1 1 Rational Numbers Warm Up Problem of

1 -1 Rational Numbers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

1 -1 Rational Numbers Problem of the Day An ice cream parlor has 6 flavors of ice cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? 21

1 -1 Rational Numbers Learn to write rational numbers in equivalent forms.

1 -1 Rational Numbers Vocabulary rational number relatively prime

1 -1 Rational Numbers A rational number is any number that can be n written as a fraction , where n d and d are integers and d 0.

1 -1 Rational Numbers The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.

1 -1 Rational Numbers You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can 12 simplify the fraction 15 to 45 by dividing both the numerator and denominator by 3. 12 of the 15 boxes are shaded. 12 15 4 of the 5 boxes are shaded. = 4 5 The same total area is shaded.

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

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

1 -1 Rational Numbers Check It Out: Example 1 A Simplify. 18 = 3 • 2 ; 9 is a common factor. 27 = 3 • 3 18 27 18 = 18 ÷ 9 27 = 2 3 Divide the numerator and denominator by 9.

1 -1 Rational Numbers Check It Out: Example 1 B Simplify. 17 – 35 17 = 1 • 17 ; There are no common factors. 35 = 5 • 7 17 17 – 35 =– 17 and 35 are relatively prime. 35

1 -1 Rational Numbers Decimals that terminate or repeat are rational numbers. To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

1 -1 Rational Numbers

1 -1 Rational Numbers Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. A. 5. 37 37 5. 37 = 5 100 7 is in the hundredths place. B. 0. 622 = 622 1000 311 = 500 2 is in the thousandths place. Simplify by dividing by the common factor 2.

1 -1 Rational Numbers Check It Out: Example 2 Write each decimal as a fraction in simplest form. A. 8. 75 = 8 75 100 3 = 8 4 B. 0. 2625 5 is in the hundredths place. Simplify by dividing by the common factor 25. 2625 0. 2625 = 10, 000 21 = 80 5 is in the tenthousandths place. Simplify by dividing by the common factor 125.

1 -1 Rational Numbers To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator numerator

1 -1 Rational Numbers Additional Example 3 A: Writing Fractions as Decimals Write the fraction as a decimal. 11 9 The fraction 1. 2 9 11. 0 – 9 20 – 1 8 2 The pattern repeats. Writing Math A repeating decimal can be written with a bar over the digits_that repeat. So 1. 2222… = 1. 2. 11 is equivalent to the decimal 1. 2. 9

1 -1 Rational Numbers Additional Example 3 B: Writing Fractions as Decimals Write the fraction as a decimal. 7 20 0. 3 5 This is a terminating decimal. 20 7. 0 0 – 0 70 – 6 0 1 00 – 1 0 0 0 The remainder is 0. The fraction 7 is equivalent to the decimal 0. 35. 20

1 -1 Rational Numbers Check It Out: Example 3 A Write the fraction as a decimal. 15 9 The fraction 1. 6 9 15. 0 – 9 60 – 5 4 6 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 15 is equivalent to the decimal 1. 6. 9

1 -1 Rational Numbers Check It Out: Example 3 B Write the fraction as a decimal. 9 40 0. 2 2 5 This is a terminating decimal. 40 9. 0 0 0 – 0 90 – 8 0 1 00 – 80 200 – 200 0 The remainder is 0. 9 The fraction is equivalent to the decimal 0. 225. 40

1 -1 Rational Numbers Lesson Quizzes Standard Lesson Quiz for Student Response Systems

1 -1 Rational Numbers Lesson Quiz: Part I Simplify. 18 1. 42 3 7 15 2. 21 5 7 Write each decimal as a fraction in simplest form. 5 27 – 3. 0. 27 4. – 0. 625 8 100 13 5. Write as a decimal 6 2. 16

1 -1 Rational Numbers 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

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

1 -1 Rational Numbers Lesson Quiz for Student Response Systems 2. Simplify 24. 30 A. 4 6 C. 6 5 B. 4 5 D. 5 4

1 -1 Rational Numbers Lesson Quiz for Student Response Systems 3. Which of the following represents the given decimal as a fraction in simplest form? 0. 43 A. 43 100 B. 100 43 C. 43 10 D. 43 1000

1 -1 Rational Numbers Lesson Quiz for Student Response Systems 4. Which of the following represents the given decimal as a fraction in simplest form – 0. 875 A. – 5 7 C. – 7 8 4 5 B. – D. – 9 10

1 -1 Rational Numbers Lesson Quiz for Student Response Systems 5. Which of the following represents the given fraction as a decimal? 51 9 A. 4. 3 B. 4. 6 C. 5. 6 D. 6. 5