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Working with Rational Numbers

Working with Rational Numbers. I will demonstrate that fractions that terminate will have denominators including only prime factors of 2 and/or 5. I will convert repeating decimals into their fraction equivalent using patterns or algebraic reasoning.

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Working with Rational Numbers

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  1. Working with Rational Numbers • I will demonstrate that fractions that terminate will have denominators including only prime factors of 2 and/or 5. • I will convert repeating decimals into their fraction equivalent using patterns or algebraic reasoning. • I will investigate repeating patterns that occur when fractions have a denominator of 9, 99, or 11.

  2. Write a terminating decimalas a fraction • 0.45 = • -0.16 = • 5.55 = • -0.35 = • 7.32 = • 0.6 =

  3. Write a repeating decimal as a fraction • You have to use algebraic reasoning to turn repeating decimals into a fraction. . . • For example, to write 0.5 or 0.555 as a fraction you have to use a formula to find the correct approximation of the repeating decimal. • Since 0.5 is repeating and the bar notation is over the 5 ONLY and the 5 is in the 10’s place, then we need to use a formula to get our approximation.

  4. Here’s the formula. . . • Let N = 0.5 or 0.555. . . Then 10N = 5.555. . . (you multiply N by 10 because only 1 digit repeats.) Subtract N=0.555 to eliminate the repeating part, 0.555 10N = 5.555 -1N = 0.555 9N = 5 9N = 5 9 = 9 N = 5 9

  5. Now, lets try this together. . . • -0.2 • -0.4 • 3.6 • 2.7 • -4.21 • -3.72

  6. Multiply Rational Numbers • 1/3 x 2/5 = • 3/4 x 1/2 = • 2/5 x 2/3 = • 1/4 x 3/5 = • 2/3 x 4/5 =

  7. Multiply Mixed Rational Numbers • 4 ½ x 2 2/3 = • 1 ½ x 1 2/3 = • 5/7 x 1 3/5 = • (-2 1/6)(-1 1/5) =

  8. Divide Rational Numbers • 7/8 ÷ 3/4 = • 2/5 ÷ 5 = • -4/5 ÷ 6/7 = • 6/7 ÷ 12 =

  9. Now, you try. . . • Write each repeating decimal as a fraction in simplest form. • 0.3 = • -1.4 = • -0.5 = • 2.1 = • 3.12 =

  10. Keep trying. . . • Multiply or divide the following rational numbers. • 3/5 x 5/7 = • 1 1/3 x 5 ½ = • -1/8 x 4/9 = • (-4/5)(-4/5) = • 2 ¾ ÷ (-2 1/5) = • 1 ½ ÷ 2 1/3 = • -3 ½ ÷ (-1 ¼) =

  11. Your assignment for today. . . • On p.619: ~ Lesson 2-1 (at the top of the page) 14 to 24 even problems ~ Lesson 2-3 (at the bottom of the page) 1 to 11 odd problems ~ Lesson 2-4 (at the top of p.620) 9 to 31 odd problems

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