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**2-1**Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation**Warm Up**Divide. 24 12 1. 36 3 2. 144 6 3. 68 17 4. 345 115 3 4 5. 1024 64 16**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**Vocabulary**rational number relatively prime**A rational numberis any number that can be written as a**fraction , where n and d are integers and d 0. n d**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.**12**15 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. = 12 4 15 5 You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3. 4 5 The same total area is shaded.**;16 is a common factor.**Remember! 16 = 0 for a ≠ 0 = 1 for a ≠ 0 = = – 80 aa 0a 1 5 = 16 ÷ 16 = –7 8 7 –8 7 8 80 ÷ 16 Additional Example 1A: Simplifying Fractions Simplify. 16 = 1 • 16 80 = 5 • 16 16 80 Divide the numerator and denominator by 16.**;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.**18 ÷ 9**18 = 27 27 ÷ 9 2 3 = Check It Out: Example 1A Simplify. 18 = 3 • 3 • 2 27 = 3 • 3 • 3 18 27 ; 9 is a common factor. Divide the numerator and denominator by 9.**17 35**17 –35 = – Check It Out: Example 1B Simplify. 17 –35 ; There are no common factors. 17 = 1 • 17 35 = 5 • 7 17 and –35 are relatively prime.**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.**–32**1 ___ __ 10 6**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.**2625 10,000**= 21 80 = 75 100 =8 3 4 =8 Check It Out: Example 2 Write each decimal as a fraction in simplest form. A. 8.75 8.75 5 is in the hundredths place. Simplify by dividing by the common factor 25. B. 0.2625 5 is in the ten-thousandths place. 0.2625 Simplify by dividing by the common factor 125.**denominator**To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator numerator**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**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**9 15**–9 0 –5 4 15 9 The fraction is equivalent to the decimal 1.6. Check It Out: Example 3A Write the fraction as a decimal. 15 9 1 .6 .0 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 6 6**40 9**–0 –8 0 – 8 0 9 40 0 2 0 0 – 2 The fraction is equivalent to the decimal 0.225. Check It Out: Example 3B Write the fraction as a decimal. 9 40 .2 0 2 5 This is a terminating decimal. 0 0 .0 0 9 0 1 0 0 The remainder is 0. 0**3 7**5 7 5 8 27100 – 2.16 Lesson Quiz: Part 1 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**Lesson Quiz: Part 2**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