antonio planned to read 1 books over the summer for the library s summer reading challenge. At the end of July he had read _ of the books. How many books had he read? Answer: Numb er model: Answer: Elliot is riding in a 100-mile bike race to raise money for a charity. So far he has completed _ 7 of the race. How 10 far has Elliot biked? Answer: Write <, >, or = to make true number sentences. Erica s garden has an area of square feet. She will use _ of the space for vegetables and _ 1 of the space for flowers. How much space will she use for vegetables? Answer:

6 Multiplying Whole Numbers and Fractions Home Link -6 1 a. What is 1 _ 6 b. What is _ 6 of 1? of 1? c. Fill in the blank to make a true number sentence. 1 _ 6 = a. What is 1? b. What is? c. What is 1? d. Fill in the blank to make a true number sentence. 1 _ = , The art teacher has 7 bottles of glue that are each _ full. He combines them so he will have fewer bottles. How many bottles of glue does he have after he combines them? The librarian needs to return books to the shelf. In one hour she finished _ of the job. How many books has she returned to the shelf so far? Answer: bottles Answer: books For Problems 7, round each decimal to the nearest tenth For Problems 10, round each decimal to the nearest hundredth

7 Finding Fractions of Fractions Home Link -7 Follow the directions to solve the problems. You will need two pieces of paper. 1 What is 1 _ of _? a. Fold the paper into fourths. Unfold it and shade two of the fourths. What is _ of _? a. Fold the paper into thirds. Unfold it and shade two of the thirds. 01 b. Fold the paper into thirds the other way, with the new folds crossing your folds from Part a. Unfold the paper and double-shade one -third of the shaded part. c. Record what your paper looks like. b. Fold the paper into fourths the other way, with the new folds crossing your folds from Part a. Unfold the paper and double-shade three-fourths of the shaded part. c. Record what your paper looks like. P ractice d. How much of the paper is double-shaded? e. Fill in the blank: 1 _ of _ is. d. How much of the paper is double-shaded? e. Fill in the blank: _ of _ is. Make an estimate. Then solve. Use your estimate to check whether your answer makes sense

8 Using Area Models to Multiply Fractions Home Link - Label the blank tick marks on the number lines. Use the number lines to write the length and width of the shaded rectangle. 0 Find the area of the shaded rectangle. (The area of the big square is 1 square unit.) Think: Into how many equal parts is the big square divided? How many parts are shaded? Write a multiplication number sentence for the area of the shaded rectangle L ength of shaded rectangle: unit Length of shaded rectangle: unit Width of shaded rectangle: unit Width of shaded rectangle: unit Area of shaded rectangle: square unit Area of shaded rectangle: square unit Number sentence: = Number sentence: = Make an esti mate. Then solve. Use your estimate to check whether your answer makes sense

9 Using an Algorithm to Multiply Fractions Home Link -9 A Fraction Multiplication Algorithm To multiply two fractions, multiply the numerators and multiply the denominators. For example: _ _ ( ) = _ ( ) = _ , 0 0 For Problems 1 6, use the algorithm to multiply the fractions. 1 1_ 1 _ = _ = _ _ = 10 _ = _ 6 = 6 _ 1 _ 7 = 7 If you multiply _ _ 6 10, will the product be more than _ or less than _ How do you know?? If you multiply _ _ 6 10, will the product be more than _ 6 10 or less than _ 6 How do you know? In Problems 9 1, write true or false. Do not multiply _ 7 _ 10 is less than _. 7_ 9 11 _ 1 is greater than 11 _ 1. _ _ is greater than _ but less than _. 6_ 7 1 _ is less than 6 _ 7 and less than 1 _. 10? _ 6 = 1 _ + _ = _ = 191

10 Home Link -10 Mystery Models Write a multiplication number sentence that represents the amount of shaded space in the pictures below. Add to the picture or create a new drawing to represent your number sentence. 0 1 Solve. 1 1 _ + _ = 1 _ 9 + _ = 6-1 _ = 6 1 _ - _ = 19

11 Finding Equivalent Fractions Home Link a. List three fractions that are equivalent to 1.,, b. Use the fractions you wrote in Part a to find three fractions equivalent to 6 _ 7. Example: =,, 1, 16 You are solving fraction addition problems. Use the information to find equivalent fractions. a. Original fraction: _ Denominator needed: 0 Multiply by: b. Original fraction: 1 _ Multiply by: Equivalent fraction: Denominator needed: 1 Equivalent fraction: Addison wanted to find a fraction equivalent to _ with 16 in the denominator. He thought: = 16, so I need to multiply _ by. He got an answer of _ 16. a. Is _ 16 equivalent to _? How do you know? Solve. b. What mistake did Addison make? What is _ of 9? What is _ of 0? 6 Explain how you found your answer for Problem. 19

12 Writing Fraction Multiplication Stories Home Link -1 Solve each multiplication problem. Then write a number story that matches the number sentence and representation. Example: 1_ _ 6 = Number Story: Mr. Danielson had a tray of pumpkin bread that was _ 6 full. After sharing his bread with students, _ 1 of what he had brought was left. What fraction of the whole tray was left? 1 _ = Number story: _ 16 = Number story: Make an estimate. Then add or subtract. Show your work on the back of this page =? =? = = 0

13 Solving Fraction Division Problems Home Link -1 Write a number model using a letter for the unknown. Solve, showing your solution strategy with representations or drawings. Summarize your work with a division number model. Check your answer using multiplication and write a number sentence to show how you checked. 1 Ben has _ 1 of a loaf of bread. If he and his friends share the _ 1 loaf equally, how much of the whole loaf will each person get? 07 Each person will get loaf of bread. (summary number model) (check using multiplication) Amanda has a piece of ribbon that is _ 1 yard long. She wants to share the ribbon with friends so that they can each wear a ribbon for Breast Cancer Awareness Month. If each of the friends gets the same amount, how much ribbon will each person get? Each person will get (summary number model) yard of ribbon. Make an estimate. Then use U.S. traditional multiplication to solve. Show your work on the back of this page (check using multiplication), 0 1 0

14 More Fraction Division Problems Home Link -1 For Problems 1 and, write a number model using a letter for the unknown. Solve, showing your solution strategy. Summarize your work with a division number model. Check your answer using multiplication, and write a number sentence to show how you checked Charity is packing a -pound container of trail mix into bags for a camping trip. Each bag holds _ 1 pound of trail mix. If Charity uses all pounds of trail mix, how many 1_ -pound bags will she have? Charity will have 1_ -pound bags. (summary number model) (check using multiplication) Davis has a thin box that is inches wide. He wants to use the box to store markers that are _ 1 -inch wide. If he lines up the markers side by side and uses the entire width of the box, how many markers can Davis fit in the box? Davis will be able to fit markers in the box. (summary number model) (check using multiplication) Make an estimate. Then solve. Show your work on the back of this page 6,9 0 07