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Warm Up

Learn to write rational numbers in equivalent forms. Understand vocabulary such as rational number and relatively prime number. Practice simplifying fractions and writing decimals as fractions. Test your knowledge with quizzes.

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Warm Up

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

  2. Warm Up Divide. 24 12 1. 36  3 2. 144  6 3. 68  17 4. 345  115 3 4 5. 1024  64 16

  3. Learn to write rational numbers in equivalent forms.

  4. Vocabulary rational number relatively prime number

  5. A rational numberis any number that can be written as a fraction , where n and d are integers and d  0. Relatively prime numbers have no common factors other than 1. n d

  6. Decimals that terminate or repeat are rational numbers.

  7. ;16 is a common factor. 16 80 = 1 for a ≠ 0 =0 for ≠ 0 7 8 0 a a a 7 8 7 8 1 5 = 16 ÷ 16 = = = 80 ÷ 16 Additional Example 1A: Simplifying Fractions Simplify. 16 = 1 • 4 • 4 80 = 5 • 4 • 4 16 80 Divide the numerator and denominator by 16. Remember

  8. ;There are no common factors. –18 29 –18 29 = Additional Example 1B: Simplifying Fractions Simplify. –18 29 18 = 2 • 9 29 = 1 • 29 18 and 29 are relatively prime.

  9. 622 1000 = 311 500 = 37 100 =5 Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. A. 5.37 7 is in the hundredths place. 5.37 B. 0.622 2 is in the thousandths place. 0.622 Simplify by dividing by the common factor 2.

  10. denominator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator numerator

  11. 9 11 –9 Writing Math –1 8 A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2. _ 11 9 The fraction is equivalent to the decimal 1.2. Additional Example 3A: Writing Fractions as Decimals Write the fraction as a decimal. 11 9 1 .2 .0 The pattern repeats. 0 2 2

  12. 20 7 –0 –6 0 0 –1 0 7 20 The fraction is equivalent to the decimal 0.35. Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. .3 0 5 This is a terminating decimal. 7 20 0 .0 0 7 0 1 0 The remainder is 0. 0

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

  14. 3 7 5 7 5 8 27100 – 2.16 Lesson Quiz: Part I Simplify. 18 42 15 21 1. 2. Write each decimal as a fraction in simplest form. 3. 0.27 4. –0.625 13 6 5. Write as a decimal

  15. Lesson Quiz: Part II 6. Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.) 0.325

  16. 3 7 5 7 A. C. 4 7 6 7 B. D. Lesson Quiz for Student Response Systems 16 28 1. Simplify .

  17. 6 5 4 6 A. C. 4 5 5 4 B. D. Lesson Quiz for Student Response Systems 24 30 2. Simplify .

  18. 43 10 43 100 A. C. 100 43 B. D. 43 1000 Lesson Quiz for Student Response Systems 3. Which of the following represents the given decimal as a fraction in simplest form? 0.43

  19. 7 8 5 7 A. C. – – 9 10 4 5 B. – D. – Lesson Quiz for Student Response Systems 4. Which of the following represents the given decimal as a fraction in simplest form –0.875

  20. A. 4.3 B. 4.6 C. 5.6 D. 6.5 Lesson Quiz for Student Response Systems 5. Which of the following represents the given fraction as a decimal? 51 9

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