Page 1 of 7 Fractions with Different Denominators BEFORE Now WHY? You added and subtracted with common denominators. You’ll add and subtract with different denominators. So you can find how much a plant has grown, as in Ex. 23. In the Real World Word Watch Review Words least common denominator (LCD), p. 239 Activities The circle graph shows how Kate spent her day. What fraction of her day did she spend playing sports? You add or subtract fractions with different denominators by finding the least common denominator (LCD). Adding and Subtracting Fractions 1. Find the LCD of the fractions. 2. Rewrite the fractions using the LCD. 3. Add or subtract the fractions. Simplify if possible. EXAMPLE with Review Need help with rewriting fractions? See p. 239. 1 Adding Fractions 1 12 1 8 Kate spent of her day playing softball and of her day playing soccer. 1 8 1 12 To answer the real-world question above, find the sum . 13 83 12 12 2 3 24 2 24 5 24 Rewrite both fractions using the LCD, 24. Add the fractions. 5 24 ANSWER Kate spent of her day playing sports. Lesson 6.3 Fractions with Different Denominators 277 Page 2 of 7 EXAMPLE with Notetaking In your summary of this chapter, you may want to include examples of adding and subtracting fractions with common and different denominators. 2 Rewriting Sums of Fractions 5 8 3 4 Find the sum . 5 8 3 2 4 2 Your turn now 5 8 6 8 11 3 , or 1 8 8 Add the fractions. Find the sum. Simplify if possible. 1 1 1. 3 9 EXAMPLE 3 4 Rewrite using the LCD, 8. 2 1 2. 3 2 3 7 5 4. 10 6 4 3 3. 5 4 Subtracting Fractions 2 4 Rainfall Last week, 3 inch of rain fell on Monday and 5 inch fell on Tuesday. How much more rain fell on Tuesday than on Monday? Solution 4 5 2 3 You need to find the difference . 4 3 5 3 25 35 12 15 10 15 2 15 Rewrite both fractions using the LCD, 15. Subtract the fractions. 2 15 ANSWER On Tuesday, inch more rain fell than on Monday. Your turn now Find the difference. Simplify if possible. 5 3 5. 6 4 7 1 6. 8 4 1 4 7. 2 9 3 5 8. 10 6 2 3 9. One lap of Speedway A is mile. One lap of Speedway B is mile. 5 4 How much longer is one lap of Speedway B? 278 Chapter 6 Addition and Subtraction of Fractions Page 3 of 7 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 713 Getting Ready to Practice 1. Vocabulary To add two fractions with different denominators, first find the _?_ of the fractions. Find the sum or difference. Simplify if possible. 3 1 2. 8 4 1 8 3. 6 9 9 1 5. 14 7 2 1 4. 3 2 1 6. Guided Problem Solving The monkey bars make up of an obstacle 4 5 1 course. The tires make up of the course. The tunnel makes up of 12 3 the course. How much shorter is the tunnel than the monkey bars and tires combined? 1 How much of the course do the monkey bars and tires make up? 2 How much of the course does the tunnel make up? 3 How much shorter is the tunnel than the other two parts combined? Practice and Problem Solving Find the sum or difference. 2 1 7. 9 3 with Example 1 2 3 Homework Exercises 7–22 7–22 7–24 Online Resources 9 1 8. 10 2 7 1 9. 10 3 5 2 10. 6 5 1 6 11. 2 7 7 2 12. 8 3 5 5 13. 12 6 13 1 14. 14 2 1 3 15. 6 4 3 5 16. 8 6 7 1 17. 10 8 3 1 18. 4 6 1 3 19. 15 5 1 11 20. 4 16 3 2 21. 4 7 6 1 22. 11 2 3 23. Plants Your peppermint plant is inch tall. After one week, it 10 1 is inch tall. How much did the plant grow in one week? 2 24. Find the Error Describe and correct the error in the solution. CLASSZONE.COM • More Examples • eTutorial Plus Lesson 6.3 1 3 1 3 5 35 35 7 2 35 Fractions with Different Denominators 279 Page 4 of 7 1 3 3 4 Algebra Evaluate the expression when x and y . 1 25. x 2 5 26. y 6 11 27. y 12 3 28. x 8 2 29. x 9 1 30. y 18 31. x y 32. y x Geometry Find the perimeter of the triangle. 33. 34. 43 in. 14 in. 35. 52 ft 87 in. 37 yd 25 ft 12 yd 72 yd 13 ft Evaluate the expression. 1 1 1 36. 2 8 4 Geography 7 1 3 38. 10 6 5 1 1 1 37. 4 6 3 Extended Problem Solving In Exercises 39– 41, use the map. The map shows the fraction of the Appalachian Trail that is in each region. Northeastern Central 1 3 1 5 39. Calculate What fraction of the trail is in the central and northeastern regions combined? 