Transcript Percents - Notre Dame Academy

Fractions, Decimals, and
Percents
Video Support
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=l
essons
Learn Alberta: percents
4.1 Connect Fractions,
Decimals, and Percents
Assignment: Let’s go shopping
You have $1000.00 to spend for Christmas.
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From magazines you will cut out 7 items
5 sale items will be on sale (include sale discounts)
Subtotal
GST (5%)
Total
Proper rounding (2 decimal places)
Items will be glued to a piece of paper with a “formal” bill
attached.
BONUS – one separate item will be a double discount
Mystery Shopper will receive a prize for spending as close to
$1000.00 without going over.
Assignment:
Let’s go shopping
ITEM
Original
Price
Percent
Reduced
Discount
Amount
(.0000)
1.
2.
3.
4.
5.
6.
7.
Subtotal
GST
Total
Discount
Amount
(.00)
Final
Price
Marking Rubric
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7 items
5 correct discounts (proper rounding)
2 correct regular items (proper rounding)
Correct Subtotal
Correct GST
Correct Total
1 double discount (proper rounding)
TOTAL
Parent Signature
_______________________________
7 marks
5 marks
2 marks
1 mark
1 mark
1 mark
2 marks
/19
Student Objective:
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After this lesson, I will be able to…
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Estimate percents as fractions or as decimals
Compare and order fractions decimals, and
percents
Estimate and solve problems involving percent
Percent
Student Objective: I will be able to problem solve using percents from 1%-100%
 What does it mean??
 “out of 100”
 Ex: 20 out of 100 or 20% or 20 or 0.20
100
“of” means x
Percent
Student Objective: I will be able to problem solve using percents from 1%-100%
Ex: 64% = 64 = 0.64
100
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Ex: 91% =
=
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Ex: 37% =
=
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Bonus
Ex: 107% =
=
Think Money
$0.10
1/10 of a dollar
10% of a dollar
$0.25
¼ of a dollar
25% of a dollar
$0.50
½ of a dollar
50% of a dollar
“Friendly” Percents
Discuss with your partner
What are FRIENDLY percent numbers “percentages”
to work with? and why?
“Friendly” Percents
25%
50%
75%
100%
Friendly Percent Numbers
Student Objective: I will be able to problem solve using percents from 1%-100%
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What is 25% of $10.00? =
What is 50% of $10.00? =
What is 75% of $10.00? =
What is 100% of $10.00? =
What strategy did you use to solve this problem?
Find a Percent of a Number
Student Objective: I will be able to problem solve using percents from 1%-100%
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Question:
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Before you start make a good estimation
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4 brothers bought their mother a birthday
present for $84.60. They each paid 25% of the
bill. How much was each brother’s share?
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Solution #1
$84.60 ÷ 2 =
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Find 50% of $84.60.
50% of $84.60 is half of $84.60
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Half of $84.60 is $42.30
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Now find 25% of $84.60
25% is half of 50%
Half of $42.30 is $21.15
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$42.30
$42.30 ÷ 2 =
$21.15
Check:
$21.15 x 4 = $84.60
Each brother’s share is $21.15
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Solution #2
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$84.60 ÷ 4 =
Why divide by 4?
$21.15
$84.60
$20
$1
$0.15
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$20
$1
$0.15
$20
$1
$0.15
$20
$1
$0.15
Check:
$21.15 x 4 = $84.60
Each brother’s share is $21.15
On Your Own…
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Question:
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Before you start make a good estimation
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Ten co-workers are buying Kayden a going
away present and will each pay 10%. They
decide to buy him a backpack for $92.30. How
much should each pay?
Answer
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Find 10% of $92.30.
Recall that 10% = 10/100 = 1/10
10% of $92.30 is one tenth of $92.30
One tenth of $92.30 is $9.23
$92.30 ÷ 10
= $9.23
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Each co-worker should pay $9.23
Apply What You Know
Student Objective: I will be able to problem solve using percents from 1%-100%
Discuss with your partner
Use mental math to find each percent.
