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Number and Operations – Fractions → Extend understanding of fraction equivalence and ordering. Lesson Lesson Lesson Lesson Lesson Lesson Lesson Lesson 47 48 49 50 51 52 53 54 CC.4.NF.1 CC.4.NF.1 CC.4.NF.1 CC.4.NF.1 CC.4.NF.1 CC.4.NF.2 CC.4.NF.2 CC.4.NF.2 Equivalent Fractions . . . . . . . . . . . . . Generate Equivalent Fractions . . . . . . . . Simplest Form . . . . . . . . . . . . . . . . Common Denominators . . . . . . . . . . . Problem Solving • Find Equivalent Fractions Compare Fractions Using Benchmarks . . . . Compare Fractions . . . . . . . . . . . . . . Compare and Order Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 . 95 . 97 . 99 .101 .103 .105 .107 Add and Subtract Parts of a Whole . . . . . . Write Fractions as Sums . . . . . . . . . . . . Rename Fractions and Mixed Numbers . . . . . Add and Subtract Mixed Numbers . . . . . . . Subtraction with Renaming . . . . . . . . . . Algebra • Fractions and Properties of Addition Add Fractions Using Models . . . . . . . . . . Subtract Fractions Using Models . . . . . . . . Add and Subtract Fractions . . . . . . . . . . Problem Solving • Multistep Fraction Problems . . . . . . . . . . . . . . . Multiples of Unit Fractions . . . . . . . . . . . Multiples of Fractions . . . . . . . . . . . . . Multiply a Fraction by a Whole Number Using Models . . . . . . . . . . . . . . . . . Multiply a Fraction or Mixed Number by a Whole Number . . . . . . . . . . . . . . . Problem Solving • Comparison Problems with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 .111 .113 .115 .117 .119 .121 .123 .125 → Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. © Houghton Mifflin Harcourt Publishing Company Lesson Lesson Lesson Lesson Lesson Lesson Lesson Lesson Lesson Lesson 55 56 57 58 59 60 61 62 63 64 Lesson 65 Lesson 66 Lesson 67 Lesson 68 Lesson 69 CC.4.NF.3a CC.4.NF.3b CC.4.NF.3b CC.4.NF.3c CC.4.NF.3c CC.4.NF.3c CC.4.NF.3d CC.4.NF.3d CC.4.NF.3d CC.4.NF.3d CC.4.NF.4a CC.4.NF.4b CC.4.NF.4b CC.4.NF.4c CC.4.NF.4c . . .127 . . .129 . . .131 . . .133 . . .135 . . .137 → Understand decimal notation for fractions, and compare decimal fractions. Lesson Lesson Lesson Lesson Lesson Lesson 70 71 72 73 74 75 CC.4.NF.5 CC.4.NF.5 CC.4.NF.6 CC.4.NF.6 CC.4.NF.6 CC.4.NF.7 Equivalent Fractions and Decimals . . . Add Fractional Parts of 10 and 100 . . Relate Tenths and Decimals . . . . . . Relate Hundredths and Decimals . . . . Relate Fractions, Decimals, and Money . Compare Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139 .141 .143 .145 .147 .149 v Name LESSON 47 1 Equivalent Fractions CC.4.NF.1 OBJECTIVE Use models to show equivalent fractions. __. Write two fractions that are equivalent to 2 6 2. Step 1 Make a model to represent __ 6 The rectangle is divided into 6 equal parts, with 2 parts shaded. Step 2 Divide the rectangle from Step 1 in half. The rectangle is now divided into 12 equal parts, with 4 parts shaded. 4 . So, __ 2 and ___ 4 are equivalent. The model shows the fraction ___ 12 6 12 © Houghton Mifflin Harcourt Publishing Company Step 3 Draw the same rectangle as in Step 1, but with only 3 equal parts. Keep the same amount of the rectangle shaded. The rectangle is now divided into 3 equal parts, with 1 part shaded. 1. So, __ 2 and __ 1 are equivalent. The model shows the fraction __ 3 6 3 Use models to write two equivalent fractions. __ 1. 2 4 __ 2. 4 6 1 4 __, __ 2 8 Number and Operations–Fractions Check students’ models. Possible answers are given. 2 8 __, ___ 3 12 93 Name 1 Equivalent Fractions CC.4.NF.1 Use the model to write an equivalent fraction. Possible answers are given. 1. 4 __ 6 2 __ 3 = 2. 3 __ 4 6 __ 8 = 8 = __ 4 3. ___ 10 5 7 __ ≠ ___ 4. 1 2 12 8 __ ≠ ___ 5. 3 4 12 4 __ = __ 6. 2 3 6 4 __ ≠ ___ 7. 5 8 10 4 __ = ___ 8. 2 6 12 1 20 = __ 9. ____ 100 5 9 __ ≠ ___ 10. 5 8 10 Problem Solving 11. Jamal finished __56 of his homework. Margaret finished __34 of her 10 homework, and Steve finished __ 12 of his homework. Which two students finished the same amount of homework? Jamal and Steve 94 12. Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots. 2, __ 4 Possible answers: __ 3 6 Lesson 47 © Houghton Mifflin Harcourt Publishing Company Tell whether the fractions are equivalent. Write = or ≠. Name LESSON 48 1 Generate Equivalent Fractions CC.4.NF.1 OBJECTIVE Use multiplication to generate equivalent fractions. 4. Write an equivalent fraction for __ 5 Step 1 Choose a whole number, like 2. Step 2 Create a fraction using 2 as the numerator and denominator: __22 This fraction is equal to 1. You can multiply a number by 1 without changing the value of the number. 2: 4 × 2 = ___ 8. __ by __ _____ Step 3 Multiply 4 5 2 5 × 2 10 8 are equivalent. 4 and ___ So, __ 5 10 4. Write another equivalent fraction for __ 5 Step 1 Choose a different whole number, like 20. 20. Step 2 Create a fraction using 20 as the numerator and denominator: ___ 20 20: 4 × 20 = ____ 80 . __ by ___ _______ Step 3 Multiply 4 5 20 5 × 20 100 © Houghton Mifflin Harcourt Publishing Company 80 are equivalent. 4 and ____ So, __ 5 100 Write two equivalent fractions. 2 1. __ 6 Possible answers are given. 4 2. ___ 10 8 , ___ 12 ___ 6 , ___ 8 ___ 18 24 __ 3. 3 8 20 30 __ 4. 3 5 18 9 , ___ ___ 24 48 Number and Operations–Fractions 21 12 ___, ___ 20 35 95 Name 1 Generate Equivalent Fractions Write two equivalent fractions for each. 1 1. __ 3 2 2. __ 3 1 ×2=2 _____ __ 3×2 6 CC.4.NF.1 Possible answers are given. 1 3. __ 2 4, ___ 8 __ 4 4. __ 5 80 8 , ____ ___ 2 4 __, __ 4 8 6 12 10 100 1 × 4 = ___ 4 _____ 3 × 4 12 Tell whether the fractions are equivalent. Write = or ≠. 3 1 = ___ 5. __ 4 12 5 __ ≠ ___ 6. 4 5 10 2 __ ≠ __ 7. 3 8 6 6 __ = __ 8. 3 4 8 10 __ = ___ 9. 5 6 12 5 6 ≠ __ 10. ___ 12 8 4 __ = ___ 11. 2 5 10 3 __ ≠ ___ 12. 2 4 12 Possible answers are given. 13. Jan has a 12-ounce milkshake. Four ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fraction of the milkshake that is vanilla? 1 2 __ and __ 3 6 96 4 14. Kareem lives __ of a mile from the 10 mall. Write two equivalent fractions that show what fraction of a mile Kareem lives from the mall. © Houghton Mifflin Harcourt Publishing Company Problem Solving 2 8 __ and ___ 5 20 Lesson 48 Name LESSON 49 1 Simplest Form CC.4.NF.1 OBJECTIVE Write and identify equivalent fractions in simplest form. A fraction is in simplest form when 1 is the only factor that the numerator and denominator have in common. __ is in simplest form. Tell whether the fraction 7 8 Look for common factors in the numerator and the denominator. Step 1 The numerator of 7_8 is 7. List all the factors of 7. 1× 7= 7 Step 2 The denominator of 7_8 is 8. List all the factors of 8. 1× 8= 8 The factors of 7 are 1 and 7. 2× 4= 8 The factors of 8 are 1, 2, 4, and 8. Step 3 Check if the numerator and The only common factor of 7 and 8 7 _ denominator of 8 have any is 1. common factors greater than 1. So, 7_8 is in simplest form. © Houghton Mifflin Harcourt Publishing Company Tell whether the fraction is in simplest form. Write yes or no. 4 1. ___ 10 2 2. __ 8 no 3 3. __ 5 no yes Write the fraction in simplest form. 4 4. ___ 12 6 5. ___ 10 1 __ 3 Number and Operations–Fractions 3 6. __ 6 3 __ 5 1 __ 2 97 Name 1 Simplest Form CC.4.NF.1 Write the fraction in simplest form. 6 1. ___ 10 __ 2. 6 8 6 = _______ 6 ÷ 2 = __ 3 ___ 10 10 ÷ 2 __ 3. 5 5 3 __ 4 5 100 5. ____ 100 2 6. __ 6 1 or 1 __ 2 __ 3 1 or 1 __ 1 2 7. __ 8 1 __ 3 1 8 4. ___ 12 4 8. ___ 10 1 __ 4 2 __ 5 6 ≠ ___ 1 9. ___ 12 12 60 6 = ____ 13. ___ 10 100 5 __ ≠ __ 10. 3 4 6 3 6 = __ 11. ___ 10 5 1 3 ≠ __ 12. ___ 12 3 9 ___ ≠ ___ 14. 11 12 10 8 2 = ___ 15. __ 5 20 1 __ = __ 16. 