module 7.2 lessons 13 and 14

Module7.2Lessons13and14.notebook

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10/20/15Module 7.2, Lessons 13 and 14

HW: Lesson 13 #1 and 2Lesson 14 #1

Do Now:

Module 2 Lesson 14 Sprint

Converting Between Fractions and Decimals

Using Equivalent Fractions


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Math Sprint

RULES

You will have 3 minutes to answer as many problems as you can.


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2


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Haveyoueverseenarecipecallfor2.7cupsofflour?Whyorwhynot?

Howdoyouthinkpeoplewouldreactifalocalgasstationpostedthepriceofgasolineasdollarspergallon?Why?

Whydoweneedtoknowhowtorepresentrationalnumbersindifferentways?


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Place Value


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S.65


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S.66


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S.66


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S.67


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S.68


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S.68


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CLOSING:

Whenaskedtowriteadecimalvalueasafraction(ormixednumber),howdowedeterminethevalueofthedenominator?


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Example 1: Can All Rational Numbers Be Written as Decimals?

a. Using the division button on your calculator, explore various quotients of integers 1 through 11. Record your fraction representations and their corresponding decimal representations in the space below.

b. What two types of decimals do you see?

S.70


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Example 2: Decimal Representations of Rational Numbers

In the chart below, organize the fractions and their corresponding decimal representations listed in example 1 according to their type of decimal.

What do these fractions have in common? What do these fractions have in common?

Terminating Non-Terminating

The denominators are only divisible by factors of 2's and 5's.

The denominators are only divisible by another factor other than factors of 2's and 5's.

S.70


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Example 3: Converting Rational Numbers to Decimals Using Long-Division

Use the long division algorithm to find the decimal value of

S.71


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Exercise 1:

Convert each rational number to its decimal form using long division

a.

b.

S.71


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Example 4: Converting Rational Numbers to Decimals Using Long-Division

Use long division to find the decimal representation of S.72


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What part of your calculation causes the decimal to repeat?

Question:


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Exercise 2

Calculate the decimal value of the fraction below using long division. Express your answers using bars over the shortest sequence of repeating digits.

a. b.

c. d.

S.72


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Exercise 2

Calculate the decimal value of the fraction below using long division. Express your answers using bars over the shortest sequence of repeating digits.

a. b.

c. d.

S.72


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Example 5: Fractions Represent Terminating or Repeating Decimals

How do we determine whether the decimal representation of a quotient of two integers, with the divisor not equal to zero, will terminate or repeat?

Iftheremainderiszero:

Iftheremainderisnotzero:

S.73


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Example 6: Using Rational Number Conversions in Problem Solving

a. Eric and four of his friends are taking a trip across the New York State Thruway. They decide to split the cost of tolls equally. If the total cost of tolls is $8, how much will each person have to pay?

b. Just before leaving on the trip, two of Eric's friends have a family emergency and cannot go. What is each person's share of the $8 toll now?

S.73


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Closing:

1.) What should you do if the remainders of a quotient of integers do not seem to repeat?

2.) What is the form for writing a repeating decimal?


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Attachments

SprintAnswerKeyMod2Lesson13.docx

Module 2 Lesson 5 Sprint 1Number Correct: _______

Round 1

1. (-2)(-1)

3

23. (9)(-2)

-18

2. (-5)(-6)

30

24. (-6)(-9)

54

3. (-11)(2)

-22

25. -10 5

-2

4. (11)(-2)

-22

26. -18 (-3)

6

5. (-11)(-2)

22

27. 21 (-7)

-3

6. (-3)(6)

-18

28. (-8)(-4)

32

7. (4)(8)

32

29. (-12)(4)

-48

8. (-6)(-6)

36

30. (5)(-1)

-5

9. (-1)(13)

-13

31. -12 6

-2

10. (-6)(0)

0

32. -15 -3

5

11. (9)(-4)

-36

33. 24 (-6)

-4

12. 25 (-5)

-5

34. (-2)(-1)(-5)

-10

13. -30 (-6)

5

35. (-3)(0)(4)

0

14. 30 (-5)

-6

36. (-2)(4)(-1)

8

15. -45 9

-5

37. (-2)(-2)(2)

8

16. 50 (-10)

-5

38. (-2)(2)(-2)

8

17. -28 (-4)

7

39. (-8)(-7)(-2)

-112

18. 36 6

6

40. (-8)(-6) (-2)

-24

19. -99 11

-9

41. (-4)(5) (-2)

10

20. -16 4

-4

42. (5)(-6) 15

-2

21. -250 (-10)

25

43. (12)(2) (-4)

-6

22. 144 (-12)

-12

44. (-82)(-71)(0)

0

Module 2 Lesson 5Number Correct: _______

Round 2

1. (-5)(-2)

10

23. (12)(-2)

-24

2. (-5)(2)

-10

24. (-6)(-4)

24

3. (-10)(4)

-40

25. -25 5

-5

4. (10)(-4)

-40

26. -18 (-6)

3

5. (-10)(-4)

40

27. 35 (-7)

-5

6. (-2)(6)

-12

28. (-8)(-3)

24

7. (4)(7)

28

29. (-12)(3)

-36

8. (-3)(-3)

9

30. (8)(-1)

-8

9. (-2)(15)

-30

31. -48 6

-8

10. (-7)(0)

0

32. -15 3

-5

11. (9)(-5)

-45

33. 24 (-8)

-3

12. 45 (-5)

-9

34. (-3)(-1)(-5)

-15

13. -36 (-6)

6

35. (-3)(0)(5)

0

14. 50 (-5)

-10

36. (-2)(5)(-1)

10

15. -36 9

-4

37. (-3)(-3)(3)

27

16. 60 (-10)

-6

38. (-3)(-3)(3)

27

17. -28 (-7)

4

39. (8)(-2)(-2)

32

18. 36 4

9

40. (-5)(-6) (-2)

-16

19. -99 -11

9

41. (-4)(3) (-2)

6

20. -44 4

-11

42. (-5)(-6) 15

2

21. -200 (-10)

20

43. (12)(3) (-4)

-9

22. 63 (-7)

-9

44. (-90)(-70)(0)

0

SMART Notebook

Page 1: Oct 18-9:01 AMPage 2: Oct 30-8:10 AMPage 3: Nov 19-8:24 AMPage 4: Nov 19-8:25 AMPage 5: Nov 5-1:13 PMPage 6: Nov 20-1:06 PMPage 7: Nov 5-10:20 AMPage 8: Nov 5-1:25 PMPage 9: Nov 5-1:29 PMPage 10: Nov 19-11:46 AMPage 11: Nov 19-11:44 AMPage 12: Nov 19-11:44 AMPage 13: Oct 29-9:51 AMPage 14: Nov 5-8:53 AMPage 15: Nov 5-9:05 AMPage 16: Nov 5-9:08 AMPage 17: Nov 5-9:12 AMPage 18: Nov 5-9:26 AMPage 19: Nov 5-9:32 AMPage 20: Nov 5-9:31 AMPage 21: Nov 5-9:31 AMPage 22: Nov 5-9:43 AMPage 23: Nov 5-9:51 AMPage 24: Nov 5-9:54 AMPage 25: Nov 19-11:47 AMAttachments Page 1

module 7.2 lessons 13 and 14

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