3 1 Rational Numbers Learn to write rational
3 -1 Rational Numbers Learn to write rational numbers in equivalent forms. Pre-Algebra
3 -1 Rational Numbers A rational number is any number that can be n written as a fraction d where n and d are integers and d ≠ 0. Decimals that terminate or repeat are rational numbers. Pre-Algebra
3 -1 Rational Numbers Numerator Pre-Algebra n d Denominator
3 -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. Pre-Algebra
3 -1 Rational Numbers You can often SIMPLIFY fractions by dividing both the numerator and denominator by the same nonzero integer. 12 You can simplify the fraction 15 to 4 by 5 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. Pre-Algebra
3 -1 Rational Numbers Example 1 A Simplify. A. 6 30 6 = 1 • 6 ; 6 is a common factor. 30 = 5 • 6 6÷ 6 6 = 30 ÷ 6 30 1 = 5 Pre-Algebra Divide the numerator and denominator by 6.
3 -1 Rational Numbers Example 1 B: Simplifying Fractions Simplify. B. 16 80 16 = 1 • 16 80 =; 16 is a common factor. 5 • 16 16 ÷ 16 16 = 80 ÷ 16 80 1 = 5 Pre-Algebra Divide the numerator and denominator by 16.
3 -1 Rational Numbers Example 1 B Simplify. B. 18 27 18 = 3 • 2 27 = 3 • 3 18 = 18 ÷ 9 27 2 = 3 Pre-Algebra ; 9 is a common factor. Divide the numerator and denominator by 9.
3 -1 Rational Numbers Example 1 C: Simplifying Fractions Simplify. C. – 18 29 18 = 2 • 9 29 = 1 • 29 – 18 = 29 29 Pre-Algebra ; There are no common factors. – 18 and 29 are relatively prime.
3 -1 Rational Numbers 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. Pre-Algebra
3 -1 Rational Numbers Example 2 A: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. A. – 0. 8 = – 8 10 4 =– 5 Pre-Algebra – 8 is in the tenths place. Simplify by dividing by the common factor 2.
3 -1 Rational Numbers Example 2 B: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. B. 5. 37 37 7 is in the hundredths place. 5. 37 = 5 100 Pre-Algebra
3 -1 Rational Numbers Example 2 C: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. C. 0. 622 = 1000 311 = 500 Pre-Algebra 2 is in the thousandths place. Simplify by dividing by the common factor 2.
3 -1 Rational Numbers A rational number is any number that can be n written as a fraction d where n and d are integers and d ≠ 0. Decimals that terminate or repeat are rational numbers. Pre-Algebra
3 -1 Rational Numbers Numerator Pre-Algebra n d Denominator
3 -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. Pre-Algebra
3 -1 Rational Numbers You can often SIMPLIFY fractions by dividing both the numerator and denominator by the same nonzero integer. 12 You can simplify the fraction 15 to 4 by 5 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. Pre-Algebra
3 -1 Rational Numbers 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. Pre-Algebra
3 -1 Rational Numbers To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator 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. Pre-Algebra
3 -1 Rational Numbers Example 3 A: Writing Fractions as Decimals Write the fraction as a decimal. A. 11 9 The fraction Pre-Algebra 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
3 -1 Rational Numbers Example 3 B: Writing Fractions as Decimals Write the fraction as a decimal. B. 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 Pre-Algebra 7 is equivalent to the decimal 0. 35. 20
3 -1 Rational Numbers Example 3 A Write the fraction as a decimal. A. 15 9 The fraction Pre-Algebra 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
3 -1 Rational Numbers Example 3 B Write the fraction as a decimal. 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 9 B. 40 Pre-Algebra
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