 A) 90% of 16
 B) 60% of 90
 C) 40% of 80
What strategies did you use?
“UnFriendly” Percents
Discuss with your partner
What are UNFRIENDLY percent numbers
“percentages” to work with? and why?
“UnFriendly” Percents
17%, 93%, 77%, 33%, 54%.......
So how do you work with these percents?
You must convert the percent to a decimal then multiple
“UnFriendly” Percents
Ex: 28% x 60 =
0.28 x 60 =
Ex: 52% of 118
Ex: 7% of 242
28% = 28 = 0.28
100
“of” means X
Apply What You Know
Student Outcome: I will be able convert %’s, decimals and fractions
Discuss with your partner
Compare ¾, 70%, and 0.72
Put them in order from smallest to biggest (ascending)
Put them in order from largest to smallest (descending)
What strategies did you use?
Solution
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¾ = 0.75
70% = 0.70
0.72 = 0.72
Converted to decimals
OR
¾ = 75%
70% = 70%
0.72 = 72%
Converted to percents
0.70 < 0.72 < 0.75 = ascending
0.75 > 0.72 > 0.70 = descending
Compare Fractions,
Decimals, and Percents.
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Solution:
Convert all the numbers to decimals, or
fractions or percents.
Show Me What You Know…
Student Outcome: I will be able convert %’s, decimals and fractions
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A) 56%, 0.48, ½ (place in ascending order)
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B) 35%, 39/100, 0.36 (place in descending order)
Assignment
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Page 129-130
11, 14b, 24, 26, 28, 29
15a
5c, 8bd, 14b, 15b
21, 24, 28
2, 3, 5ab, 8bd, 12ab
14b, 16
Show Me What You Know #1
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Question #1
25% of $50.00
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Question #2
Find 10% of $72.40
4.2 Fractions, Decimals, and
Percents
Math Links page 132
Objective
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After this lesson I will be able to…
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Convert between fractions, decimals, and
percents
Estimate percent values
Distinguish between terminating and repeating
decimals
Relate fractions to terminating and repeating
decimals.
Example
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Look at the following hockey statistics
Which goalie is having the best save percentage? Why?
Goalie
Shots Saves
on Goal
M. Kiprusoff
673
606
M. Vernon
586
545
P. Reddock
797
726
T. Bunz
709
658
Save %
Decimal
Save %
Using Your Table
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Goalies can be rated on “save percentages.”
This statistic is the ratio of saves to shots on
goal.
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Save Percentage = Number of Saves
Shots on Goal
Extending Your Thinking!!
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Using our chart, decide which goalie is
having the best season.
Is it better to have a higher or lower save
percentage?
How are the decimal and fraction forms of
the save percentage related?
Which form is more useful? Why?
Convert Fractions to Decimals
and Percents
Team
Wins
Losses
Miami
59
23
New Jersey
42
40
Los Angeles
34
48
Winning %
(Decimal)
Team Percentage = Number of wins
Total game played
Winning %
On Your Own
Student Outcome: I will be able convert %’s, decimals and fractions
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A) What is the team percentage for each
team? (leave answer as a fraction)
B) Change each fraction to a decimal
number rounded to the nearest thousandth
C) Use your rounded decimal value to show
the approximate percent value for each
team
Solution A
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Total Games = wins + losses
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Miami: Total Games = 59 + 23 =82
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New Jersey: 42 + 40 = 82
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Team Percentage = 59/82
Team Percentage = 42/48
Los Angeles: 34 + 48 = 82
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Team Percentage = 34/82
Solution B
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Convert each fraction to a decimal.
