Bell work

How else can I describe the portion? How many pieces are in the whole?  Yesterday, you worked with different fractions and found ways to rewrite those fractions as repeating and terminating decimals.  In this lesson, you will reverse your thinking and will instead represent decimals as fractions.  As you work with your team today, ask each other these questions to focus your discussion: How else can I describe the portion? How many pieces are in the whole?

2-18. Complete the Representations of a Portion Web for each number below. An example for  2 3 is shown. 7 10 b. 0.75 c. Three-fifths 5 8 e. With your team, explain how you rewrote 0.75 as a fraction in part (b). Is there more than one way?  Be as specific as possible.

2-19. Since 0.7 is described in words as “seven-tenths,” it is not a surprise that the equivalent fraction is  7 10    .  Use the names of fractions (like “twenty-three hundredths”) to rewrite each terminating decimal as a fraction.  First try to use what you know about place value to write the fraction. With your calculator, check to be sure the fraction is equal to the decimal. a. 0.19 b. 0.391 c. 0.001   d. 0.019 e. 0.3 f. 0.524   

2-21. Katrina is now responsible for finding the decimal equivalent for each of the numbers below.  She thinks these fractions have something to do with the decimals and fractions in problem 2-19, but she is not sure. Use your calculator to change each fraction into a decimal.  Add the decimal information to the card.  Can you find a pattern?   19 99   d. 1 999   391 999   e. 524 999 c.     3 9 f. 19 999      g. What connections do these fractions have with those you found in problem 2-19?  Be ready to share your observations with the class. h. Use your pattern to predict the fraction equivalent for      .  Then test your guess with a calculator.  i. Use your pattern to predict the decimal equivalent for 65 99    .  Check your answer with your calculator.

2-22. REWRITING REPEATING DECIMALS AS FRACTIONS                     Jerome wants to figure out why his pattern from problem 2-21 works.  He noticed that he could eliminate the repeating digits by subtracting, as he did in this work:   This gave him an idea.  “What if I multiply by something before I subtract, so that I’m left with more than zero?” he wondered.  He wrote: “The repeating decimals do not make zero in this problem.  But if I multiply by 100 instead, I think it will work!”  He tried again:

2-22 continued…. Discuss Jerome’s work with your team.  Why did he multiply by 100?  How did he get 99 sets of      ?  What happened to the repeating decimals when he subtracted?  “I know that 99 sets of        are equal to 73 from my equation,”Jerome said.  “So to find what just one set of        is equal to, I will need to divide 73 into 99 equal parts.”  Represent Jerome’s idea as a fraction.  Use Jerome’s strategy to rewrite       as a fraction.  Be prepared to explain your reasoning.

2-23. DESIGN A DECIMAL DEPARTMENT Congratulations!  Because of your new skills with rewriting fractions and decimals, you have been put in charge of the Designer Decimals Department of the Fraction Factory.  People write to your department and order their favorite fractions rewritten as beautiful decimals. Recently, your department has received some strange orders.  Review each order below and decide if you can complete it.  If possible, find the new fraction or decimal.  If it is not possible to complete the order, write to the customer and explain why the order cannot be completed.   Order 1:  “I’d like a terminating decimal to represent  44 99 .” Order 2:  “Could you send me 0.208 as two different fractions, one with 3000 in the denominator and one with 125 in the denominator?” Order 3:  “Please send me   written as a fraction.”

Practice: Convert from fraction to decimal 1 20 37 20 11 20 69 50 5. 11 25 6. 31 25 7. 7 8 8. 4 10 Extra Practice: http://www.math-drills.com/fractions/fractions_convert_to_decimal_001.html