1. Bellwork:
We will do a Number Talk today.
Monday

4. Multiplying and Dividing Fractions and Decimals

5. Fractions Review
Common Denominator- a number with which both of the denominators share at least one factor that is not the number 1
For 4 and 7, then a common denominator is 28.
Improper Fraction- the numerator is larger than the denominator
8 5
Mixed Number- whole number with a fraction
2 1 6
Simplify- reduce the numerator and the denominator by the same number
÷4 ÷4 = 2 3

6. Multiplying Fractions Review
Multiply straight across, then simplify
numerator x numerator
denominator x denominator
5 7 x =
x =

7. Dividing Fractions Review
Change division to multiplication by taking the reciprocal (flipping numerator and denominator)
Multiply straight across, then simplify
numerator x numerator
denominator x denominator
5 7 ÷ =
÷ =

8. Multiply and divide with negatives
Use the same rule for integers:
Same signs are POSITIVE
P x P = P
N x N = P
Different signs are NEGATIVE
P x N = N
N x P = N
The negative sign could be…
in front of the fraction - 1 2
On the numerator −1 2
On the denominator 1 −2
***If there is a negative sign on both the numerator and the denominator, it is positive ( 2 negatives make a
positive) −1 −2 = 1 2

9. Examples

10. Multiplying decimals Review
Multiply (ignoring decimals)
Count the total number of decimal places are in the problem
Move your decimal that many places to the left
1.23(3.5) =
1.456 x 2.2 =

11. Dividing decimals Review
The first number or the numerator goes inside
The second number or denominator is on the outside
If you have a decimal number on the outside:
Move the decimal to the right until you have a whole number
Move the decimal inside the same number of spaces as you did on the outside
Put the decimal point directly above where it is inside
Add zeroes as needed (you may not use a remainder)
4.16 ÷ 0.8= =

12. Multiply and divide with negatives
Use the same rule for integers:
Same signs are POSITIVE
P / P = P
N / N = P
Different signs are NEGATIVE
P / N = N
N / P = N

13. Examples

14. Practice Book Pg. 390

15. Bellwork:
Combine like terms using your integer rules.
tUESDAY

16. Adding and subtracting fractions and decimals

17. Adding and subtracting Fractions Review
Make sure you have common denominators
Adjust your numerators if necessary
Add/Subtract numerators straight across
Use the same denominator
Make mixed numbers (if necessary)
How many times can the denominator go into the numerator? That’s the whole number
What's leftover? That’s the numerator = =

18. Add and subtract with negatives
Use the same rule for adding integers:
Same signs, ADD
P + P = P
N + N = N
Different signs, SUBTRACT
N + P = depends
P + N = depends
The negative sign could be…
in front of the fraction - 1 2
On the numerator −1 2
On the denominator 1 −2
Use the same rule for subtracting integers:
BOX IT
KEEP the 1st number the same
Change subtraction to ADDITION
Take the OPPOSITE of the second number
Then follow addition rules
***If there is a negative sign on both the numerator and the denominator, it is positive ( 2 negatives make a
positive) −1 −2 = 1 2

19. Examples

20. Adding and subtracting decimal Review
Line up your decimals
You may have to add zeroes after the decimal point
Add/ Subtract like you normally would
Bring down your decimal
1.23−0.5 = =

21. Add and subtract with negatives
Use the same rule for adding integers:
Same signs, ADD
P + P = P
N + N = N
Different signs, SUBTRACT
N + P = depends
P + N = depends
Use the same rule for subtracting integers:
BOX IT
KEEP the 1st number the same
Change subtraction to ADDITION
Take the OPPOSITE of the second number
Then follow addition rules

22. Examples

23. Practice Book Pg. 384

24. wEDNESDAY Bellwork: Angles- obtuse, acute, right
Classify each triangle by its sides and angles. Equal sides and equal angles, if any, are indicated in each diagram.
Sides- scalene, isosceles, equilateral
Angles- obtuse, acute, right
wEDNESDAY

