Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Rational Numbers 3-1 Warm Up Divide. 1. 36 3 3. 68 17 12 4 5. 1024 64 16 2. 144 6 4. 345 115 24 3 Learn to write rational numbers in equivalent forms. Vocabulary rational number relatively prime A rational number is any number that can n be written as a fraction , where n and d d are integers and d 0. Decimals that terminate or repeat are rational numbers. Numerator n d Denominator 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. You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify 12 4 the fraction to by dividing both the 15 5 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. Example: Simplifying Fractions Simplify. 5 A. 10 5 =1•5 10 = 2 • 5 5÷5 5 = 10 ÷ 5 10 1 = 2 ;5 is a common factor. Divide the numerator and denominator by 5. Example: Simplifying Fractions Simplify. B. 16 80 16 = 1 • 16 ;16 is a common factor. 80 = 5 • 16 16 ÷ 16 16 = 80 ÷ 16 80 1 = 5 Divide the numerator and denominator by 16. Example: Simplifying Fractions Simplify. C. –18 29 18 = 2 • 9 29 = 1 • 29 –18 –18 = 29 29 ;There are no common factors. –18 and 29 are relatively prime. Try This Simplify. A. 6 30 6 = 1 • 6 ;6 is a common factor. 30 = 5 • 6 6÷6 6 = 30 ÷ 6 30 1 = 5 Divide the numerator and denominator by 6. Try This Simplify. 18 = 3 • 3 • 2 ;9 is a common factor. 27 = 3 • 3 • 3 B. 18 27 18 = 18 ÷ 9 27 ÷ 9 27 = 2 3 Divide the numerator and denominator by 9. Try This Simplify. C. 17 –35 17 = 1 • 17 ;There are no common factors. 35 = 5 • 7 17 17 17 and –35 are =– –35 35 relatively prime. To write a finite decimal as a fraction, identify the place value of the farthest digit to the right. Then write all of the digits after the decimal points as the numerator with the place value as the denominator. Example: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. A. –0.8 –8 is in the tenths place. –0.8 = –8 10 =– 4 5 Simplify by dividing by the common factor 2. Example: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. B. 5.37 37 5.37 = 5 100 7 is in the hundredths place. Example: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. C. 0.622 622 0.622 = 1000 311 = 500 2 is in the thousandths place. Simplify by dividing by the common factor 2. Try This Write the decimal as a fraction in simplest form. –4 is in the tenths place. A. –0.4 –4 –0.4 = 10 =– 2 5 Simplify by dividing by the common factor 2. Try This Write the decimal as a fraction in simplest form. B. 8.75 5 is in the hundredths place. 75 Simplify by dividing by the 8.75 = 8 100 common factor 25. 3 = 8 4 Try This Write each decimal as a fraction in simplest form. C. 0.2625 5 is in the ten-thousandths place. 2625 Simplify by dividing by 0.2625 = 10,000 the common factor 125. 21 = 80 To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator denominator numerator When writing a long division problem from a fraction, put the numerator inside the “box,” or division symbol. It may help to write the numerator first and then say “divided by” to yourself as you write the division symbol. Example: Writing Fractions as Decimals Write the fraction as a decimal. A. 11 9 The fraction 1 .2 9 11 .0 –9 20 –1 8 2 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. 11 is equivalent to the decimal 1.2. 9 Example: Writing Fractions as Decimals Write the fraction as a decimal. 7 B. 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 Try This Write the fraction as a decimal. A. 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 Try This Write the fraction as a decimal. 0.2 2 5 40 9.0 0 0 This is a terminating decimal. –0 90 –8 0 1 00 – 80 200 – 2 00 0 The remainder is 0. 9 The fraction is equivalent to the decimal 0.225. 40 B. 9 40 Lesson Quiz: Part 1 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 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