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Module7.2Lessons13and14.notebook
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October20,2015
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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Haveyoueverseenarecipecallfor2.7cupsofflour?Whyorwhynot?
Howdoyouthinkpeoplewouldreactifalocalgasstationpostedthepriceofgasolineasdollarspergallon?Why?
Whydoweneedtoknowhowtorepresentrationalnumbersindifferentways?
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Place Value
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S.65
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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.
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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
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Exercise 1:
Convert each rational number to its decimal form using long division
a.
b.
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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.
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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:
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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?
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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