40. Explain What fraction of the trail is in the southern region? Explain how you got your answer. Southern ? 15 41. Compare Which two regions N together make up the longer path, the northeastern and central regions or the central and southern regions? ■ Appalachian Trail As of 2002, the length of the Appalachian Trail was set at 2168.8 miles. The Appalachian Trail is about how many times as long as the distance across your town? 42. Writing Write and solve a real-world 2 1 problem in which you would add and . 3 2 3 1 43. Critical Thinking Your friend finds the sum using the common 4 2 denominator 8. Will your friend get the correct answer? Explain. Mental Math Evaluate the expression using mental math. 2 1 3 44. 3 3 7 280 Chapter 6 Addition and Subtraction of Fractions 5 5 4 45. 12 9 9 2 3 46. 1 5 5 Page 5 of 7 Challenge Use the information about musical notes given at the right. Eighth Note 47. What is the combined value of one eighth note, one quarter note, and one half note? Quarter Note 48. What note do you need to add to Half Note the notes in Exercise 47 to equal one whole note? 49. What note do you need to add to Whole Note three eighth notes and two quarter notes to equal one whole note? Mixed Review Find the sum. (Lesson 6.2) 1 3 50. 8 8 3 3 51. 5 5 6 1 52. 7 7 Choose a Strategy Use a strategy from the list to solve the following problem. Explain your choice of strategy. 7 11 53. 12 12 Problem Solving Strategies Guess, Check, and Revise Make a List ■ Work Backward ■ Look for a Pattern ■ ■ 54. Of all the pairs of whole numbers whose sum is 15, find the pair that has the greatest product. Basic Skills Order the numbers from least to greatest. 55. 540, 455, 504, 450, 545 56. 1020, 1211, 1002, 1202, 1200 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 57. Multiple Choice Two boards are nailed together. One board is 3 5 inch thick. The other board is inch thick. What is their 4 6 combined thickness in inches? 7 10 A. inch 4 5 B. inch 7 12 C. 1 inches 3 4 D. 1 inches 2 58. Short Response You put ounce of lemon juice in a measuring 3 7 cup. After you add some water, the cup measures ounce. 8 How much water did you add? Show how you found the answer. Lesson 6.3 Fractions with Different Denominators 281 Page 6 of 7 6.1TO 6. 3 Notebook Review Check Your Definitions Review the vocabulary definitions in your notebook. Copy the review examples in your notebook. Then complete the exercises. mixed number, p. 244 improper fraction, p. 244 round, p. 686 fraction , p. 228 least common denominator (LCD), p. 239 Use Your Vocabulary 1 1. Writing Explain how to round 3 to the nearest whole number. 2 3 1 2. Copy and complete: The LCD of and is _?_. 8 6 6.1 Can you estimate with fractions and mixed numbers? EXAMPLE Estimate the sum or difference. 4 7 1 a. 5 12 ≈ 1 2 5 1 b. 4 6 1 4 ≈ 5 1 1 2 1 4 ✓ Estimate the sum or difference. 9 2 3. 10 9 5 7 4. 12 8 1 5 5. 6 4 5 8 3 1 6. 3 2 4 6 6.2 Can you add and subtract fractions with common denominators? EXAMPLE Find the sum or difference. 3 1 4 a. 10 10 10 11 5 6 b. 12 12 12 2 5 1 2 ✓ Find the sum or difference. 2 4 7. 9 9 282 Chapter 6 3 3 8. 4 4 Addition and Subtraction of Fractions 4 2 9. 5 5 7 11 10. 16 16 Page 7 of 7 6.3 Can you add and subtract fractions with different denominators? EXAMPLE Find the sum or difference. a. 4 22 2 14 72 7 1 1 1 14 14 14 5 14 b. 3 33 5 53 1 15 3 35 9 15 5 15 4 15 ✓ Find the sum or difference. 1 4 11. 10 5 5 1 12. 8 2 3 2 13. 4 7 8 5 14. 9 6 about Lessons 6.1–6.3 15. Estimation Do you get a closer estimate if you round a mixed number to the nearest half or to the nearest whole number? Explain. 16. Critical Thinking When you add or subtract fractions with different denominators, do you have to use the LCD? Explain. Review Quiz 1 Estimate the sum or difference. 9 1 1. 10 6 2 4 2. 11 7 2 11 3. 7 4 15 16 5 7 4. 3 1 8 9 8 3 7. 13 13 2 11 8. 15 15 Find the sum or difference. 7 5 5. 8 8 5 4 9. 18 9 7 1 6. 10 10 2 3 10. 3 4 2 1 11. 11 2 13. Geometry Estimate the perimeter of the figure at the right. 3 3 12. 10 4 35 yd 14 6 yd 5 12 4 yd 3 32 4 yd 1 Lessons 6.1–6.3 Notebook Review 283

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