4 8 2 Problem Solving 17. At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys. In simplest form, what fraction of the babies born on Tuesday were boys? 3 __ 4 98 18. Cristina uses a ruler to measure the length of her math textbook. She 4 meter long. says that the book is __ 10 Is her measurement in simplest form? If not, what is the length of the book in simplest form? 2 meter No; __ 5 Lesson 49 © Houghton Mifflin Harcourt Publishing Company Tell whether the fractions are equivalent. Write = or ≠. Name LESSON 50 1 Common Denominators OBJECTIVE Use equivalent fractions to represent a pair of fractions with a common denominator. CC.4.NF.1 A common denominator is a common multiple of the denominators of two or more fractions. 2 and __ 3 as a pair of fractions with common denominators. Write __ 3 4 Step 1 Identify the denominators of 2_3 and 3_4 . Step 2 List multiples of 3 and 4. Circle common multiples. Step 3 Rewrite 2_3 as a fraction with a denominator of 12. Step 4 Rewrite 3_4 as a fraction with a denominator of 12. 2 and __ 3 __ 3 4 The denominators are 3 and 4. 3: 3, 6, 9, 12, 15, 18 4: 4, 8, 12, 16, 20 12 is a common multiple of 3 and 4. 2 × 4 = ___ 8 __ = 2 ______ 3 3 × 4 12 3 × 3 = ___ 9 __ = 3 ______ 4 4 × 3 12 2 and __ 3 as ___ 8 and ___ 9. So, you can rewrite __ 3 4 12 12 © Houghton Mifflin Harcourt Publishing Company Write the pair of fractions as a pair of fractions with a common denominator. Possible answers are given. 1 and __ 1 1. __ 2 3 2 and __ 5 2. __ 4 8 4 5 __, __ 8 8 3 2 __, __ 6 6 1 and __ 3 3. __ 2 5 1 and __ 5 4. __ 4 6 10 3 , ___ ___ 5 , ___ 6 ___ 12 12 10 10 2 and __ 2 5. __ 5 3 4 and ___ 7 6. __ 5 10 10 6 , ___ ___ 15 15 Number and Operations–Fractions 8 , ___ 7 ___ 10 10 99 Name 1 Common Denominators CC.4.NF.1 Write the pair of fractions as a pair of fractions with a common denominator. Possible answers are given. 3 __ and __ 1. 2 3 4 2 __ and __ 2. 1 4 3 3 and __ 1 3. ___ 10 2 Think: Find a common multiple. 3: 3, 6, 9, 12, 15 4: 4, 8, 12, 16, 20 8 , ___ 9 ___ 12 12 3 and __ 3 4. __ 5 4 3 , ___ 8 ___ 12 12 2 and __ 7 5. __ 4 8 7 4, __ __ 8 8 15 12, ___ ___ 20 20 2 and ___ 5 6. __ 3 12 5 8 , ___ ___ 12 12 5 3 , ___ ___ 10 10 1 and __ 1 7. __ 4 6 2 3 , ___ ___ 12 12 2 __ ≠ __ 8. 1 2 5 3 __ = __ 9. 1 2 6 3 __ = __ 12. 6 8 4 2 __ ≠ __ 13. 3 4 3 5 3 ≠ __ 10. __ 4 6 3 6 = __ 11. ___ 10 5 4 2 ≠ __ 14. ___ 10 5 3 __ = ___ 15. 1 4 12 Problem Solving 16. Adam drew two same size rectangles and divided them into the same number of equal parts. He shaded 1_3 of one rectangle and 1_4 of other rectangle. What is the least number of parts into which both rectangles could be divided? 12 parts 100 17. Mera painted equal sections of her bedroom wall to make a pattern. She painted 2_5 of the wall white and 1_2 of the wall lavender. Write an equivalent fraction for each using a common denominator. 4 and ___ 5 Possible answer: ___ 10 10 Lesson 50 © Houghton Mifflin Harcourt Publishing Company Tell whether the fractions are equivalent. Write = or ≠. Name LESSON 51 Problem Solving • Find Equivalent Fractions OBJECTIVE Use the strategy make a table to solve problems using equivalent fractions. 1 CC.4.NF.1 Kyle’s mom bought bunches of balloons for a family party. Each bunch has 4 balloons, and __14 of the balloons are blue. If Kyle’s mom bought 5 bunches of balloons, how many balloons did she buy? How many of the balloons are blue? Read the Problem What do I need to find? I need to find how many balloons Kyle’s mom bought and how many of the balloons are blue. What information do I need to use? Each bunch has 1 out of 4 balloons that are blue, and there are 5 bunches. How will I use the information? I will make a table to find the total number balloons Kyle’s mom bought and the fraction of balloons that are blue. Solve the Problem © Houghton Mifflin Harcourt Publishing Company I can make a table. Number of Bunches 1 2 3 4 5 Total Number of Blue Balloons Total Number of Balloons 1 __ 4 2 __ 8 3 ___ 4 ___ 5 ___ 12 16 20 Kyle’s mom bought 20 balloons. 5 of the balloons are blue. Make a table to solve. Check students’ tables. 1. Jackie is making a beaded bracelet. 2. Ben works in his dad’s bakery The bracelet will have no more than packing bagels. Each package can 1 __ 12 beads. 3 of the beads on the have no more than 16 bagels. __34 of bracelet will be green. What other the bagels in each package are plain. fractions could represent the part What other fractions could represent of the beads on the bracelet that the part of the bagels in each will be green? package that will be plain? 2, __ 3, ___ 4 __ 6 9 12 Number and Operations–Fractions 9 , ___ 12 6, ___ __ 8 12 16 101 Name Problem Solving • Find Equivalent Fractions Solve each problem. 1 CC.4.NF.1 Possible answers are given. 1. Miranda is braiding her hair. Then she will attach beads to the braid. She wants __13 of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red? 2, __ 3, ___ 4 __ 6 9 12 2. Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple? 20 or __ 1 ____ 3. Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle? 5 1, __ 2 and __, __ At the 1 3 2 3 final locations 4. Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box. Number of Blueberry Mufﬁns 2 4 8 Total Number of Mufﬁns 6 12 24 36 How many blueberry muffins should Preston put in a box with 36 muffins? 12 blueberry muffins 102 Lesson 51 © Houghton Mifflin Harcourt Publishing Company 100 Name 1 Compare Fractions Using Benchmarks LESSON 52 CC.4.NF.2 OBJECTIVE Compare fractions using benchmarks. A benchmark is a known size or amount that helps you understand a different size or amount. You can use __12 as a benchmark. Sara reads for __36 hour every day after school. Connor reads for 2 __ hour. Who reads for a longer amount of time? 3 Compare the fractions. 3 __ 6 2 __ 3 Step 1 Divide one circle into 6 equal parts. Divide another circle into 3 equal parts. Step 2 Shade __36 of the first circle. How many parts will you shade? 3 parts JXiX :feefi Step 3 Shade __23 of the second circle. How many parts will you shade? 2 parts Step 4 Compare the shaded parts of each circle. Half of Sara’s circle is shaded. More than half of Connor’s circle is shaded. 3 __ is less than 2 __. 6 3 2 3 < __ __ 6 3 © Houghton Mifflin Harcourt Publishing Company So, Connor reads for a longer amount of time. 2 and __ 3. Write < or >. 1. Compare __ 8 4 ' ( ) 1 8 1 8 1 8 1 8 1 8 1 8 1 8 ( ' 1 8 ( ) 1 4 2 < __ 8 1 4 ( 1 4 1 4 3 __ 4 Compare. Write < or >. 8 1 < ___ 2. __ 4 10 __ > 1 __ 3. 7 8 3 5 < 1 __ 4. ___ 12 2 8 2 < ___ 5. __ 8 12 __ > 4 __ 6. 4 6 8 7 > 2 __ 7. ___ 12 4 Number and Operations–Fractions 103 Name 1 Compare Fractions Using Benchmarks CC.4.NF.2 Compare. Write < or >. 1 < ___ 6 1. __ 8 10 4 < 4 __ 2. ___ 12 6 __ < 1 __ 3. 2 8 2 3 < 3 __ 4. __ 5 3 5 __ > ___ 5. 7 8 10 9 > 1 __ 6. ___ 12 3 4 < 7 __ 7. __ 6 8 __ < 2 __ 8. 2 4 3 __ > 1 __ 9. 3 5 4 6 > 2 __ 10. ___ 10 5 2 __ < ___ 11. 1 8 10 __ 12. 2 3 4 < 5 __ 13. __ 5 6 __ < 5 __ 14. 3 5 8 __ > 3 __ 15. 8 8 4 1. ___ 6 is __ is less than __ Think: 1 8 2 10 __. more than 1 2 Problem Solving 16. Erika ran __38 mile. Maria ran __34 mile. Who ran farther? Maria 104 17. Carlos finished __13 of his art project on Monday. Tyler finished __12 of his art project on Monday. Who finished more of his art project on Monday? Tyler Lesson 52 © Houghton Mifflin Harcourt Publishing Company 5 > ___ 12 Name 1 Compare Fractions LESSON 53 CC.4.NF.2 OBJECTIVE Compare fractions by first writing them as fractions with a common numerator or a common denominator. Theo filled a beaker __24 full with water. Angelica filled a beaker __38 full with water. Whose beaker has more water? 2 and __ 3. Compare __ 4 8 Step 1 Divide one beaker into 4 equal parts. Divide another beaker into 8 equal parts. Theo 2 of the first beaker. Step 2 Shade __ 4 __ of the second beaker. Step 3 Shade 3 8 1 4 Half of Theo’s beaker is shaded. Less than half of Angelica’s beaker is shaded. 2 3 __ __ 4 is greater than 8 . 