28. All Operations with rational Numbers

29. Individual Practice Work on a column at a time Get checked If correct:
Try the next column for a chance to earn bonus points
If incorrect:
Fix your mistakes and try another column for an opportunity to get a 100%

30. Individual Practice: AC
Work on half the sheet at a time
Get checked
If correct:
Try the next half for a chance to earn bonus points
If incorrect:
Fix your mistakes and try the other half for an opportunity to get a 100%

31. Agenda: Worksheet due Tuesday for a grade if you did not finish
Bellwork:
David wants to fill his backyard swimming pool. His garden hose delivers 40 gallons in 5 minutes. How many gallons of water will be in the pool after 20 minutes? 1 hour?
Show Your Work
20 min. ______________
1 hour _______________
Thursday
Agenda: Worksheet due Tuesday for a grade if you did not finish

32. Terminating and Repeating Decimals

33. Step One - Divide
Divide 3 into the first number in the dividend.
3 will go into 4 one time.
Write a 1 above the 4 because that’s the current dividend. 1
3) 495

34. Step Two - Multiply
Multiply the divisor times the first number in the quotient.
Write the answer below the number you just divided into. 1
3) 495 3

35. 1 3) 495 3 1 Step Three - Subtract Subtract.
Be sure to line up your numbers carefully. 1
3) 495 3 1

36. Step Four – Bring Down
Draw an arrow and bring the second digit in the dividend down. 1
3) 495 3 1 9

37. Step Five – Repeat
Repeat the steps in the same manner as before, as shown in the next set of slides. 1
3) 495 3 1 9

38. Repeat Step One - Divide
Divide 3 into the new number.
3 will go into 19 six times.
Write a 6 above the 9 because that’s the current dividend. 1 6
3) 495 3 1 9

39. Repeat Step Two - Multiply
Multiply the divisor into the new number in your quotient.
3 x 6 = 18
Write 18 below the number you just divided into. 1 6
3) 495 3 1 9 18

40. Repeat Step Three - Subtract1 6
3) 495 3 1 9 18 1

41. Repeat Step Four – Bring Down1 6
If there are more digits in the dividend, repeat the procedure.
Bring the third digit in the dividend down.
3) 495 3 1 9 18 1 5

42. Repeat Step Five – Repeat1 6 5
If there are more digits in the dividend, repeat the procedure.
If there are no more digits in the dividend, write the final subtraction answer as a remainder.
If there is no remainder, you’re finished! Pat yourself on the back for a job well done.
3) 495 3 1 9 18 1 5 15

43. When you have a fraction…
Begin long division
Add decimal and zeros as needed
Align decimal and divide

44. Express as a decimal. Example: 3 7 5 Begin long division . 8 3 .003 7 5
Begin long division . 8 3
.00
Add decimal and zeros as needed
-24
Align decimal and divide 6
-56
Answer will: 4
-40
* Terminate OR
* Repeat

45. The top number ALWAYS gets “caught” in the division box.
Example: =
= .625
*Remember:
The top number ALWAYS gets “caught” in the division box.
Also: when dividing don’t forget your decimal, line up your answer, and add zeros as needed to bring down.

46. Express
as a decimal.
You try: 7 5 . 4 3
.00
-28 2
-20

47. A decimal that stops or “terminates” is a terminating decimal
If the same block of digits in a decimal repeats without end, the decimal is a repeating decimal
Show a repeating block by putting a bar over the repeating digits. = =
Example:

48. Here is another example and a few to try
Here is another example and a few to try. *remember- divide the numerator by the denominator.
Example:
Now you try a few: 1. 2. 3.