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Miami: 59/82 = 0.720
New Jersey: 42/82 = 0.512
Los Angeles: 34/82 = 0.415
Solution C
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To convert to a percent, multiply the
decimal by 100
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Miami: 0.72 x 100% = 72%
New Jersey: 0.512 x 100% = 51.2%
Los Angeles: 0.415 x 100% = 41.5%
Assignment
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Page 137-138
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5cd, 6cd, 7
Practical Quiz #2
Fill in the chart
Event
30% off
DVD’S
Tip is 12%
Exam Mark
is 86%
Fraction
Decimal
Percent
4.2 Change Fractions to
Repeating Decimals
Student Outcome: I will be able convert %’s, decimals and fractions
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What is a Repeating Decimal?
 A decimal number with a digit or group of digits that
repeats forever
 Repeating decimals are shown with a bar
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Ex: 1
=
0.33333
=
0.3
3
Ex: 5
6
=
0.833333
=
0.83
Learn Alberta: Repeating Decimals
http://www.learnalberta.ca/content/memg/index.html?term=Division03/Repeating_Decimal/index.html
Using a Calculator
Student Outcome: I will be able convert %’s, decimals and fractions
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Change the following fractions into a repeating decimal.
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A) 1/3
=
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B) 5/9
=
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C) 5/6
=
Assignment
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Page 138-139
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8cd, 9cd,10ab, 11ab,
4.2 Estimate Percents
Student Outcome: I will be able to make estimations using %’s
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Ex: Paige has answered 94 questions
correctly out of 140 questions.
Estimate her mark as a percent.
Solution
Student Outcome: I will be able to make estimations using %’s
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Think: What is 50% of 140?
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Think: what is 10% of 140?
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70 + 14 = 84
TOO LOW
50% + 10% + 10% = 70% of 140
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140 ÷ 10 = 14
50% + 10% = 60% of 140
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Half of 140 is 70
70 + 14 + 14 = 98
TOO HIGH
The answer is between 60% and 70%, but closer
to 70%
4.2 Change Terminating
Decimals Into Fractions
Student Outcome: I will learn about terminating decimals and how to convert
them to fractions.
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What is it…
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Terminating Decimal
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A decimal number in which the digits stop
Examples include 0.4, 0.86, 0.125
Terminating Decimal Numbers into
Fractions
Student Outcome: I will learn about terminating decimals and how to convert
them to fractions.
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Question:
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A) What fraction of a dollar is $0.75?
B) Change 0.652 to a fraction
Solution
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A) The decimal number 0.75 is a terminating
decimal. The last digit is in the hundredths
place, so the denominator is 100.
 0.75 = 75
100
So, $0.75 is 75/100 of a dollar or ¾ of a dollar
$0.75 is 75¢
Or, 3 quarters
How would we say each decimal and write
it as a fraction?
Ex #1
0.123
Ex #2
0.056
Ex #3
0.009
Ex#4
0.450
Ex #5
14.773 (Bonus)
Key Ideas
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To change a fraction to a decimal number, divide
the numerator by the denominator.
 Ex: 3/8 = 3 ÷ 8 = 0.375
Repeating decimal numbers can be written using
a bar notion
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Ex: 1/3 = 0.333… = 0.3
To express a terminating decimal number as a
fraction, use place value to determine the
denominator
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0.9 = 9/10
0.59 = 59/100
1.463 = 1463/1000
Assignment
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Page 137-139
5ab, 8b, 15d, 19, 20, 21
17
5ab, 7, 8b, 10c, 14d
19
5ab, 8ab,10cd,14cd,16
Assignment
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Page 143-145
2, 12, 18, 19, 20, 21, 22
16
3, 6, 8, 12, 13, 18,
19
2, 5, 6, 8, 11, 13, 14
Tangram Website
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http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities
GAME TIME
Fraction-Spiral Game
(see handout)
Game – Page 150
ITEM
Original Price
Percent Reduced
Discount
Amount
(.0000)
Discount
Amount
(.00)
Final Price
Ex:Cordless Drill
$109.99
25%
$27.4975
$27.50
$82.49
Ex: Curling Iron
$34.75
n/a
n/a
n/a
$34.75
1.
2.
3.
4.
5.
6.
7.
Subtotal
GST
Total
Double Discount
(first step/discount)
Double Discount
(second step/discount)