1 4 2 > __ 3 __ 1 4 4 8 So, Theo’s beaker has more water. © Houghton Mifflin Harcourt Publishing Company ' 2 and __ 3. 2. Compare __ 3 6 ( ) ( 1 2 1 4 ' ( ) 1 3 1 2 1 4 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 Step 4 Compare the shaded parts of each beaker. 1 and __ 1. 1. Compare __ 2 4 Angelica 1 4 Which is greater? 1 4 1 __ 2 1 6 ( 1 3 1 6 1 6 Which is less? 1 3 1 6 1 6 1 6 3 __ 6 Compare. Write <, > , or = . 1 < 3 __ 3. __ 2 4 Number and Operations–Fractions 6 < 5 __ 4. ___ 12 8 __ = 4 __ 5. 2 3 6 __ > 1 __ 6. 3 8 4 105 Name 1 Compare Fractions CC.4.NF.2 Compare. Write <, > , or = . 3 < __ 5 1. __ 4 6 2 > __ 2 3. __ 4 5 2 1 = ___ 2. __ 10 5 Think: 12 is a common denominator. 7 __ < ___ 4. 3 5 10 1 4 > __ 5. ___ 12 6 1 __ < __ 8. 2 5 2 __ = 2 __ 9. 4 4 8 1 __ = __ 6. 2 6 3 2 __ < __ 7. 1 3 4 7 > __ 2 10. ___ 12 4 3 __ < __ 11. 1 8 4 Problem Solving 12. A recipe uses __23 cup of flour and 5 __ cup of blueberries. Is there more 8 flour or more blueberries in the recipe? flour 106 13. Peggy completed __56 of the math homework and Al completed __45 of the math homework. Did Peggy or Al complete more of the math homework? Peggy Lesson 53 © Houghton Mifflin Harcourt Publishing Company 3 = ______ 3 × 3 = ___ 9 __ 4 4 × 3 12 5 5 × 2 = 10 __ = ______ ___ 6 6 × 2 12 9 < 10 ___ ___ 12 12 Name 1 Compare and Order Fractions LESSON 54 CC.4.NF.2 OBJECTIVE Compare and order fractions. 3, __ 1, and __ 1 in order from least to greatest. Write __ 8 4 2 Step 1 Identify a common denominator. Multiples of 8: 8, 16, 24 Multiples of 4: 4, 8, 12, 16 Multiples of 2: 2, 4, 6, 8 Use 8 as a common denominator. Step 2 Use the common denominator to write equivalent fractions. 3 __ 8 1 × 2 = __ 2 __ = 1 ______ 4 4× 2 8 1= 1 × 4 = __ 4 __ ______ 2 2× 4 8 Step 3 Compare the numerators. 2< 3< 4 Step 4 Order the fractions from least to greatest, using < or > symbols. 2 < __ 3 < __ 4 __ 8 8 8 1 < __ 3 < __ 1. So, __ 4 8 2 © Houghton Mifflin Harcourt Publishing Company Write the fraction with the greatest value. 2, __ 1, __ 1 1. __ 3 4 6 2 __ 3 3 , __ 1, __ 2 2. ___ 10 2 5 1 __ 2 1, ___ 5 , ___ 9 3. __ 8 12 10 9 ___ 10 Write the fractions in order from least to greatest. 9 , __ 1, __ 4 4. ___ 10 2 5 1 4 < ___ 9 __ < __ 2 5 10 Number and Operations–Fractions 3, __ 7, __ 1 5. __ 4 8 2 1 3 < __ 7 __ < __ 2 4 8 2, __ 3, __ 5 6. __ 3 4 6 2 3 < __ 5 __ < __ 3 4 6 107 Name 1 Compare and Order Fractions CC.4.NF.2 Write the fractions in order from least to greatest. 2 , ___ 8 __, ___ 1. 5 8 12 10 2, __ 5 __, __ 2. 1 5 3 8 Use benchmarks and a number line. 5 is close to __ 1. ___ 2 is close to 0. ___ 8 is close to 1. Think: __ ' 2 12 ) () 10 ( ) , / ( / (' 2 < __ 5 < ___ 8 ___ 12 8 1 5 < __ 2 __ < __ 5 8 3 10 1, __ 2, ___ 6 3. __ 2 5 10 7 , ___ 4, ___ 5 4. __ 6 12 10 6 2 1 < ___ __ < __ 5 2 10 1, __ 3, __ 1 5. __ 4 6 8 5 < ___ 7 < __ 4 ___ 10 3, ___ 7 __, __ 6. 1 8 6 12 8 , 7. ____ 100 3 < ___ 7 1 __ < __ 8 6 12 12 1 1 < __ 3 __ < __ 8 4 6 6 7, __ 1 __, __ 8. 3 4 8 5 3, ___ 7 __ 5 10 8 < __ 3 < ___ 7 ____ 100 5 1 < __ 3 < __ 7 __ 10 5 4 8 Problem Solving 9. Amy’s math notebook weighs 1 __ pound, her science notebook 2 weighs __78 pound, and her history notebook weighs __34 pound. What are the weights in order from lightest to heaviest? 3 pound, __ 7 pound 1 pound, __ __ 2 108 4 8 10. Carl has three picture frames. The thicknesses of the frames are 3 4 __ inch, __ inch, and __56 inch. What are 5 12 the thicknesses in order from least to greatest? 3 inch, __ 4 inch, __ 5 inch ___ 12 5 6 Lesson 54 © Houghton Mifflin Harcourt Publishing Company 8 Name 1 Add and Subtract Parts of a Whole LESSON 55 CC.4.NF.3a OBJECTIVE Understand that to add or subtract fractions, they must refer to parts of the same wholes. Justin has 3_8 pound of cheddar cheese and 2_8 pound of brick cheese. How much cheese does he have in all? 1 Step 1 Use fraction strips to model the problem. Use three 1_8 -strips to represent 3_8 pound of cheddar cheese. 1 8 Step 2 Join two more 1_8 -strips to represent the amount of brick cheese. 5 _ 8 1 8 1 1 8 Step 3 Count the number of 1_8 -strips. There are five 1_ -strips. Write the amount as a 8 fraction. Justin has 1 8 1 8 1 8 1 8 pound of cheese. 1 8 2=5 3 + __ __ __ 8 8 8 Step 4 Use the model to write an equation. Suppose Justin eats 1_8 pound of cheese. How much cheese is left? Step 1 Use five 1_8 -strips to represent the 5_8 pound of cheese. Step 2 Remove one 1_8 -strip to show the amount eaten. 1 1 8 1 8 1 8 Step 3 Count the number of 1_8 -strips left. There are 4 four 1_ fraction strips. There is _8 pound left. 8 1 8 1=4 5 __ - __ __ 8 8 8 Step 4 Write an equation for the model. © Houghton Mifflin Harcourt Publishing Company 1 8 Use the model to write an equation. 1. 1 1 1 5 1 1 5 1 5 5 1 5 2. 1 1 5 1 5 1 5 1 5 1 1 3 1 3 1 + __ 3 = __ 4 __ 5 5 5 3. 1 1 4 1 4 1 4 1 1 4 Number and Operations–Fractions 3 5 1 4 1 = __ 4 3 + __ __ 4 2 - __ 1 = __ 1 __ 4 4. 1 1 4 1 4 1 4 1 4 3 3 1 1 1 1 1 1 6 6 6 6 6 2 = __ 3 5 __ - __ 6 6 6 109 Name 1 Add and Subtract Parts of a Whole CC.4.NF.3a Use the model to write an equation. 1. 1 Think: 3 __ 5 2 __ 8 + 8 2=5 3 + __ __ __ 8 8 8 = 2. 5 __ 8 3. 1 4 - __ 3 = __ 1 __ 5 5 5 5 1 + __ 2 = __ 3 __ 4 4 4 Use the model to solve the equation. 5. 4. 2 + __ 3= __ 6 6 5 5 __ 6 3 - __ 2= __ 5 5 1 __ 5 Problem Solving 6. Jake ate 4_8 of a pizza. Millie ate 3_8 of the same pizza. How much of the pizza was eaten by Jake and Millie? 7 __ of the pizza 8 7. Kate ate 1_4 of her orange. Ben ate 2_4 of his banana. Did Kate and Ben eat 1_4 + 2_4 = 3_4 of their fruit? Explain. No; one whole refers to an orange and the other whole to a banana. 110 Lesson 55 © Houghton Mifflin Harcourt Publishing Company 1 Name LESSON 56 1 Write Fractions as Sums CC.4.NF.3b OBJECTIVE Decompose a fraction by writing it as a sum of fractions with the same denominators. A unit fraction tells the part of the whole that 1 piece represents. A unit fraction always has a numerator of 1. 4 Bryan has __ 10 pound of clay for making clay figures. He wants 1 to use __ 10 pound of clay for each figure. How many clay figures can he make? 4 Use fraction strips to write __ 10 as a sum of unit fractions. 4 Step 1 Represent __ 10 with fraction strips. 1 1 __ Step 2 Each __ 10 is a unit fraction. Write a 10 addend 1 4 __ for each __ 10 -strip you used to show 10 . 1 1 __ 1 1 1 __ 1 1 __ __ Step 3 Count the number of addends. The number of addends represents the number of clay figures Bryan can make. So, Bryan can make 4 clay figures. 10 10 10 10 Write the fraction as the sum of unit fractions. © Houghton Mifflin Harcourt Publishing Company 1. 2. 3= __ 6 1 __ 6 + 1 __ 6 + 1 __ 6 2 __ = 4 3. 1 __ 4 1 __ + 4 + 1 __ 5 + 4. 4= __ 8 1 __ 8 1 __ + 8 + Number and Operations–Fractions 1 __ 8 + 1 __ 8 5= __ 5 1 __ 5 1 __ 5 + 1 __ 5 + 1 __ 5 111 Name 1 Write Fractions as Sums CC.4.NF.3b Write the fraction as a sum of unit fractions. 1+1 1+1 __ __ + __ __ 5 5 5 5 4= 1. __ 5 3= 2. __ 8 1 +__ 1 1 + __ __ 8 8 8 __ four times. Think: Add 1 5 6 = 3. ___ 12 1 + ___ 1 1 + ___ ___ 12 12 12 1 + ___ 1 + ___ 1 + ___ 12 12 12 4= 4. __ 4 1 + __ 1 + __ 1 1 __ + __ 4 4 4 4 Write the fraction as a sum of fractions three different ways. 7 5. ___ 10 __ 6. 6 6 2 + ___ 3 + ___ 2 7 = ___ ___ 10 10 10 10 7 = ___ 4 + ___ 2 + ___ 1 ___ 10 10 10 10 7 = ___ 5 + ___ 1 + ___ 1 ___ 10 10 10 10 Possible answers are given. 6 4 + __ 1 + __ 1 __ = __ 6 6 6 6 2 + __ 2 + __ 2 6 __ = __ 6 6 6 6 6 3 + __ 2 + __ 1 __ = __ 6 6 6 6 7. Miguel’s teacher asks him to color 4_8 of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. How can Miguel color the sections of his grid to follow all the rules? 8. Petra is asked to color 6_6 of her grid. She must use 3 colors: blue, red, and pink. There must be more blue sections than red sections or pink sections. What are the different ways Petra can color the sections of her grid and follow all the rules? 