# Operations on Decimal Numbers by j7rBzHO0

VIEWS: 53 PAGES: 55

• pg 1
```									        Place Value
 The place value chart below shows 1247.63
Thousands   Hundreds Tens   Ones   Decimal   Tenths   Hundredths
Point
1          2       4      7       .        6           3

 The number 1248.63 is one more than 1247.63

The number 1147.63 is one hundred less than 1247.63

The number 1247.83 is two tenths more than 1247.63
Review
   Where is the decimal place?

   34
   \$5698
   508
   67.89
HIDDEN DECIMAL
Review
   Arrange each set of numbers from greatest
to least! What strategy did you use?
   A) 1.8, 2.8, 1.9

   B) 365.7, 358, 365.9
Review – Learn Alberta Place Values
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Place_Value/index.html
Review – Adding and Subtracting Decimals
What do you need to do?

1.   Line up the decimals
2.   Add zeros into place values that are empty (if you wish)

3.   Ex: 12.3 + 2. 4 =      12.3           12.3
+ 2.4         + 02.4
14.7           14.7
Review – Adding and Subtracting Decimals
What do you need to do?

1.   Line up the decimals
2.   Add zeros into place values that are empty (if you wish)

3.   Ex: 187.415 + 34.6 =
187.415
187.415
+       34.6                       +     034.600
2.1 Add and Subtract Decimals
Student Outcome: I can use different strategies to estimate decimals.

   Pg 44 Vocabulary:
 Estimate:

   to approximate an answer
   Overestimate:
   Estimate that is larger than the actual answer
   Underestimate:
   Estimate that is smaller than the actual answer
Front-End Estimation
Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #1
   87.85 + 14.60 + 273.52 = 375.97
   80.00 + 10.00 + 200.00 = 290.00

Using front-end estimation: 290 is an ok estimation
Front-End Estimation
Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #2
   537.85 - 174.60 = 363.25
   500.00 - 100.00 = 400.00

Using front-end estimation: 400 is a good estimation
Front-End Estimation
Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #3            49.45 + 239.99 + 87.06 = 376.50
____ + _____ + ____ = _______

Example #4            708 – 45.89 = 662.11
___ - ____ = _________
Relative Size
Student Outcome: I can use different strategies to estimate decimals.

Use Relative Size:
   Estimating each number to the nearest ten, hundred, thousand etc.

Example #1
87.85 + 14.60 + 73.52 = 175.97
 87.85 is between 80 and 90, and closer to 90.00

 14.60 is between 10 and 20, and closer to 10.00

 73.52 is between 70 and 80, and closer to 70.00

90.00 + 10.00 + 70.00 = 170.00
Using relative size: 170.00 is a good estimation
Relative Size
Student Outcome: I can use different strategies to estimate decimals.

Use Relative Size:
   Estimating each number to the nearest ten, hundred, thousand etc.

Example #2              39.01 + 62.77 = 101.78
____ + ____ = ________

Example #3              567.28 – 21.99 + 38.34 = 583.63
_____ - ____ + _____ = _______
Compensation
Student Outcome: I can use different strategies to estimate decimals.

Use Compensation: (try to round up - round down)
   Estimating each number to the nearest ten, hundred, thousand etc.

Example #1
87.85 + 14.60 + 73.52 = 175.97
 87.85 is closer to 90.00 (round up)

 14.60 is closer to 10.00 (round down)

 73.52 is closer to 70.00 (round down)

90.00 + 10.00 + 70.00 = 170.00
Using compensation: 170 is a good estimation
Compensation
Student Outcome: I can use different strategies to estimate decimals.

Use Compensation: (try to round up - round down)
   Estimating each number to the nearest ten, hundred, thousand etc.

Example #2              12.45 + 71.12 – 19.43 = 64.14
____ + ____ - ____ = ____

Example #3              567.89 – 123.00 = 444.89
_____ - _____ = _____
Compatible (Friendly) Numbers
Student Outcome: I can use different strategies to estimate decimals.

Use Compatible numbers: (5’s, 10’s 50’s 100’s 1000’s)

Example #1
87.85 + 14.60 + 73.52 = 175.97

    87.85 is closer to 90 or 85
    14.60 is closer to 10 or 15
    73.52 is closer to 70 or 75

Two possible answers, but still others
90+10+70 = 170       or       85+15+75 = 175
Try It On Your Own!
   Rewrite each question using front-end
estimation.