49. Repeating Decimals
Try a few: 1)
( …) = 2) =
( …)

50. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟓 𝟖

51. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟐 𝟔

52. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟒 𝟓

53. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟕 𝟖

54. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟓 𝟗

55. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟑 𝟓

56. Whiteboard Practice!
Change to decimal then determine whether its terminating or repeating
𝟓 𝟏𝟎

57. Accelerated: How to turn a repeating decimal into a fraction
Write as a fraction.
x = .33
100x =
- x = x
99x = 33
= 99
X = or 1 3

58. Accelerated: How to turn a repeating decimal into a fraction
Write .89 as a fraction. x = .89

59. Accelerated: How to turn a repeating decimal into a fraction
Write .6 as a fraction. x = .6

60. Accelerated: How to turn a repeating decimal into a fraction
Write .724 as a fraction. x = .724

61. Agenda: Worksheet due Tuesday for a grade if you did not finish
Bellwork:
You have a Bellwork Quiz today.
You may get out your bellwork 1- 4 to use for your quiz.
fRIDAY
Agenda: Worksheet due Tuesday for a grade if you did not finish

62. Terminating and Repeating Decimals

63. Challenge Questions
Write a fraction that is equivalent to a terminating decimal between 0.5 and 0.75.

64. Challenge Questions The value of pi is 3.1415926…
A mathematician, Archimedes, believed that pi was between and Was he correct?

65. Challenge Questions
A unit fraction is a fraction that has 1 as its numerator. Write the four greatest unit fractions that are repeating decimals.

66. Challenge Questions
Fractions is simplest form that have denominators of 4, 8, 16, and 32 produce terminating decimals.
Fractions is simplest form that have denominators of 6, 12, 18, and 24 produce repeating decimals.
What causes the difference?

67. Start Practice sheet due Thursday

68. Bellwork:
mONDAY

69. All Operations with rational Numbers

70. Bellwork:
Tuesday

71. All Operations with rational Numbers-word problems

72. WEDNESDAY Review K z B GRAB SHEET FROM BACK TABLE
Fill in MATH board with letters A-Z in the alphabet:
Put letters in board randomly & only use once!
MUST USE MARKER!!!
Do not put letters in order
Do not try to spell words 
Have out a blank sheet of paper K z B
WEDNESDAY Review

73. Rational Review

74. Fill in the blanks with the choices to the right by comparing the rationals.
___________ < ______________ < _____________
- 𝟖 𝟏𝟐
-0.59
-0.7

75. At 10 am, Jane began a shopping spree using her credit card
At 10 am, Jane began a shopping spree using her credit card. By 3 pm, her bank account balance was -$ If her balance changed by -$10.50 per hour, how much did Jane have at 10 am before she began shopping?

76. Solve:
12(-3)=
-27 / -3=
-18 – 20 = =

77. Which situation can be described using this number line?
The temperature decreases by 5 degrees and then increases by 7 degrees.
John loses $3 then finds $4.
On the first play, the football team lost 5 yards. On the next play, the football team gained 4 yards.

78. Label each fraction Terminating (T) or repeating (R)
25 99
18 48
2 9
9 80

79. On December 30th, the temperature was -11°F in the afternoon
On December 30th, the temperature was -11°F in the afternoon. By the evening, the temperature dropped 6 degrees. The next day, on December 31st, the temperature rose 14 degrees. What was the temperature on December 31st?

80. Peggy has $200 in her piggy bank
Peggy has $200 in her piggy bank. She take out of the money in order to buy a new bike. Out of the money she took from her piggy bank, she only used to purchase the bike. How much money does Peggy have leftover from her bike purchase that can be returned to her piggy bank?

81. Order least to greatest: 𝟐 𝟑 , 0.66, 𝟔 𝟏𝟎 , 0.06, 0.555

82. Choose all fractions that simplify to -10 -2 ¼(-4 ½) -66 ¼ ÷ 6 5 8 -10 1 6 – 1 6 -5 1 3 + (-4 2 3 )

83. In Bill’s family, both parents can eat ¾ of an 8-slice pizza on their own and all 3 children can eat ¼ of an 8-slice pizza on their own. Due to a mistake made by Pizza Plus, the family only received two 8-slice pizzas. How many MORE SLICES does the family need to fill up on pizza?

84. Have out cover sheet and pencil
After
the
test:
Thursday: Test

85. Test

86. After the Test Challenge:
fRIDAy

87. Finish Test/ Challenge question