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## Word & Letter Play The Value of Months

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**Word & Letter Play**The Value of Months If March = 43 and May = 39, then by the same logic, what does July equal? STRATEGY:Look for a pattern – think of ways letters are represented by numbers**Word & Letter Play**The Value of Months Each letter is replaced by the number of its position in the English alphabet. Then the numbers are added together. 68 STRATEGY:Look for a pattern – think of ways letters are represented by numbers**Warm Up**Problem of the Day Lesson Presentation Lesson Quizzes**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**n**d A rational numberis any number that can be written as a fraction , where n and d are integers and d 0.**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 • 4 • 4 80 = 5 • 4 • 4 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.**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**Rational Numbers**The real number system consists of rational and irrational numbers. Rational numbers can be expressed in fractional form, , where a (the numerator) and b (the denominator) are both integers and b = 0. The decimal form of the number either terminates or repeats. Counting numbers, whole numbers, integers, and non-integers are all rational numbers. a b**Counting numbers are the natural numbers.**{1, 2, 3, 4, 5, 6, …} Whole numbers consist of the counting numbers and zero. {0, 1, 2, 3, 4, 5, …} Integers consist of the counting numbers, their opposites, and zero. {…, -3, -2, -1, 0, 1, 2, 3, …}**Non-integers consist of fractions that can be written as**terminating or repeating decimals. • A terminating decimal comes to a complete stop. • A repeating decimal continues the same digit or block of digits forever. 1 3 2 5.25 0.6 -9.261 7 3**Irrational Numbers**Irrational numbers are numbers that cannot be written as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimals because the decimal form of the number never ends and never repeats. The most common irrational number is pi (п). The value of п is 3.141592654…**Example 1**Tell whether each real number is rational or irrational. -23.75 rational decimal terminates 4.750918362… irrational decimal does not terminate 5 9 √15 irrational decimal form does not terminate rational number is in fraction form**Lesson Quizzes**Standard Lesson Quiz Lesson Quiz for Student Response Systems**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**Lesson Quiz: Part II**6. Alex 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**Lesson Quiz for Student Response Systems**16 28 1. Simplify . A. C. B.D. 5 7 3 7 4 7 6 7**Lesson Quiz for Student Response Systems**24 30 2. Simplify . A. C. B.D. 6 5 4 6 4 5 5 4**Lesson Quiz for Student Response Systems**3. Which of the following represents the given decimal as a fraction in simplest form? 0.43 A. C. B.D. 43 10 43 100 100 43 43 1000**Lesson Quiz for Student Response Systems**4. Which of the following represents the given decimal as a fraction in simplest form? –0.875 A. – C. – B. – D. – 5 7 7 8 4 5 9 10**Lesson Quiz for Student Response Systems**5. Which of the following represents the given fraction as a decimal? A. 4.3 B. 4.6 C. 5.6 D. 6.5 51 9