   A) 45 + 33 + 92 = 170
____ + ____ + ____ = ____

   B) \$475.12 - \$210.38 = \$264.74
_________ - ________ = ________
Is your estimate higher or lower than the calculated
answer? _____________
Try It On Your Own!
   Use any strategy to estimate the answers.

   A) 45 + 33 + 92 = 170
____ + ____ + ____ = ____
____ + ____ + ____ = ____

   B) \$475.12 - \$210.38 = \$264.74
________ - ______ = _______
________ - ______ = _______
Try It On Your Own!
   Using estimation, where would you put the
decimal point in the answer? Why?
   A) 631.5 + 902.4 + 217.83 = 175173
______ + ______+ ______ = _______

   B) \$475.12 - \$210.38= \$26474
_______ - _______ = _______
Try These On Your Own!
   For Homework Due Tomorrow!
   Pg 48. #4, 7, 8ac, 10ac, 14, 20, 21
   Extend 22, 24, 25

   Page 2.1 worksheet
Practical Quiz #1
Using Estimation, fill in the blanks where would
you put the decimal point in the answer?
   A) 81     + 14.074 + 201.897 = 296971
______ + ______    + ______   = _______

   B) \$782.56 - \$258.76 = \$5238
_______ - _______   = _______
Assignment – Let’s go shopping
Student’s will receive their handout to
select their items and money to
purchase merchandise.

\$500.00
Multiplying Decimal Numbers
Student Outcome: I can estimate by +,-,x,÷ decimals.

   Problem: Page 52
   Ashley and Marshall’s family keep busy travelling
across the country by solving sudoku puzzles!
During a stop, they look in a convenience store for
more puzzles.
   Marshall finds sudoku books on sale for \$1.69. he
wants to buy five books and has \$9.00.
   Help him estimate the total cost of the five puzzle
books!
   \$1.69 x 5 = ______?
Multiplying Decimal Numbers
Student Outcome: I can estimate by +,-,x,÷ decimals.

   1. Marshall estimates the total bill as \$5.00
   a) How do you think Marshall got his estimate?
   b) Is Marshall’s estimate over or under the total?
   How do you know?
   2. Ashley estimates the total bill as \$10.00
   a) How do you think Ashley got her estimate?
   b) Is Ashley’s estimate over or under the total?
 How do you know?
DID YOU
KNOW!!!!
Sudoku
 Sudoku was invented hundreds
of years ago, and traded around
the world by ancient
mathematicians.
Each digit from 1 to 9 must occur
in:
Each row
Each column
Each 3 x 3 square.
Multiplying Decimals
Student Outcome: I can estimate by +,-,x,÷ decimals.

   Use front-end estimation and relative size to
estimate:
   2.65 x 3.72
   Front-End Estimation:

   Relative Size:
Multiplying Decimals
Student Outcome: I can estimate by +,-,x,÷ decimals.

Estimate to make sure your answer is reasonable!
 Multiply 1.54 x 25

   What strategy will you use?
Multiplying Decimals
Student Outcome: I can estimate by +,-,x,÷ decimals.

   Use a calculator to solve the equation:
Multiply 1.54 x 25

   Things I know:     25 x 1 = 25
   Things I know      25 x 2 = 50

   Why would the answer lie between 25 and 50.
Multiplying Decimals
Student Outcome: I can estimate by +,-,x,÷ decimals.

   Using paper and pencil
   Multiply without decimals add decimals to
product
   Estimate an answer. Why?

   Ex: 2.6 x 3.7=                26
x 37
962
Multiplying Decimals Learn Alberta

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

Slides 1-5
Practice Makes Perfect
   Page 57
   3, 6ab, 9, 13, 14,17
   Extend 20, 21
Dividing Decimal Numbers
Student Outcome: I can estimate by +,-,x,÷ decimals.

   Example 1:
   A) 15.4 ÷ 3.6 = 4.27778

Front-End Estimation:
 Things I know: 15 ÷ 3 = 5

   The answer closest to 5 is 4.27778
Dividing Decimal Numbers Using a Number Line

Ex: 10 ÷ 2 =
Use Estimation to Place the Decimal Point.
Student Outcome: I can problem solve using decimals.

   Example #2:
Four friends buy 1.36L of pure orange juice and
divide it equally.
   A) Estimate each person’s share.
   B) Calculate each person’s share.
Use Estimation to Place the
Decimal Point.
