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Warm Up

This interactive lesson covers converting fractions to decimals, identifying terminating and repeating decimals, and simplifying fractions. It also includes quizzes, examples, and helpful hints for student understanding.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 4 12 9 23 7 18 25 18 or 1 Warm Up Write each fraction in the simplest form. 1. 2. 3. 4. 18 46 1 3 21 63 1 3 100 72

  3. Problem of the Day Martin recorded how much a bean plant grew each week. The first week the plant grew of an inch, of an inch the second week, and of an inch the third week. During which week did the plant grow the least? 7 8 4 7 7 9 week 1

  4. Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

  5. Vocabulary terminating decimal repeating decimal

  6. In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat. The statistics on the next slide are for the 2006 Major League Baseball season.

  7. Hits at Bats 195 576 576 195 ÷ 576 ≈ 0.339 195 224 695 224 695 224 ÷ 695 ≈ 0.322 To convert a fraction to a decimal, divide the numerator by the denominator.

  8. 1.00 Additional Example 1: Writing Fractions as Decimals Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 9 5 5 3 1 4 B. C. A. 1 .8 1 .6 6 6 0.2 5 9.0 5 5.000 3 4 – 8 – 3 – 5 20 20 40 – 20 – 18 – 40 20 0 0 – 18 9 5 5 3 1 4 = 1.8 ≈ 1.67 = 0.25 20 – 18 2

  9. Helpful Hint You can use a calculator to check your division: 1 9 5 33 4 = 0.25 ÷ 1.8 5 ÷ = 3 1.66… ÷ =

  10. 3.00 Check It Out: Example 1 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 6 5 7 3 3 4 B. C. A. 1 .2 2 .3 3 3 0.7 5 6.0 5 7.000 3 4 – 2 8 – 6 – 5 20 10 10 – 20 – 9 – 10 10 0 0 – 9 6 5 7 3 3 4 = 1.2 ≈ 2.33 = 0.75 10 – 9 1

  11. The decimals 0.75 and 1.2 in Example 1 are terminating decimals because the decimals comes to an end. The decimal 0.333…is a repeating decimal because the decimal repeats a pattern forever. You can also write a repeating decimal with a bar over the repeating part. 0.333… = 0.3 0.8333… = 0.83 0.727272… = 0.72

  12. Additional Example 2: Using Mental Math to Write Fractions as Decimals Write each fraction as a decimal. 4 5 A. Multiply to get a power of ten in the denominator. 4 5 2 2 8 10 = x = 0.8 37 50 B. Multiply to get a power of ten in the denominator. 37 50 2 2 74 100 = x = 0.74

  13. Check It Out: Example 2 Write each fraction as a decimal. 3 5 A. Multiply to get a power of ten in the denominator. 3 5 2 2 6 10 = x = 0.6 18 25 B. Multiply to get a power of ten in the denominator. 18 25 4 4 72 100 = x = 0.72

  14. Reading Math You read the decimal 0.018 as “eighteen thousandths.” Additional Example 3: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. B. 1.55 A. 0.018 18 1,000 155 100 0.018 = 1.55 = 18 ÷ 2 1,000 ÷ 2 155 ÷ 5 100 ÷ 5 = = 31 20 11 20 9 500 or 1 = =

  15. Check It Out: Example 3 Write each decimal as a fraction in simplest form. B. 1.30 A. 0.015 15 1,000 130 100 0.015 = 1.30 = 130 ÷ 10 100 ÷ 10 15 ÷ 5 1,000 ÷ 5 = = 3 200 3 10 13 10 = or 1 =

  16. Additional Example 4: Sports Application A football player completed 1,546 of the 3,875 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth. Completion Rate What the Calculator Shows Fraction 1,546 3,875 ENTER ÷ 0.398967742 0.399 1546 3875 His completion rate is 0.399.

  17. Check It Out: Example 4 Johnny Unitas, a former professional quarterback, completed 2,830 of the 5,186 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth. What the Calculator Shows Fraction Completion Rate 2,830 5,186 ENTER ÷ 0.546 0.54569996 2830 5186 His completion rate is 0.546.

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. Lesson Quiz Write each fraction as a decimal. 1. 3. 4. Write each decimal as a fraction in simplest form. 5. 0.42 7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 16 5 21 8 2.625 3.2 2. 7 10 11 20 0.55 0.7 5 8 69 8 21 50 6. 8.625 or 8 0.70

  20. Lesson Quiz for Student Response Systems 1. Which of the following represents the fraction as a decimal? A. 3.4 B. 3.5 C. 3.6 D. 3.7 18 5

  21. Lesson Quiz for Student Response Systems 2. Which of the following represents the fraction as a decimal? A. 0.65 B. 0.75 C. 0.85 D. 0.95 13 20

  22. Lesson Quiz for Student Response Systems 3. Which of the following represents the decimal 0.32 as a fraction in simplest form? A. C. B.D. 6 25 8 25 7 25 1 5

  23. Lesson Quiz for Student Response Systems 4. Which of the following represents the decimal 6.125 as a fraction in simplest form? A. or 8 C. or 6 B. or 6 D. or 6 37 6 1 6 49 6 1 6 49 8 31 5 1 8 1 5

  24. Lesson Quiz for Student Response Systems 5. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate? A. 0.65 B. 0.66 C. 0.67 D. 0.68

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