1 1 blue, and __ 2 green __ red, __ 8 8 8 2 red, __ 1 pink; 3 blue, __ __ 112 6 6 6 1 red, __ 1 pink; 4 blue, __ __ 6 6 6 3 blue, __ 1 red, __ 2 pink __ 6 6 6 Lesson 56 © Houghton Mifflin Harcourt Publishing Company Problem Solving Name LESSON 57 1 Rename Fractions and Mixed Numbers CC.4.NF.3b OBJECTIVE Write fractions greater than 1 as mixed numbers and write mixed numbers as fractions greater than 1. A mixed number is made up of a whole number and a fraction. You can use multiplication and addition to rename a mixed number as a fraction greater than 1. 5 as a fraction. Rename 2__ 6 First, multiply the denominator, or the number of parts in the whole, by the whole number. 2 6 × 2 = 12 total number 17 of parts 5 = 6 number of 6 parts in the whole Then, add the numerator to your product. 12 + 5 = 17 5 = ___ 17. So, 2__ 6 6 You can use division to write a fraction greater than 1 as a mixed number. 16 as a mixed number. Rename ___ 3 __ as a mixed number, divide the numerator by To rename 16 3 the denominator. © Houghton Mifflin Harcourt Publishing Company Use the quotient and remainder to write a mixed number. 1. ___ = 5__ So, 16 3 3 , *q ( (, ( Write the mixed number as a fraction. 2= 1. 3 __ 3 11 ___ 3 __ = 2. 43 5 23 ___ 5 Write the fraction as a mixed number. 2 1 6__ 6__ 32 19 5 3 ___ ___ 5. 6. = = 5 3 Number and Operations–Fractions __ = 3. 43 8 15 = 7. ___ 4 35 ___ 8 __ 33 4 __ = 4. 21 6 51 = 8. ___ 10 13 ___ 6 1 5___ 10 113 Name 1 Rename Fractions and Mixed Numbers CC.4.NF.3b Write the mixed number as a fraction. __ 1. 23 5 Think: __ + 5 __ + 3 __. Find 5 5 5 5 13 ___ 5 __ 2. 41 3 __ 5. 41 8 7 6. 1___ 10 __ 3. 12 5 13 ___ 3 7 __ 11 ___ 5 __ 7. 51 2 17 ___ 10 33 ___ 8 __ 4. 32 3 3 __ 8. 23 8 11 ___ 2 19 ___ 8 Write the fraction as a mixed number. ___ 10. 20 10 __ 51 6 ___ 11. 15 8 __ 17 8 2 23 13. ___ 10 19 14. ___ 5 11 15. ___ 3 __ 34 5 3 2___ 10 ___ 12. 13 6 __ 21 6 9 16. __ 2 __ 32 3 __ 41 2 Problem Solving 17. A recipe calls for 2 2_4 cups of raisins, but Julie only has a 1_4 -cup measuring cup. How many 1_4 cups does Julie need to measure out 2 2_4 cups of raisins? 1 cups ten __ 4 114 18. If Nancy needs 3 1_4 cups of oatmeal, how many 1_4 cups of oatmeal will she use? 1 cups thirteen __ 4 Lesson 57 © Houghton Mifflin Harcourt Publishing Company ___ 9. 31 6 Name LESSON 58 1 Add and Subtract Mixed Numbers CC.4.NF.3c OBJECTIVE Add and subtract mixed numbers. 1 __ + 2__ Find the sum. 31 4 4 Add the whole number and fraction parts. • Add the whole numbers: 3 + 2 = 5 1 1 2 • Add the fractions: __ + __ = __ 4 4 4 Write the sum as a mixed number, so the 1 + 2__ 1 = 5__ 2 fractional part is less than 1. 3__ 4 4 4 1 __ - 3__ Find the difference. 45 8 8 Subtract the fraction and the whole number parts. 5 1 4 • Subtract the fractions: __ - __ = __ 8 8 8 • Subtract the whole numbers: 4- 3= 1 5 - 3__ 1 = 1__ 4 4__ 8 8 8 © Houghton Mifflin Harcourt Publishing Company Find the sum or difference. 1. 4 3 __ 5 __ + 43 5 __ 82 5 2. 5. 3 2__ 8 __ + 81 8 __ 104 8 9 6. 11___ 10 7 - 3___ 10 2 8___ 10 Number and Operations–Fractions 2 7__ 3 __ - 31 3 1 4__ 3 3. 7 4___ 12 5 + 6___ 12 11 __ 4. 123 4 1 - 6__ 4 2 6__ 4 7. __ 73 5 3 + 4__ 5 __ 121 5 8. 3 8__ 6 1 - 3__ 6 __ 52 6 115 Name 1 Add and Subtract Mixed Numbers CC.4.NF.3c Find the sum. Write the sum as a mixed number, so the fractional part is less than 1. 1. __ 64 5 3 + 3 __ 5 __ = 10 2 __ 97 5 5 2. __ 41 2 1 + 2 __ 2 7 3. __ 22 3 2 + 3 __ 3 __ 61 3 4. __ 64 5 4 + 7 __ 5 __ 14 3 5 5. __ 93 6 2 + 2 __ 6 __ 11 5 6 6. 4 8 ___ 12 6 + 3 ___ 12 10 11 ___ 12 7. __ 43 8 5 + 1 __ 8 6 8. 5 9 ___ 10 3 + 6 ___ 10 8 15 ___ 10 11. __ 64 5 3 - 3__ 5 __ 31 5 12. Write the fraction as a mixed number. __ 67 8 3 - 4 __ 8 __ 24 8 10. __ 42 3 __ - 31 3 __ 11 3 __ 73 4 1 - 2 __ 4 __ 52 4 Problem Solving 13. James wants to send two gifts by mail. One package weighs 2 3_4 pounds. The other package weighs 1 3_4 pounds. What is the total weight of the packages? __ pounds 42 4 116 14. Tierra bought 4 3_8 yards blue ribbon and 2 1_8 yards yellow ribbon for a craft project. How much more blue ribbon than yellow ribbon did Tierra buy? __ yards 22 8 Lesson 58 © Houghton Mifflin Harcourt Publishing Company 9. Name 1 Subtraction with Renaming LESSON 59 CC.4.NF.3c OBJECTIVE Rename mixed numbers to subtract. Fraction strips can help you subtract mixed numbers or subtract a mixed number from a whole number. 2 __ - 2__ Find the difference. 31 3 3 Step 1 Model the number you are subtracting from, 3 1_3 . Step 2 Because you cannot subtract 2_3 from 1_3 without renaming, change one of the 1 strips to three 1_3 strips. Then subtract by crossing out two wholes and two 1_3 strips. 1So, 3__ 3 2 = __ 2. 2__ 3 3 __ Find the difference. 2 - 11 4 Step 1 Model the number you are subtracting from, 2. © Houghton Mifflin Harcourt Publishing Company Step 2 Because you cannot subtract 1_4 from 1 without renaming, change one of the 1 strips to four 1_4 strips. Then subtract by crossing out one whole and one 1_4 strip. 1 = __ 3. So, 2 - 1__ 4 4 Find the difference. 3 __ 2 5 __ 1. 3 - 2 = 5 1 - 1__ 3= 2. 2__ 4 4 3. 2 __ 4 __ 33 5 4 - 2__ 5 4 __ 5 Number and Operations–Fractions 4. 1 3___ 12 ___ -211 12 2 ___ 12 5. __ 45 8 7 __ -2 8 6 1__ 8 117 Name 1 Subtraction with Renaming CC.4.NF.3c Find the difference. __ 51 3 2 -3 __ 3 _ → 44__3 → 3_2__3 2. 9. 13. __ 71 6 5 - 2__ 6 _ 2 4 __ 6 1 3 __ 4 3 -1 __ 4 _ 2 1__ 4 3. __ -3 2 5 __ 23 5 __ 12 3 3 5. 12 ___ 10 7 -7 ___ 10 __ 6 4___ 10 6 __ 51 4 3 -2 __ 4 _ 2 2__ 4 __ 73 5 4 -4 __ 5 _ __ 24 5 4. 3 9 __ 8 7 -8 __ 8 _ 4 __ 8 8. 1 10 __ 2 1 -8 __ 2 __ 2 6. 1 8 __ 6 __ -3 5 6 _ __ 42 6 7. 10. 3 9 ___ 12 7 -4 ___ 12 __ 8 4___ 12 11. 1 9 ___ 10 7 -8 ___ 10 __ 4 ___ 10 12. 14. 5 4 __ 8 7 -1 __ 8 _ __ 26 8 15. 1 5 ___ 12 8 -3 ___ 12 __ 5 1___ 12 16. __ 91 3 2 __ 3 _ 2 8__ 3 7 3 -1 __ 5 2 5__ 5 Problem Solving 17. Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 1_8 pounds for a small fish bowl. How much is left? __ pounds 37 8 118 18. Xavier made 25 pounds of roasted almonds for a fair. He has 3 1_2 pounds left at the end of the fair. How many pounds of roasted almonds did he sell at the fair? __ pounds 211 2 Lesson 59 © Houghton Mifflin Harcourt Publishing Company 1. Name LESSON 60 1 Algebra • Fractions and Properties of Addition CC.4.NF.3c OBJECTIVE Use the properties of addition to add fractions. Properties of addition can help you group and order addends so you can use mental math to find sums. The Commutative Property of Addition states that when the order of two addends is changed, the sum is the same. 6+ 3= 3+ 6 The Associative Property of Addition states that when the grouping of addends is changed, the sum is the same. (3 + 6) + 4 = 3 + (6 + 4) 3 + 4__ 7 + 6__ 5. Use the properties and mental math to add 10__ 8 8 8 3 + 4__ 7 + 6__ 5 Step 1 Look for fractions that combine to make 1. 10__ 8 8 8 © Houghton Mifflin Harcourt Publishing Company Step 2 Use the Commutative Property to order the addends so that the fractions 3 + 4__ 5 + 4__ 7 7 + 6__ 5 = 10__ 3 + 6__ with a sum of 1 are together. 10__ 8 8 8 8 8 8 7 5) + 4__ __ + 6__ Step 3 Use the Associative Property to group = (103 8 8 8 the addends that you can add mentally. Step 4 Add the grouped numbers and then add the other mixed number. 7 = (17) + 4__ 8 Step 5 Write the sum. __ = 217 8 Use the properties and mental math to find the sum. ( ) 1 + 1 __ 4 2 + 4 __ 1. 3 __ 5 5 5 ( ) 7 + 1 ___ 3 4 + 6 ___ 2. 5 ___ 10 10 10 __ 92 5 ( ) 5 + 3 ___ 7 11 + 1 ___ 4. 2 ___ 12 12 12 11 7 ___ 12 Number and Operations–Fractions ( 4 13 ___ 10 ( 16 ) 7 + 63 1 __ + __ 5. 4 __ 8 8 8 3 11 __ 8 ) 1 __ + 5 + 3 __ 3. 7 3 4 4 ( ) 2 + 41 4 __ + 7 __ 6. 9 __ 6 6 6 __ 21 1 6 119 Name 1 Fractions and Properties of Addition CC.4.NF.3c Use the properties and mental math to find the sum. ( ) 1 __ + 22 __ + 1__ 1. 