   Solution:
   A) To estimate, round 1.36L to a number that is
easier to work with.
   Try 1.2                                12 ÷ 4 = 3 So
1.2 ÷ 4 = 0.3
   1.2 ÷ 4 = 0.3 Underestimate
   Try 1.
   1.6 ÷ 4 = 0.4 Overestimate

16 ÷ 4 = 4 So                     Things I know
1.6 ÷ 4 = 0.4
Dividing Decimals
Student Outcome: I can problem solve using decimals.

   Problem Questions:
   1. How many pens do you think you can buy
with \$6.00 if one pen costs \$0.40
 Use both front-end estimation and relative

size estimation to find your educated guess.

Strategy Used:
Working Together!!
   Pg 66 #10
   A package of 7 fish hooks costs \$17.99
   How much will one fish hook cost?
1)   Estimate
2)   Calculate- by hand and with calculator
3)   Did you over/under estimate?

ANSWER:        \$17.99 ÷ 7 = \$2.57
Working Together!
   Pg 66 #11
   Ashley wants to find how many 355 mL cans
of juice are in a 2-L bottle.
   A) Show Ashley how to estimate the answer

   B) Show Ashley how to calculate the answers
Practical Quiz #2
What is the cost of each purchase before tax?

Show your work!!

3 oatmeal cereal bars for \$7.50
Dividing Decimals Learn Alberta
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

Slides 6-10
Assignment
   Page 65 – 67
   #4, 8, 12, 13, 14, 17, 19
   Extend #21, 22
BEDMAS
Student Outcome: I can solve problems using order of operations.

   Remember the order by the
phrase
   B - BRACKETS
   E - EXPONENTS
   D/M – DIVIDE OR MULTIPLY
   A/S – ADD OR SUBTRACT
The “B” and “E”
Student Outcome: I can solve problems using order of operations.

   The “B” stands for items in brackets
   Do all items in the brackets first

(2 + 3)
The “E” stands for Exponents
Do anything that has a exponent (power)

8 2
The “DM”
Student Outcome: I can solve problems using order of operations.

   Represents divide and multiply
   Do which ever one of these comes first
in the problem

Work these two operations
from left to right
The “AS”
Student Outcome: I can solve problems using order of operations..

   Represents Add and Subtract
   Do which ever one of these comes first
   Work left to right
   You can only work with 2 numbers at a
time.
1) 5 + (12 – 3)   2) 8 – 3 x 2 + 7
5+ 9              8 - 6 +7
14                2 + 7
9
3) 39 ÷ (9 + 4)
39 ÷ 13
3
4)   10 + 8 ÷ 2 – 6   5)   15 x 103
10 + 4 - 6           15 x 1,000
14 - 6               15 000
8
6)   36 ÷ (1 + 2)2     7) 3 x 104
36 ÷ 32              3 x 10 000
36 ÷ 9                30 000
4
8)   (5 – 1)3 ÷ 4   9)   14 + 3(7 -2) – 2 x 5
43 ÷ 4            14 + 3 x 5 - 2 x 5
64 ÷ 4            14 + 15 - 2 x 5
16               14 + 15 – 10
29 – 10
19
Order of Operations – Learn Alberta
    http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.
INTE&lesson=html/object_interactives/order_of_operations/use_it.html
Let’s Practice
Student Outcome: I can solve problems using order of operations.

   Place the operations shown in square
brackets to make each statement true.
   9__ 5__5 = 50     (+, x)

   15 __ 3 __2 = 24 (x,-)
Let’s Practice
Student Outcome: I can solve problems using order of operations.

   What are the missing numbers?

   A) _____ + 5 x 6 = 32

   B) _____ - 3.2 ÷ 0.5 = 5
Practical Quiz #3
Solve. Show all your steps.
a) On the front:   18 + 3 – 3 x 5

b)   On the back   (2 x 3) – 4 + 8 ÷ 4
Assignment
   Page 71-73
   # 5, 6ab, 7ab, 9ab, 11, 14, 17, 18a, 19
   Extend #22, 23, 24
Assignment – Chapter Review
   Page 74-75
   #1-4, 5ab, 6ab, 7ab, 8, 9ab, 10-12,
13ab, 14ab, 15, 16, 17ab, 18ab, 19ab,
20ab
Assignment – Wrap it Up!!
   Page 77

   This will be completed at home using a
computer. Please fill in all blanks with
parent.
   Student to receive handout for support.
GAME – Page 78

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