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Pre-Algebra

Pre-Algebra. August 18, 2011 Please find your seat and get ready for class by getting your agenda and class materials out. Write the following in your agenda: Topic: Compare and Order Rational Numbers

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Pre-Algebra

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  1. Pre-Algebra August 18, 2011 Please find your seat and get ready for class by getting your agenda and class materials out. Write the following in your agenda: Topic: Compare and Order Rational Numbers Learning Objective: Students will express rational numbers as decimals and decimals to fractions to compare and order rational numbers.

  2. Warm Up Write as a fraction in simplest form • .56 2. 1.87 3. .035 Write as a decimal. 4. 5. 6.

  3. Warm Up Write as a fraction in simplest form • .56 2. 1.87 3. .035 Write as a decimal. 4. 5. 6. .875 .8 1.8

  4. Compare and Order Rational Numbers Topic: Compare and Order Rational Numbers Level of Thinking: Apply and express Do: Students will express rational numbers as decimals and decimals to fractions to compare and order rational numbers.

  5. Compare and Order Rational Numbers Essential Question: Explain why expressing rational numbers as decimals and decimals as fractions is important when comparing and ordering rational numbers.

  6. Compare and Order Rational Numbers As of the All-Star Baseball 2011 game, which Arizona Diamondback player had the better batting average, Stephen Drew with a .259 batting average or Chris Young with a batting average?

  7. Compare and Order Rational Numbers Vocabulary Rational number – any number that can be expressed in fraction form such as , where a and b are integers and b does not equal (≠) 0. Terminating decimal – a decimal whose digits end. Repeating decimal- a decimal whose digits repeat in groups of one or more. Bar notation- in repeating decimals, the line or bar placed over the digits that repeat.

  8. Compare and Order Rational Numbers Rational Numbers ½ 0.4 Integers 1 Whole Numbers -8 0, 1, 2, 3

  9. Compare and Order Rational Numbers Any fraction can be expressed as a decimal by dividing the numerator (top number) by the denominator (bottom number). It is helpful to know commonly used fraction – decimal equivalences. Can you think of any others?

  10. Compare and Order Rational Numbers Fractions as decimals: Write as a decimal. Add a decimal and zeros to the 5 because 8 cannot go into 5. =0.625

  11. Compare and Order Rational Numbers The decimal 0.625 has a special name. Can you say this type of decimal? The decimal 0.625 is a “terminating decimal” because the division ends or terminates with a zero.

  12. Compare and Order Rational Numbers Write as a decimal. means 1 + ½ . To change ½ into a decimal, divide 1 by 2. 1 ½ can be written as 1.5

  13. Compare and Order Rational Numbers Practice: Express fractions or mixed numbers as terminating decimals. Show your work! 1. 2.

  14. Compare and Order Rational Numbers Terminating decimals as Fractions Write the terminating decimal 0.45 as a fraction. 0.45 = Write it like you say it. = Simplify 0.45 =

  15. Compare and Order Rational Numbers Write a Mixed Number as a decimal. The three dots mean the 6 keeps repeating.

  16. Compare and Order Rational Numbers A decimal like 1.6666…. is called a repeating decimal because it does not terminate but has a 6 that repeats. Use bar notation to write repeating decimals. Place the bar only over the digits that repeat. When repeating decimals occur in real-life situations, they are usually rounded to a certain place value.

  17. Compare and Order Rational Numbers Such as a baseball pitcher winning 6 out of 11 games he started. To find his winning average to the nearest thousandth place you would divide 6 by 11: = 0.545454… Look to the ten thousandth place. 4< 5 = 0.545 0.545 is the pitcher’s winning average. Use the rounding rules, so the 5 in the thousandths place stays the same

  18. Compare and Order Rational Numbers algebra!! To write a repeating decimal as a fraction, we will use First let n = 0.6 or 0.666… n = 0.666… let n = 0.666… 10n = 6.666… multiply by 10 because 1 digit repeats -n = 0.666… subtract to eliminate repeating digits 9n= 6divide by nine on each side 9 9 n = simplify n = Let’s try another example!

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  20. Compare and Order Rational Numbers Student Practice: On your whiteboard, write each decimal as a fraction or mixed number. -0.14 8.75 0.3 1.4 Continue with independent practice in your handout when done, compare with your partner.

  21. Compare and Order Rational Numbers Answer questions, when done compare with your partner. 1. Give an example of a repeating decimal where two digits repeat. Explain why your number is a rational number. • Write 5.321321321… using bar notation. 3. Identify the fraction that cannot be expressed as the same type of decimal as the other three fractions.; Explain why.

  22. Compare and Order Rational Numbers Answer questions, when done compare with your partner. 1. Give an example of a repeating decimal where two digits repeat. Explain why your number is a rational number. • Write 5.321321321… using bar notation. 5.321 • Identify the fraction that cannot be expressed as the same type of decimal as the other three fractions.; Explain why.

  23. Compare and Order Rational Numbers The table shows the portion of some common materials and products that are recycled. Do we recycle more or less than half of the paper we produce? Explain. Less, 5 is less than half of 11 or 5.5 Do we recycle more or less than half of the aluminum cans? Explain. More, 5 is greater than half of 8 or 4

  24. Compare and Order Rational Numbers Which items have a recycle rate less than one half? paper, glass Which items have a recycle rate greater than one half? aluminum cans, scrap tires Using this estimation method, can you order the rates from least to greatest? No; the rates are being compared to ½ , not to each other.

  25. Compare and Order Rational Numbers Sometimes you can use estimation to compare rational numbers. Another method is to compare two fractions with common denominators. Or you can also compare decimals.

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  27. Compare and Order Rational Numbers

  28. Compare and Order Rational Numbers Explain how to use a number line to determine which of two rational numbers is the lesser number. Sample answer: Graph both numbers on a number line. The number further to the left is the lesser number.

  29. Compare and Order Rational Numbers

  30. Compare and Order Rational Numbers Order the numbers from least to greatest. Then write a rule that helps you compare two positive fractions with the same numerator. Sample answer: When two positive fractions have the same number numerator, the one with the bigger denominator is the smaller number.

  31. Compare and Order Rational Numbers From the least to the greatest, the times are So, the Junior Gemini has the shortest ride time, and the Millennium Force has the longest ride time.

  32. Compare and Order Rational Numbers Closure: Why is it important to express rational numbers as fractions or decimals to compare and order rational numbers. Rational numbers need to be in the same form (all fraction or all decimal) to compare then rational numbers can be ordered in their original form. Who had the better batting average, Stephen Drew or Chris Young? Chris Young .262 batting average

  33. Compare and Order Rational Numbers 1. Explain why 0.28 is less than 0.28. Since 0.28 = 0.280000000 and 0.28 = 0.2828282828… 0.28 is less than 0.28 2. Name two fractions that are less than ½ and two fractions that are greater than ½ .

  34. Compare and Order Rational Numbers Greatest to least; since the numerators are the same, the values of the fractions decrease as the denominators increase.

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