51 3 3 3 __ + (4) 51 3 ( ( ) 1 __ + 4 2 __ + 5__ 4. 6 3 4 4 4 ( 2 17__ 5 ) ( 2 4 + 9 __ __ + 10 __ 5. 6 3 6 6 6 __ 162 4 ) ( __ 112 5 ) 1 + 20___ 2 + 15 ___ 7 8. 14___ 10 10 10 1 12__ 8 ) 1 4 + 3 __ __ + 1__ 6. 62 5 5 5 __ 263 6 7 + 31 1 __ + 1__ 7. 7__ 8 8 8 ) 4 __ + 3 2 __ + 5 __ 3. 8 1 5 5 5 __ 165 8 1 9__ 3 ( ( ) 5 + 27 __ + 3 __ __ 2. 101 8 8 8 ( ) 2 + 8___ 5 7 + 9___ 9. 13___ 12 12 12 2 31___ 12 50 10. Nate’s classroom has three tables of different lengths. One has a length of 4 1_2 feet, another has a length of 4 feet, and a third has a length of 2 1_2 feet. What is the length of all three tables when pushed end to end? 11 feet 120 11. Mr. Warren uses 2 1_4 bags of mulch for his garden and another 4 1_4 bags for his front yard. He also uses 3_4 bag around a fountain. How many total bags of mulch does Mr. Warren use? 1 bags 7__ 4 Lesson 60 © Houghton Mifflin Harcourt Publishing Company Problem Solving Name 1 Add Fractions Using Models LESSON 61 CC.4.NF.3d OBJECTIVE Use models to represent and find sums involving fractions. Fractions with like denominators have the same denominator. You can add fractions with like denominators using a number line. 4 + __ 1. Model __ 6 6 Step 1 Draw a number line labeled with sixths. Model the fraction 4_6 by starting at 0 and shading 4 sixths. ' Step 2 Add the fraction 1_6 by shading 1 more sixth. ' ( ' - ( - * - + - , - - ( ' - Step 3 How many sixths are there in all? 5 sixths ) - ( - ) - * - + - , - - Write the number of sixths as a fraction. 5 5 sixths = __ 6 4 + __ 1 = __ 5 __ 6 6 1 + __ 4. 1. Model __ 5 5 5 __ 5 1 + __ 4= __ © Houghton Mifflin Harcourt Publishing Company 5 5 6 ' ' , ( ( , ) , * , + , , , Find the sum. Use a model to help. 2 + ___ 4 2. ___ 10 10 ' 6 ___ 10 1 __ + __ 3. 1 4 4 ( ' ( ) * + , - . / 0 (' (' (' (' (' (' (' (' (' (' (' (' ' 2 __ 4 Number and Operations–Fractions ' + ( ( + ) + * + + + 121 Name 1 Add Fractions Using Models CC.4.NF.3d Find the sum. Use fraction strips to help. 2 + __ 1= 1. __ 6 6 ) - 3 __ 6 4 + ___ 5 = 2. ___ 10 10 3 __ 3 2 + __ 1= 4. __ 4 4 3 __ 4 9 ___ 10 ( - 1 + __ 2= 3. __ 3 3 2 + ___ 4 = 5. ___ 12 12 6 ___ 12 1 + __ 2= 6. __ 6 6 3 __ 6 3 + ___ 9 = 7. ___ 12 12 12 ___ 12 4= __ + __ 8. 3 8 8 7 __ 1 + __ 2= 10. __ 5 5 3 __ 3 + __ 1= 9. __ 4 4 4 __ 4 8 5 4 11. Lola walks __ 10 mile to her friend’s 5 house. Then she walks __ 10 mile to the store. How far does she walk in all? 9 mile ___ 10 13. Jacqueline buys 2_4 yard of green ribbon and 1_4 yard of pink ribbon. How many yards of ribbon does she buy in all? 3 __ yard 4 122 12. Evan eats 1_8 of a pan of lasagna and his brother eats 2_8 of it. What fraction of the pan of lasagna do they eat in all? 3 __ of the pan 8 14. Shu mixes 32_ pound of peanuts with 1_3 pound of almonds. How many pounds of nuts does Shu mix in all? 3 pound __ 3 Lesson 61 © Houghton Mifflin Harcourt Publishing Company Problem Solving Name 1 Subtract Fractions Using Models LESSON 62 CC.4.NF.3d OBJECTIVE Use models to represent and find differences involving fractions. You can subtract fractions with like denominators using fraction strips. 5 - __ 2. Model __ 8 8 Step 1 Shade the eighths you start with. Shade 5 eighths. 2. Step 2 Subtract __ 8 Think: How many eighths are taken away? Cross out 2 of the shaded eighths. Step 3 Count the shaded eighths that remain. There are 3 eighths remaining. Step 4 Write the number of eighths that remain as a fraction. 3 3 eighths = __ 8 5 - __ 2 = __ 3 __ 8 8 8 3 - __ 2. 1. Model __ 3 3 © Houghton Mifflin Harcourt Publishing Company 3 - __ 2= __ 3 3 1 __ 3 Subtract. Use fraction strips to help. 5 - __ 1 2. __ 6 6 5 1= __ - __ 6 6 6 - ___ 3 3. ___ 10 10 4 __ 6 Number and Operations–Fractions 6 - ___ 3 = ___ 10 10 3 ___ 10 123 Name 1 Subtract Fractions Using Models Subtract. Use fraction strips to help. __ 1= 3 __ - __ 1. 4 5 5 5 CC.4.NF.3d 2 __ 4 3 - __ 1= 2. __ 4 4 ) + 1= __ - __ 3. 5 6 6 4 __ 6 1= __ - __ 4. 7 8 8 2= 5. 1 - __ 3 1 __ 3 8 - ___ 2 = 6. ___ 10 10 3 - __ 1= 7. __ 4 4 2 __ 4 7 - __ 5= 8. __ 6 6 6 __ 8 6 ___ 10 2 __ 6 Problem Solving 9. Ena is making trail mix. She buys the items shown in the table. How many more pounds of pretzels than raisins does she buy? Item Pretzels Peanuts Raisins 5 pound __ 8 10. How many more pounds of granola than banana chips does she buy? Banana Chips Granola Weight (in pounds) 7 _ © Houghton Mifflin Harcourt Publishing Company Use the table for 9 and 10. 8 4_ 8 2_ 8 3_ 8 5_ 8 2 __ pound 8 124 Lesson 62 Name LESSON 63 1 Add and Subtract Fractions CC.4.NF.3d OBJECTIVE Solve word problems involving addition and subtraction with fractions. You can find and record the sums and the differences of fractions. 2 + __ 4 Add. __ 6 6 Step 1 Model it. Step 2 Think: How many sixths are there in all? There are 6 sixths. 6 6 sixths = __ 6 Step 3 Record it. Write the sum as an addition equation. 2 + __ 4 = __ 6 __ 6 6 6 6 - ___ 2 Subtract. ___ 10 10 Step 1 Model it. Step 2 Think: There are 6 tenths. I take away 2 tenths. How many tenths are left? There are 4 tenths left. 4 4 tenths = ___ 10 Step 3 Record it. Write the difference as a subtraction equation. 6 - ___ 2 = ___ 4 ___ 10 10 10 © Houghton Mifflin Harcourt Publishing Company Find the sum or difference. 1. 7 eighth-size parts - 4 eighth-size parts = 7 - __ 4= __ 8 8 3 __ 8 7 ___ 11 - ___ 4 = 2. ___ 12 12 2 + __ 2= 5. __ 4 4 3 eighth-size parts 12 4 __ 4 Number and Operations–Fractions 4 ___ 2 + ___ 2 = 3. ___ 10 10 4 - __ 3= 6. __ 5 5 10 1 __ 5 6 - __ 4= 4. __ 8 8 2 __ 1 + __ 2= 7. __ 3 3 3 __ 8 3 125 Name 1 Add and Subtract Fractions CC.4.NF.3d Find the sum or difference. ___ 4 + ___ 8 = 12 1= __ - __ 1. ___ 2. 3 12 12 12 6 6 + () / () 2 __ 6 4 - __ 3= 3. __ 5 5 1 __ 5 3 __ ) - 6 + ___ 3 = 4. ___ 10 10 9 ___ 3= 5. 1 - __ 8 5 __ 8 2= __ + __ 6. 1 4 4 9 - ___ 5 = 7. ___ 12 12 4 ___ 5 - __ 2= 8. __ 6 6 3 __ 6 2 + __ 1 = 9. __ 3 3 10 12 4 3 __ 3 Problem Solving 10. Guy finds how far his house is from several locations and makes the table shown. How much farther away from Guy’s house is the library than the cafe? Distance from Guy’s House Location Library School Store 5 mile ___ 10 Cafe Yogurt Shop 11. If Guy walks from his house to school and back, how far does he walk? Distance (in miles) 9 __ 10 5 __ 10 7 __ 10 4 __ 10 6 __ 10 © Houghton Mifflin Harcourt Publishing Company Use the table for 10 and 11. 10 mile ___ 10 126 Lesson 63 Name 1 Problem Solving • Multistep Fraction Problems LESSON 64 CC.4.NF.3d OBJECTIVE Use the strategy act it out to solve multistep fraction problems. 3 _ 5 Jeff runs mile each day. He wants to know how many days he has to run before he has run a whole number of miles. Read the Problem What do I need to find? I need to find how many days Jeff needs to run 3_5 mile until he has run a whole number of miles. What information do I need to use? 3 __ Jeff runs 5 mile a day. He wants the distance run to be a whole number . How will I use the information? © Houghton Mifflin Harcourt Publishing Company I can use a number line and act out patterns to the problem. Solve the Problem Describe how to act it out. Use a number line. ' ,( ), ,* __ mile Day 1: 3 5 __ mile Day 2: 6 5 Number and Operations–Fractions (* (+ * (( -, ., /, 0, ) ((, () , , , , 3 __ 5 + 3 __ 5 = 6 __ 5 __ mile more 1 whole mile and 1 5 3 9 3 3 __ __ __ __ 9 __ 5 5 5 + + = 5 Day 3: mile 5 __ mile more 1 whole mile and 4 5 3 3 3 3 12 __ __ __ __ ___ 12 ___ 5 5 5 5 + + + = 5 Day 4: mile 5 __ mile more 2 whole miles and 2 5 3 3 3 3 15 3 __ __ __ __ __ ___ 15 ___ 5 5 5 5 5 + + + + = 5 Day 5: mile 5 3 whole miles So, Jeff will run a total of 3 miles in 5 days. 1. Lena runs 2_3 mile each day. She wants to know how many days she has to run before she has run a whole number of miles. 