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Rational and Irrational Numbers

Rational and Irrational Numbers. Objective: I will identify rational and irrational numbers and identify repeating and terminating decimals MAFS.8.NS.1: Know that there are numbers that are not rational, and approximate them by rational numbers.

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Rational and Irrational Numbers

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  1. Rational and Irrational Numbers Objective: I will identify rational and irrational numbers and identify repeating and terminating decimals MAFS.8.NS.1: Know that there are numbers that are not rational, and approximate them by rational numbers. MAFS.8.NS.1.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (MP.2, MP.6, MP.7

  2. Do Now • Change into decimal form. Identify if it is rational or irrational. Explain • 157/50 • 2/3 • 5/13

  3. Rational and Irrational 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.

  4. 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.

  5. ;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 Simplifying Fractions Simplify. 16 = 1 • 4 • 4 80 = 5 • 4 • 4 16 80 Divide the numerator and denominator by 16.

  6. ; there are no common factors. –18 29 –18 29 = Simplifying Fractions Simplify. –18 29 18 = 2 • 9 29 = 1 • 29 18 and 29 are relatively prime.

  7. 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.

  8. Writing Math A repeating decimal can be written with a bar over the digits that repeat. So 1.3333… = 1.3. _

  9. 622 1000 = 311 500 = 37 100 =5 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.

  10. Rational and Irrational Numbers • Reflection: How do you change a repeating decimal into a fraction.

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