2-1 Rational Numbers 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

2-1 Rational 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

2-1 Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2-1 Rational Numbers Warm Up Divide      64

2-1 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

2-1 Rational Numbers Learn to write rational numbers in equivalent forms.

2-1 Rational Numbers rational number relatively prime Vocabulary

2-1 Rational Numbers A rational number is any number that can be written as a fraction, where n and d are integers and d  0. n d

2-1 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.

2-1 Rational Numbers 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 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. The same total area is shaded =

2-1 Rational Numbers Additional Example 1A: Simplifying Fractions = = ;16 is a common factor = Divide the numerator and denominator by 16. = 16 ÷ ÷ 16 Simplify. = 0 for a ≠ 0 = 1 for a ≠ 0 = = – Remember! 0a0a a –7 8 7 –8 7878

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

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

2-1 Rational Numbers = – –35 17 = = 5 7 ; There are no common factors. 17 and 35 are relatively prime. 17 –35 Check It Out: Example 1B Simplify.

2-1 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.

2-1 Rational Numbers

2-1 Rational Numbers 5.37 A is in the hundredths place = 5= 5 Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form B is in the thousandths place = = Simplify by dividing by the common factor 2.

2-1 Rational Numbers 8.75 A is in the hundredths place = 8= 8 = 8= Simplify by dividing by the common factor 25. Write each decimal as a fraction in simplest form. Check It Out: Example B is in the ten-thousandths place ,000 = = Simplify by dividing by the common factor 125.

2-1 Rational Numbers denominator numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator

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

2-1 Rational Numbers This is a terminating decimal The remainder is – –6 0 –1 0 0 Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. The fraction is equivalent to the decimal

2-1 Rational Numbers 9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 1 – –5 4 Write the fraction as a decimal. Check It Out: Example 3A The fraction is equivalent to the decimal

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

2-1 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

2-1 Rational Numbers 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, …}

2-1 Rational Numbers 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

2-1 Rational Numbers 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 …

2-1 Rational Numbers Example 1 Tell whether each real number is rational or irrational rational decimal terminates …irrational decimal does not terminate 5 9 √15irrational decimal form does not terminate rational number is in fraction form

2-1 Rational Numbers

2-1 Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

2-1 Rational Numbers Lesson Quiz: Part I Simplify Write each decimal as a fraction in simplest form – Write as a decimal –

2-1 Rational Numbers 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.) Lesson Quiz: Part II

2-1 Rational Numbers 1. Simplify. A. C. B. D. Lesson Quiz for Student Response Systems

2-1 Rational Numbers 2. Simplify. A. C. B. D. Lesson Quiz for Student Response Systems

2-1 Rational Numbers 3. Which of the following represents the given decimal as a fraction in simplest form? 0.43 A. C. B. D. Lesson Quiz for Student Response Systems

2-1 Rational Numbers 4. Which of the following represents the given decimal as a fraction in simplest form? –0.875 A. –C. – B. –D. – Lesson Quiz for Student Response Systems

2-1 Rational Numbers 5. Which of the following represents the given fraction as a decimal? A. 4.3 B. 4.6 C. 5.6 D. 6.5 Lesson Quiz for Student Response Systems 51 9