3 days + , 2. Mack is repackaging 6_8 -pound bags of birdseed into 1-pound bags of birdseed. What is the least number of 6_8 -pound bags of birdseed he needs in order to fill 1-pound bags without leftovers? 6 -pound bags four __ 8 127 Name 1 Problem Solving • Multistep Fraction Problems CC.4.NF.3d Read each problem and solve. 1. Each child in the Smith family was given an orange cut into 8 equal sections. Each child ate 5_8 of the orange. After combining the leftover sections, Mrs. Smith noted that there were exactly 3 full oranges left. How many children are in the Smith family? 1 8 1 8 3 8 1 8 1 8 + 1 8 3 8 1 8 1 8 1 8 + 1 8 3 8 1 8 + 1 8 3 8 1 8 1 8 + 1 8 3 8 1 8 1 8 + 1 8 3 8 1 8 1 8 + 1 8 3 8 1 8 1 8 + 1 8 3 8 1 8 = 3 There are 8 addends, so there are 8 children in the Smith family. 8 children 2. Val walks 2 3_5 miles each day. Bill runs 10 miles once every 4 days. In 4 days, who covers the greater distance? Val © Houghton Mifflin Harcourt Publishing Company 3. Chad buys peanuts in 2-pound bags. He repackages them into bags that hold 65_ pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that he can fill the 5_6 -pound bags without having any peanuts left over? five 2-pound bags 4. A carpenter has several boards of equal length. He cuts 3 _ of each board. After cutting the boards, the carpenter 5 notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with? 10 boards 128 Lesson 64 Name LESSON 65 1 Multiples of Unit Fractions CC.4.NF.4a OBJECTIVE Write a fraction as a product of a whole number and a unit fraction. A unit fraction is a fraction with a numerator of 1. You can write a fraction as the product of a whole number and a unit fraction. 7 Write __ 10 as the product of a whole number and a unit fraction. 7 Write __ 10 as the sum of unit fractions. 1 1 1 1 ___ ___ ___ 7 = ___ ___ + 10 + 10 + 10 10 10 1 ___ + + 10 1 ___ 1 ___ + 10 10 Use multiplication to show repeated addition. 7 = 1 ___ × ___ 7 10 10 1 ___ 7 = × 10 So, ___ 7 10 . The product of a number and a counting number is a multiple of the number. You can find multiples of unit fractions. 1. List the next 4 multiples of __ 8 Make a table and use repeated addition. 1 1 × __ 8 1 2 × __ 8 __ 3× 1 8 1 __ 1 + __ 1 __ 1 + __ 1 + __ 1 __ 1 __ 8 2 __ © Houghton Mifflin Harcourt Publishing Company 8 8 8 8 8 1 are The next 4 multiples of __ 8 8 3 __ 8 2 __ 8 8 , 1 4 × __ 8 1 5 × __ 8 1 + __ 1 + __ 1 + __ 1 __ 8 8 8 8 4 __ 8 1 + __ 1 + __ 1 + __ 1 + __ 1 __ 3 __ 8 , 4 __ 8 8 8 5 __ 8 , and 8 5 __ 8 8 8 . Write the fraction as the product of a whole number and a unit fraction. 1 1 1 5 = 2 × __ __ = __ = 5 × ___ 7 × __ 1. 2 2. ___ 3. 7 5 12 2 5 12 2 List the next four multiples of the unit fraction. 3 4 5 2 __ __ __ __ __, __, 4. 1 5. 1 4 4 4 4 4 6 , , , Number and Operations–Fractions 2 __ 6 , 3 __ 6 , 4 __ 6 , 5 __ 6 129 Name 1 Multiples of Unit Fractions CC.4.NF.4a Write the fraction as a product of a whole number and a unit fraction. 1 1 __ 7 = 7 × __ 5× 1 __ = __ = 5 × __ 1. 5 2. __ 3. 5 6 8 3 6 8 3 4= 7. __ 6 1 9 × ___ 10 1 4 × __ 6 3= 5. __ 4 8 = 8. ___ 20 1 3 × __ 4 11 = 6. ___ 12 1 8 × ___ 20 List the next four multiples of the unit fraction. 2 3 4 5 __ __ __ __ 1, __, 10. 1 11. __ 5 5 5 5 8 , , , 5 13 = 9. ____ 100 2 __ 8 , 3 __ 8 , 1 11 × ___ 12 1 13 × ____ 100 4 __ 8 , 5 __ 8 Problem Solving 12. So far, Monica has read 5_6 of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day? 1 of the book __ 6 130 13. Nicholas buys 3_8 pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich? 1 pound __ 8 Lesson 65 © Houghton Mifflin Harcourt Publishing Company 9 = 4. ___ 10 Name LESSON 66 1 Multiples of Fractions CC.4.NF.4b OBJECTIVE Write a product of a whole number and a fraction as a product of a whole number and a unit fraction. You have learned to write multiples of unit fractions. You can also write multiples of other fractions. 2. Write the next 4 multiples of __ 5 Make a table. 2 1 × __ 5 2 2 × __ 5 __ 3× 2 5 2 4 × __ 5 2 5 × __ 5 2 __ 2 2 __ + __ 5 5 4 __ 5 2 + __ 2 2 + __ __ 2 2 2+ 2 __ + __ __ + __ 5 5 5 5 8 __ 5 2 + __ 2 + __ 2 + __ 2 2 + __ __ 5 2 __ 5 5 5 6 __ 5 5 4 __ 2 are So, the next 4 multiples of __ 6 __ 5 5 8 __ 5 5 10 ___ 5 5 10 ___ 5 . , , , and 5 2 as the product of a whole number and a unit fraction. Write 3 × __ 5 2. Use a number line. Make three jumps of __ 5 6 25_ 33_ 5 5 © Houghton Mifflin Harcourt Publishing Company ' ( , ) , 1 23_ 5 5 5 * , + , , , 1 43_ 5 5 , . , 1 63_ 5 / , 0 , 1 83_ 5 1 2 = __ 6, or 6 × __ So, 3 × __ 5. 5 5 List the next four multiples of the fraction. 6 12 15 9 ___ __ ___ 3, __ __, 1. __ 2. 5 4 4 4 4 6 , , , 4 10 ___ 6 , 15 ___ 6 20 ___ 6 , , 25 ___ 6 Write as the product of a whole number and a unit fraction. 3. 4. ' ( ) * + , - . / 0 (' / / / / / / / / / / 3= 3 × __ 8 1 9 × __ 8 Number and Operations–Fractions ' ( * 2= 4 × __ 3 ) * * * + * , * - . / 0 (' * * * * * 1 8 × __ 3 131 Name 1 Multiples of Fractions CC.4.NF.4b List the next four multiples of the fraction. 6 9 12 15 __ ___ ___ __, __ __, 1. 3 2. 2 5 5 5 5 5 6 , , , 4, 3. __ 8 8 __ 8 , 12 ___ 8 16 ___ 8 , 20 ___ , 8 4 __ 6 5, 4. ___ 10 6 __ 6 , 8 __ 6 , 15 ___ 10 , 10 ___ 10 , 10 ___ , 20 ___ 10 , 6 25 ___ 10 Write the product as the product of a whole number and a unit fraction. 5. 6. ' ( , ) , 4= 2 × __ 5 * , + , , , - . / 0 (' , , , , , 1 8 × __ 5 ' ( * 2= 5 × __ 3 ) * * * + * , * - . / 0 (' * * * * * 1 10 × __ 3 7. Jessica is making 2 loaves of banana bread. She needs 3_4 cup of sugar for each loaf. Her measuring cup can only hold 1_4 cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread? 6 132 8. A group of four students is performing an experiment with salt. Each student must add 3_8 teaspoon of salt to a solution. The group only has a 1_8 -teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment? 12 Lesson 66 © Houghton Mifflin Harcourt Publishing Company Problem Solving Name LESSON 67 1 Multiply a Fraction by a Whole Number Using Models CC.4.NF.4b OBJECTIVE Use a model to multiply a fraction by a whole number. You can use a model to multiply a fraction by a whole number. 3. Find the product of 4 × __ 5 __ each. Use fraction strips. Show 4 groups of 3 5 1 1 1 1 1 3 __ = __ 1 group of 3 5 5 5 5 5 5 5 1 5 1 5 1 5 1 5 1 5 6 __ = __ 2 groups of 3 5 5 1 5 1 5 1 5 1 5 1 5 9 __ = __ 3 groups of 3 5 5 1 5 1 5 1 5 1 5 1 5 12 __ = ___ 4 groups of 3 5 5 3 = ___ 12. So, 4 × __ 5 5 Multiply. 2. © Houghton Mifflin Harcourt Publishing Company 1. 5= 2 × __ 6 10 ___ 6 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 7= 3 × __ 8 2= 3. 6 × __ 3 12 ___ 3 9 = 4. 2 × ___ 10 5= 6. 4 × __ 8 20 ___ 8 2= 7. 7 × __ 5 Number and Operations–Fractions 18 ___ 10 14 ___ 5 21 ___ 8 3= 5. 5 × __ 4 15 ___ 4 4= 8. 8 × __ 6 32 ___ 6 133 Name 1 Multiply a Fraction by a Whole Number Using Models CC.4.NF.4b Multiply. 5= 1. 2 × __ 6 10 ___ 6 2= 2. 3 × __ 5 6 __ 3 = 3. 7 × ___ 10 21 ___ 5 = 4. 3 × ___ 12 15 ___ 3= 5. 6 × __ 4 18 ___ 2= 6. 4 × __ 8 8 __ 8 7= 8. 2 × __ 8 14 ___ 4= 9. 6 × __ 5 24 ___ 5 10 ___ 3 4 8 10 Problem Solving 10. Matthew walks 5_8 mile to the bus stop each morning. How far will he walk in 5 days? 25 ___ miles 8 134 11. Emily uses 2_3 cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins? 6 cups __ 3 Lesson 67 © Houghton Mifflin Harcourt Publishing Company 2= 7. 5 × __ 3 12 5 Name LESSON 68 1 Multiply a Fraction or Mixed Number by a Whole Number CC.4.NF.4c OBJECTIVE Multiply a fraction by a whole number to solve a problem. To multiply a fraction by a whole number, multiply the numerators. Then multiply the denominators. A recipe for one loaf of bread calls for 2 1_4 cups of flour. How many cups of flour will you need for 2 loaves of bread? Step 1 Write and solve an equation. 1 as a fraction. __. Write 2__ Write 2 as 2 1 4 2 × __ 9 2 × 2 1_4 = __ 1 4 × 9 = 2______ 1× 4 Multiply the numerators. Then multiply the denominators. ___ = 18 4 Simplify. } } } } Step 2 Write the product as a mixed number. 