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Page 1 of 5 Mixed Numbers and Improper Fractions BEFORE Now WHY? You wrote equivalent fractions. You’ll rewrite mixed numbers and improper fractions. So you can compare lengths, such as the pole vault records in Ex. 36. Measuring Inches You can use a ruler to measure lengths to the nearest half, fourth, eighth, or sixteenth of an inch. Word Watch The length of the line segment mixed number, p. 244 improper fraction, p. 244 proper fraction, p. 245 5 8 21 8 is 2 inches, or inches. 5 8 The number 2 , read as “two and five eighths,” is a mixed number. A mixed number is the sum of a whole number part and a fraction part. 21 8 An improper fraction , such as , is any fraction in which the numerator is greater than or equal to the denominator. EXAMPLE 1 Measuring to a Fraction of an Inch Industrial Arts You need to measure a piece of wood for a birdhouse. Write the length as a mixed number and as an improper fraction. Solution 3 4 First write the length as a mixed number: 3 inches. 15 4 Then count fourths to write the length as an improper fraction: inches. 3 4 There are 15 fourths in 3 . Your turn now 15 1. in. 2 244 Chapter 5 Number Patterns and Fractions Draw a line segment that has the given length. 1 2. 6 in. 4 Page 2 of 5 Rewriting Mixed Numbers In the activity on page 243, you may have seen that 1 whole can be written in different forms. You can use these forms of 1 to help you write mixed numbers as improper fractions. 1 1 2 2 tch Out! Wa 3 3 1 1 EXAMPLE 2 4 4 1 5 5 1 1 Rewriting Mixed Numbers 3 5 Write 4 as an improper fraction. In Example 2, don’t forget to add the 3 fraction part, , after you 5 write the whole part as a fraction. 3 5 20 3 5 1 whole , so 4 wholes , or . 23 5 Simplify the numerator. 45 5 5 5 4 20 5 Rewriting Improper Fractions You can also write an improper fraction as a mixed number. First divide the numerator by the denominator, and then put the remainder over the denominator. Make sure that the fraction part is a proper fraction , which is a fraction in which the numerator is less than the denominator. EXAMPLE 3 Rewriting Improper Fractions 16 3 Write as a mixed number. 1 Divide 16 by 3. 5 R1 31 6 15 1 1 3 2 3. 3 3 1 still remains. 3 1 3 5 5 2 Write the mixed number. Your turn now After you divide, Write the mixed number as an improper fraction. 1 4. 2 4 5 5. 4 6 Write the improper fraction as a mixed number. 22 6. 5 34 7. 13 Lesson 5.6 41 8. 12 Mixed Numbers and Improper Fractions 245 Page 3 of 5 Comparing Numbers To compare and order mixed numbers and improper fractions, begin by writing them all in the same form. Sports EXAMPLE 4 Ordering Numbers 5 8 3 4 Baseball Bats The widths of three baseball bats are 2 , 2 , and 9 inches. Order the widths from least to greatest. 4 Solution 1 Write all of the widths as improper fractions. 5 8 16 5 8 21 8 3 4 2 83 4 11 4 9 4 2 2 Rewrite all of the widths using the LCD, 8. ■ Baseball bats 11 11 2 22 4 42 8 21 8 Baseball bats come in many different weights. To find out which bat size is best for you, divide your height, in inches, by 3. Then add 6. This is the weight, in ounces, of a baseball bat that is appropriate for you. What is the best bat weight for you? 9 92 18 4 42 8 3 Compare the fractions. 18 8 21 8 21 8 22 8 9 4 5 8 5 8 9 4 5 8 3 4 ANSWER The widths, from least to greatest, are , 2 , and 2 inches. INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 712 Getting Ready to Practice 1. Vocabulary Explain what it means for a fraction to be an improper fraction. Copy and complete the statement. ? 1 2. 6 2 2 ? 1 3. 3 4 4 ? 17 4. 5 3 3 ? 11 5. 2 4 4 Copy and complete the statement with <, >, or . 7 1 6. _?_ 1 4 4 246 Chapter 5 3 4 Because < and < , you know that < 2 and 2 < 2 . Number Patterns and Fractions 2 11 7. 3 _?_ 3 3 2 28 8. 5 _?_ 5 5 4 20 9. 2 _?_ 7 7 Page 4 of 5 Practice and Problem Solving with Example 1 2 3 4 Homework Exercises 10–12 13–20, 32–35 21–28 29–31 Measurement Use a ruler to measure the candle to the end of its wick. Write the answer as a mixed number and as an improper fraction. 10. 11. 11 12. Draw a line segment that has a length of inches. 4 Online Resources CLASSZONE.COM • More Examples • eTutorial Plus Write the mixed number as an improper fraction. 1 13. 4 2 5 14. 1 8 2 15. 3 5 3 16. 5 4 2 17. 7 3 9 18. 1 10 1 19. 10 2 1 20. 12 4 Write the improper fraction as a mixed number. 8 21. 3 25 22. 6 18 23. 5 15 24. 4 13 25. 2 22 26. 3 12 27. 7 33 28. 4 Order the numbers from least to greatest. 7 3 29. , 2 , 3 2 4 23 19 1 30. , , 4 5 4 2 41 17 1 31. 5, , , 5 8 3 6 Write 1 as a fraction using the given denominator. 32. 4 33. 6 34. 10 35. 14 36. Pole Vaulting The pole vault records for four different schools are shown in the table. Which school’s record is the highest? School Pole vault height (feet) Oakmont Chester 49 3 16 3 8 Central Perry 33 2 16 9 16 Critical Thinking Find a mixed number that is between the numbers. 3 11 37. 1 , 5 5 9 38. , 5 2 27 39. 3, 8 4 29 40. 5 , 9 5 41. Challenge Your friend is thinking of an improper fraction that is more 1 than 2 and less than 2 . The sum of the numerator and the 4 denominator is 19. What is your friend’s number? Lesson 5.6 Mixed Numbers and Improper Fractions 247 Page 5 of 5 Mixed Review Evaluate the expression. (Lesson 1.5) 42. 20 x, when x 2 43. x 2, when x 21 44. 15 x 4, when x 3 45. 3x y, when x 4 and y 6 Write the decimal in words. (Lesson 3.1) 46. 14.1 47. 23.5 48. 64.92 49. 78.15 Basic Skills Round the number to the place value of the red digit. 50. 8701 51. 9900 52. 2457 53. 4391 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 17 54. Multiple Choice Which mixed number is equivalent to ? 5 2 1 1 2 B. 2 C. 3 D. 3 A. 1 5 5 5 5 5 55. Multiple Choice A jewelry box is 4 inches wide. Write this mixed 8 number as an improper fraction. 20 8 F. inches 32 8 G. inches What Does it Say? To find the saying below, write the improper fractions as mixed numbers. Find the mixed number below the number line and write the corresponding letter in the blank above the improper fraction. 248 Chapter 5 Number Patterns and Fractions 37 8 H. inches 37 5 I. inches