1. F OCUS 1: P ROPORTIONAL R EASONING Standards: 7.RP.1, 7.NS.2d, 7.NS.3, 7.EE.4a, 7.G.1 Resource: Connected Math Program 2 Bits and Pieces III: Investigation 3.4

2. B ITS AND P IECES III Computing with Decimals and Percents Investigation #3.4- CMP2

3. M ATHEMATICAL & P ROBLEM -S OLVING L EARNING G OAL : I NV. 3.4 R EPRESENTING F RACTIONS AS D ECIMALS Understand and predict the decimal representation of a fraction (terminating or repeating)

4. G ETTING R EADY FOR P ROBLEM 3.4 Last year, you learned that you can express any fraction with a whole number numerator and a whole number denominator as a decimal by dividing the numerator by the denominator. What do you notice about these fractions converted into decimals?

5. V OCABULARY T ERMS ! The fractions ½ and ¼ have decimal representations that end or terminate. Decimals like these are called terminating decimals. Notice that 1/3 and 1/11 have decimal representations that repeat over and over. Decimals like these are called repeating decimals.

6. You know that decimals are easy to write as fractions with 10, 100, 1000, etc. in the denominator. You can see that fractions with 10, 100, 1000, etc. in their denominators have terminating decimal forms. 1. Why do fractions like ½ and ¼ also have terminating decimal forms? 2. Are there fractions equivalent to ½ and ¼ that have 10, 100, 1000, etc. as their denominators? 0.23 = 23/100 0.7 = 7/10 0.070= 70/1000

7. C ONTINUE …. 3. What are some other fractions that are terminating? 4. How do you know that 1/8 can be expressed as a terminating decimal? 5. Is there another way to show that 1/8 is a fraction with a power of 10 in the denominator? 6. What other fractions are equivalent to the decimal 0.125?

8. 3.4 R EPRESENTING FRACTIONS AS D ECIMALS A. Write each fraction as a decimal. Tell whether the decimal is terminating or repeating. If it is repeating, tell which digits repeat. 2/53/85/635/108/99 For the fractions that have terminating decimal forms, try to find an equivalent fraction that has 10, 100, 1000, etc. as a denominator.

9. Part B: 1. Find two other fractions that have a terminating decimal form. 2. For each fraction you found in part 1, write three fractions that are equivalent. 3. Find the decimal form for the fractions you found in part 2. 4. What do you notice about the decimal form for a set of equivalent fractions?

10. Part C: Find a fraction that is equivalent to each of the following terminating decimals. 0.352.145689.0502.14560 Explain how your answers for 2.1456 and 2.14560 compare.

11. Part D 1. Find three fractions that have repeating decimals forms. 2. Can you find an equivalent form for any of these fractions that has 10, 100, 1000, etc. in the denominator? Why or why not?

12. Part E 1. Describe any differences in the forms of repeating and terminating decimals that you have found.

13. E XPLORE 3.4 H AVE YOU THOUGHT ABOUT ?  Examine the factors of the denominators of the fractions  Can you find fractions equivalent to ones you are considering that have smaller denominators?  Consider the factors of the denominator to be sure you have all fractions with smaller denominators as referred to as simplifying the fraction.

14. C LASS D ISCUSSION AND S HARING  The question we want to answer is, “How can you tell if a fraction has a repeating or a terminating decimal form?”  What kinds of denominators of fractions in lowest terms seem to give terminating or repeating decimal forms?  Look at our list carefully and see whether you can come up with some ideas.

15. P RE -A LGEBRA H OMEWORK A.C.E Application, Connections, & Extensions #25, 26, 27, 35-40 Copy your answers in your math workbook