18 1 + __ 1 + __ 1+1 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 1 + __ 1 + __ ___ = __ __ + __ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 = © Houghton Mifflin Harcourt Publishing Company = 4 + __ 42 4 , or + 1 __ 4 + __ 41 2 __ 41 2 So, you will need 1 __ 4 1 + 1 6 2___ 10 Number and Operations–Fractions 1 1 1 + __ + __ 4 4 Combine the wholes. Then combine the remaining parts. Add. Write the sum as a mixed number. cups of flour. Multiply. Write the product as a mixed number. __ __ 2= 3= 11 14 1. 3 × __ 2. 4 × __ 5 8 5 8 3 = 4. 2 × 1___ 10 + 2= 5. 4 × 1__ 3 __ 62 3 1= 3. 5 × __ 3 1= 6. 7 × 1__ 6 2 1__ 3 1 8__ 6 135 Name 1 Multiply a Fraction or Mixed Number by a Whole Number CC.4.NF.4c 3= 3. 5 × __ 4 __ 33 4 1= 4. 4 × 1__ 5 4 4__ 5 1= 5. 2 × 2__ 3 __ 42 3 1= 6. 5 × 1__ 6 __ 55 6 7= 7. 2 × 2__ 8 __ 56 8 3= 8. 7 × 1__ 4 __ 121 4 3= 9. 8 × 1__ 5 __ 124 5 Problem Solving 10. Brielle exercises for 3_4 hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days? 2 hours 4__ 4 136 11. A recipe for quinoa calls for 2 2_3 cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need? 2 cups 10__ 3 Lesson 68 © Houghton Mifflin Harcourt Publishing Company Multiply. Write the product as a mixed number. 5 4 3 = 1___ 3 = 1__ 1. 5 × ___ 2. 3 × __ 10 5 10 5 Name LESSON 69 1 Problem Solving • Comparison Problems with Fractions CC.4.NF.4c OBJECTIVE Use the strategy draw a diagram to solve comparison problems with fractions. The Great Salt Lake in Utah is about 4_5 mile above sea level. Lake Titicaca in South America is about 3 times as high above sea level as the Great Salt Lake. About how high above sea level is Lake Titicaca? Read the Problem Solve the Problem What do I need to find? I need to find about how high above sea level Lake Titicaca is. Great Salt Lake is about sea level. times as high above How will I use the information? © Houghton Mifflin Harcourt Publishing Company I can draw a diagram to compare the heights. 2 2__ So, Lake Titicaca is about 5 4 __ 5 4 __ 5 4 __ 5 t Write an equation and solve. t is the height above sea level of Lake Titicaca, in miles. 4 __ 5 3 t= × Write an equation. 12 ___ 5 t= Multiply. 2 2__ 5 t= Write the fraction as a mixed number. miles above sea level. 1. Amelia is training for a triathlon. She swims 3_5 mile. Then she runs about 6 times farther than she swims. About how far does Amelia run? __ miles 33 5 Number and Operations–Fractions Lake Titicaca 4 __ 5 } What information do I need to use? 4 __ The Great Salt Lake is about 5 mile above sea level. Lake Titicaca 3 Draw a comparison model. Compare the heights above sea level of the Great Salt Lake and Lake Titicaca, in miles. 2. Last week, Meg bought 1 3_4 pounds of fruit at the market. This week, she buys 4 times as many pounds of fruit as last week. In pounds, how much fruit does Meg buy this week? 7 pounds 137 Name 1 Problem Solving • Comparison Problems with Fractions CC.4.NF.4c Read each problem and solve. 1. A shrub is 1 2_3 feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree? t is the height of the tree, in feet. 2 t = 3 × 1__ 3 __ t=3×5 3 15 ___ t= 3 t=5 shrub tree So, the tree is 5 feet tall. __ 12 3 __ 12 3 __ 12 3 __ 12 3 5 feet 2. You run 1 3_4 miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day? 7 miles © Houghton Mifflin Harcourt Publishing Company 3. At the grocery store, Ayla buys 1 1_3 pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy? 2 pounds 2__ 3 4. When Nathan’s mother drives him to school, it takes 51_ hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school? 4 __ hour 5 138 Lesson 69 Name LESSON 70 1 Equivalent Fractions and Decimals CC.4.NF.5 OBJECTIVE Record tenths and hundredths as fractions and decimals. 20 Lori ran ___ mile. How many tenths of a mile did she run? 100 20 Write ___ as an equivalent fraction with a denominator of 10. 100 Step 1 Think: 10 is a common factor of the numerator and the denominator. Step 2 Divide the numerator and denominator by 10. 20 = __________ 20 ÷ 10 = ___ 2 ____ 100 100 ÷ 10 10 2 mile. So, Lori ran __ 10 Use a place-value chart. 20 Step 1 Write ___ as an equivalent decimal. 100 Ones 0 · Tenths · 2 Hundredths 0 Step 2 Think: 20 hundredths is Ones 0 2 tenths 0 hundredths · Tenths · 2 So, Lori ran 0.2 mile. © Houghton Mifflin Harcourt Publishing Company Write the number as hundredths in fraction form and decimal form. 9 1. ___ 10 4 3. ___ 10 2. 0.6 60 ; 0.60 ____ 90 ; 0.90 ____ 100 40 ; 0.40 ____ 100 100 Write the number as tenths in fraction form and decimal form. 70 4. ____ 100 80 5. ____ 100 7 ; 0.7 ___ 10 Number and Operations–Fractions 6. 0.50 8 0.8 ___ 10; 5 ; 0.5 ___ 10 139 Name 1 Equivalent Fractions and Decimals CC.4.NF.5 Write the number as hundredths in fraction form and decimal form. 5 1. ___ 10 5 = _______ 50 5 × 10 = ____ ___ 10 10 × 10 100 Think: 5 tenths is the same as 5 tenths and 0 hundredths. Write 0.50. 50 ; 0.50 ____ 100 9 2. ___ 10 3. 0.2 90 ; 0.90 ____ 4. 0.8 20 ; 0.20 ____ 100 80 ; 0.80 ____ 100 100 Write the number as tenths in fraction form and decimal form. 10 6. ____ 100 4 ; 0.4 ___ 10 7. 0.60 1 ; 0.1 ___ 6 ; 0.6 ___ 10 10 Problem Solving 6 8. Billy walks __ mile to school 10 6 each day. Write __ as hundredths in 10 fraction form and in decimal form. 60 ; 0.60 ____ 100 140 9. Four states have names that begin with the letter A. This represents 0.08 of all the states. Write 0.08 as a fraction. 8 ____ 100 Lesson 70 © Houghton Mifflin Harcourt Publishing Company 40 5. ____ 100 Name Add Fractional Parts of 10 and 100 LESSON 71 OBJECTIVE Add fractions when the denominators are 10 or 100. 1 CC.4.NF.5 35 Sam uses 100 glass beads for a project. Of the beads, ___ are gold 100 4 __ and 10 are silver. What fraction of the glass beads are gold or silver? 35 and ___ 4. Add ____ 100 10 Step 1 Decide on a common denominator. Use 100 . 4 as an equivalent fraction with a denominator of 100. Step 2 Write __ 10 4 = ________ 4 × 10 = ____ 40 ___ 10 10 × 10 100 35 40 ___ Step 3 Add ___ 100 and 100 . 35 + ____ 40 = ____ 75 ____ 100 100 100 Add the numerators. Use 100 as the denominator. 75 ____ So, 100 of the glass beads are gold or silver. Add $0.26 and $0.59. Step 1 Write each amount as a fraction of a dollar. © Houghton Mifflin Harcourt Publishing Company 26 $0.26 = ___ of a dollar 100 26 59 Step 2 Add ___ and ___ . 100 100 26 + ____ 59 = ____ 85 ____ 100 100 100 59 $0.59 = ___ of a dollar 100 Add the numerators. 100 is the common denominator. Step 3 Write the sum as a decimal. 85 = 0.85 ____ 100 So, $0.26 + $0.59 = $0.85 . Find the sum. 95 75 + ___ 2 = ____ 1. ____ 100 10 100 Number and Operations–Fractions 2. $0.73 + $0.25 = $ 0.98 . 98 73 + ____ 25 = ____ ____ 100 100 100 141 Name 1 Add Fractional Parts of 10 and 100 CC.4.NF.5 Find the sum. 2 + ____ 43 1. ___ 10 100 2 Think: Write __ as a fraction with 10 a denominator of 100: 2 × 10 = ____ 20 _______ 20 43 63 ___ + ___ = ___ 100 100 100 10 × 10 100 63 ____ 100 17 + ___ 6 2. ____ 100 10 9 + ___ 4 3. ____ 100 10 7 + ____ 23 4. ___ 10 100 49 ____ 77 ____ 100 93 ____ 100 100 5. $0.48 + $0.30 6. $0.25 + $0.34 7. $0.66 + $0.06 $0.78 $0.59 $0.72 38 8. Ned’s frog jumped ___ meter. Then 100 4 __ his frog jumped 10 meter. How far did Ned’s frog jump in all? 78 meter ____ 100 142 5 9. Keiko walks __ kilometer from 10 school to the park. Then she 19 kilometer from the park walks ___ 100 to her home. How far does Keiko walk in all? 69 kilometer ____ 100 Lesson 71 © Houghton Mifflin Harcourt Publishing Company Problem Solving Name 1 Relate Tenths and Decimals LESSON 72 CC.4.NF.6 OBJECTIVE Record tenths as fractions and as decimals. Write the fraction and the decimal that are shown by the point on the number line. 0 10 5 10 10 10 0.0 0.5 1.0 Step 1 Count the number of equal parts of the whole shown on the number line. There are ten equal parts. This tells you that the number line shows tenths. Step 2 Label the number line with the missing fractions. What fraction is shown by the point on the number line? 0 10 1 10 2 10 3 10 4 10 0.0 5 10 6 10 7 10 8 10 9 10 0.5 10 10 1.0 The fraction shown by the point on 8 the number line is __ . 10 Step 3 Label the number line with the missing decimals. What decimal is shown by the point on the number line? 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 © Houghton Mifflin Harcourt Publishing Company 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 The decimal shown by the point on the number line is 0.8. So, the fraction and decimal shown by the point on the number line 8 and 0.8. are __ 10 Write the fraction or mixed number and the decimal shown by the model. 1. 0 10 5 10 10 10 0.0 0.5 1.0 2 ; 0.2 ___ 10 Number and Operations–Fractions 2. 0 2 10 5 2 10 2 10 10 2.0 2.5 3.0 6 ; 2.6 2 ___ 10 143 Name 1 Relate Tenths and Decimals CC.4.NF.6 Write the fraction or mixed number and the decimal shown by the model. 1. 2. Think: The model is divided into 10 equal parts. Each part represents one tenth. 6 ; 0.6 ___ 2 ; 1.2 1___ 10 10 3. 2 0 10 5 2 10 2.0 2.5 4. 0 4 10 4.0 3 ; 2.3 2___ 10 5 4 10 4 10 10 4.5 5.0 8 ; 4.8 4___ 10 Write the fraction or mixed number as a decimal. 1 6. 3___ 10 0.4 7 7. ___ 10 3.1 0.7 5 8. 6___ 10 9 9. ___ 10 6.5 0.9 Problem Solving 10. There are 10 sports balls in the equipment closet. Three are kickballs. Write the portion of the balls that are kickballs as a fraction, as a decimal, and in word form. 3 ; 0.3; three tenths ___ 10 144 11. Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat? Write your answer as a decimal. 1.4 pizzas Lesson 72 © Houghton Mifflin Harcourt Publishing Company 4 5. ___ 10 Name LESSON 73 1 Relate Hundredths and Decimals CC.4.NF.6 OBJECTIVE Record hundredths as fractions and as decimals. Write the fraction or mixed number and the decimal shown by the model. Step 1 Count the number of shaded squares in the model and the total number of squares in the whole model. Number of shaded squares: 53 Step 2 Write a fraction to represent the part of the model that is shaded. 53 Number of shaded squares = ____ ______________________ Total number of squares 100 © Houghton Mifflin Harcourt Publishing Company Step 3 Write the fraction in decimal form. Total number of squares: 100 53 . The fraction shown by the model is ____ 100 53 . Think: The fraction shown by the model is ____ 100 53 . 0.53 names the same amount as ____ 100 The decimal shown by the model is 0.53. 53 and 0.53. The fraction and decimal shown by the model are ____ 100 Write the fraction or mixed number and the decimal shown by the model. 1. 2. 24 ; 0.24 ____ 100 Number and Operations–Fractions 96 ; 0.96 ____ 100 145 Name 1 Relate Hundredths and Decimals CC.4.NF.6 Write the fraction or mixed number and the decimal shown by the model. 1. Think: The whole is divided into one hundred equal parts, so each part is one hundredth. 77 ; ____ 100 2. 0 100 10 100 20 100 30 100 40 100 50 100 60 100 0 0.10 0.20 0.30 0.40 0.50 0.60 29 ; 0.29 ____ 0.77 100 3. 4. 20 4 30 4 40 4 50 4 60 4 70 4 80 4 100 100 100 100 100 100 100 4.20 4.30 4.40 4.50 4.60 4.70 4.80 62 ; 4.62 4____ 100 54 ; 1.54 1____ 100 Write the fraction or mixed number as a decimal. 11 6. 8____ 100 0.37 98 7. ____ 100 8.11 0.98 50 8. 25____ 100 6 9. ____ 100 25.50 0.06 Problem Solving 10. There are 100 pennies in a dollar. What fraction of a dollar is 61 pennies? Write it as a fraction, as a decimal, and in word form. 61 ; 0.61; sixty-one hundredths ____ 100 146 11. Kylee has collected 100 souvenir thimbles from different places she has visited with her family. Twenty of the thimbles are carved from wood. Write the fraction of thimbles that are wooden as a decimal. 0.20 Lesson 73 © Houghton Mifflin Harcourt Publishing Company 37 5. ____ 100 Name LESSON 74 Relate Fractions, Decimals, and Money OBJECTIVE Translate among representations of fractions, decimals, and money. 1 CC.4.NF.6 Write the total money amount. Then write the amount as a fraction and as a decimal in terms of a dollar. Step 1 Count the value of coins from greatest to least. Write the total money amount. $ 0.25 $ 0.35 $ 0.40 $ 0.45 $ 0.50 Step 2 Write the total money amount as a fraction of a dollar. The total money amount is $0.50, which is the same as 50 cents. Think: There are 100 cents in a dollar. 50 cents = ____ 50 So, the total amount written as a fraction of a dollar is: __________ 100 cents 100 Step 3 Write the total money amount as a decimal. © Houghton Mifflin Harcourt Publishing Company Think: I can write $0.50 as 0.50. 50 written as a fraction of a dollar, and The total money amount is ____ 100 0.50 written as a decimal. Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of a dollar. 1. 2. 80 ; 0.80 $0.80; ____ 100 Number and Operations–Fractions 45 ; 1.45 $1.45; 1____ 100 147 Name 1 Relate Fractions, Decimals, and Money CC.4.NF.6 Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars. 1. 2. 56 ; 0.56 $0.56; ____ 100 18 ; 0.18 $0.18, ____ 100 Write as a money amount and as a decimal in terms of dollars. 79 4. ____ 100 25 3. ____ 100 $0.25; 0.25 31 5. ____ 100 $0.79; 0.79 8 6. ____ 100 $0.31; 0.31 42 7. ____ 100 $0.08; 0.08 $0.42; 0.42 Write the money amount as a fraction in terms of dollars. 9. $0.03 10. $0.66 11. $0.95 87 ____ 3 ____ 66 ____ 95 ____ 100 100 100 12. $1.00 100 1 ____, or __ 100 1 100 Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars. 13. 2 quarters 2 dimes 14. 3 dimes 4 pennies 70 ; 0.70 $0.70; ____ 100 34 ; 0.34 $0.34; ____ 100 15. 8 nickels 12 pennies 52 ; 0.52 $0.52; ____ 100 Problem Solving 16. Kate has 1 dime, 4 nickels, and 8 pennies. Write Kate’s total amount as a fraction in terms of a dollar. 38 ____ 100 148 75 17. Nolan says he has ___ of a dollar. 100 If he only has 3 coins, what are the coins? three quarters Lesson 74 © Houghton Mifflin Harcourt Publishing Company 8. $0.87 Name LESSON 75 1 Compare Decimals CC.4.NF.7 OBJECTIVE Compare decimals to hundredths by reasoning about their size. Alfie found 0.2 of a dollar and Gemma found 0.23 of a dollar. Which friend found more money? To compare decimals, you can use a number line. Step 1 Locate each decimal on a number line. 0.0 0.10 0.20 0.30 Step 2 The number farther to the right is greater. 0.23 > 0.2, so Gemma found more money. To compare decimals, you can compare equal-size parts. Step 1 Write 0.2 as a decimal in hundredths. 0.2 is 2 tenths, which is equivalent to 20 hundredths. 0.2 = 0.20 Step 2 Compare. 23 hundredths is greater than 20 hundredths. © Houghton Mifflin Harcourt Publishing Company so 0.23 > 0.2. So, Gemma found more money. Compare. Write <, >, or =. 1. 0.17 > 0.13 2. 0.8 > 0.08 3. 0.36 < 0.63 4. 0.4 = 0.40 5. 0.75 > 0.69 6. 0.3 < 0.7 7. 0.45 > 0.37 8. 0.96 > 0.78 Number and Operations–Fractions 149 Name 1 Compare Decimals CC.4.NF.7 Compare. Write <, >, or =. 1. 0.35 < 0.53 2. 0.6 = 0.60 3. 0.24 < 0.31 Think: 3 tenths is less than 5 tenths. So, 0.35 < 0.53 4. 0.94 > 0.9 5. 0.3 < 0.32 6. 0.45 > 0.28 7. 0.39 < 0.93 Use the number line to compare. Write true or false. 0 0.1 8. 0.8 > 0.78 0.2 0.3 0.4 9. 0.4 > 0.84 true false 0.5 0.6 0.7 0.8 10. 0.7 < 0.70 false 0.9 1.0 11. 0.4 > 0.04 true Compare. Write true or false. false 13. 0.24 = 0.42 false 14. 0.17 < 0.32 true 15. 0.85 > 0.82 true Problem Solving 16. Kelly walks 0.7 mile to school. Mary walks 0.49 mile to school. Write an inequality using <, >, or = to compare the distances they walk to school. Possible answer: 0.7 > 0.49 150 17. Tyrone shades two decimal grids. He shades 0.03 of the squares on one grid blue. He shades 0.3 of another grid red. Which grid has the greater part shaded? The grid shaded red Lesson 75 © Houghton Mifflin Harcourt Publishing Company 12. 0.09 > 0.1