Fractions, Decimals, and Percents. Video Support essons Learn Alberta: percents.
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Transcript of Fractions, Decimals, and Percents. Video Support essons Learn Alberta: percents.
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Fractions, Decimals, and Percents
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Video Support
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons
Learn Alberta: percents
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4.1 Connect Fractions, Decimals, and Percents
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Assignment: Let’s go shopping
You have $1000.00 to spend for Christmas.
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.
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Assignment: Let’s go shopping
ITEM Original Price
Percent Reduced
DiscountPrice
(.0000)
Discount Price (.00)
Final Price
1. 2. 3. 4. 5. 6. 7.
Subtotal
GST
Total
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Marking Rubric
7 items 7 marks 5 correct discounts (proper rounding) 5 marks 2 correct regular items (proper rounding) 2 marks Correct Subtotal 1 mark Correct GST 1 mark Correct Total 1 mark 1 double discount (proper rounding) 2 marks
TOTAL /19
Parent Signature
_______________________________
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Student Objective: After this lesson, I will be able to…
Estimate percents as fractions or as decimals Compare and order fractions decimals, and
percents Estimate and solve problems involving percent
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PercentStudent Objective: I will be able to problem solve using percents from 1%-100%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
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Percent Student Objective: I will be able to problem solve using percents from 1%-100%Student Objective: I will be able to problem solve using percents from 1%-100%
Ex: 64% = 64 = 0.64
100 Ex: 91% = =
Ex: 37% = =
Bonus Ex: 107% = =
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Think Money
$0.25¼ of a dollar25% of a dollar
$0.50½ of a dollar50% of a dollar
$0.101/10 of a dollar10% of a dollar
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“Friendly” Percents
Discuss with your partner
What are FRIENDLY percent numbers “percentages” to work with? and why?
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“Friendly” Percents 25% 50% 75% 100%
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Friendly Percent Numbers Student Objective: I will be able to problem solve using percents from 1%-100%Student Objective: I will be able to problem solve using percents from 1%-100%
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?
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Find a Percent of a Number Student Objective: I will be able to problem solve using percents from 1%-100%Student Objective: I will be able to problem solve using percents from 1%-100%
Question: Before you start make a good estimation
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 Find 50% of $84.60. 50% of $84.60 is half of $84.60
Half of $84.60 is $42.30 Now find 25% of $84.60 25% is half of 50% Half of $42.30 is $21.15
Check: $21.15 x 4 = $84.60 Each brother’s share is $21.15
$84.60 ÷ 2 =
$42.30
$42.30 ÷ 2 = $21.15
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Solution #2 Why divide by 4?
$84.60
$20 $20 $20 $20
$1 $1 $1 $1
$0.15 $0.15 $0.15 $0.15
Check: $21.15 x 4 = $84.60 Each brother’s share is $21.15
$84.60 ÷ 4 =
$21.15
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On Your Own… Question: Before you start make a good estimation
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?
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Answer 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
Each co-worker should pay $9.23
$92.30 ÷ 10 = $9.23
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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?
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“UnFriendly” Percents
Discuss with your partner
What are UNFRIENDLY percent numbers “percentages” to work with? and why?
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“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
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“UnFriendly” Percents
Ex: 28% x 60 = 28% = 28 = 0.28
0.28 x 60 = 100
Ex: 52% of 118 “of” means X
Ex: 7% of 242
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Apply What You KnowStudent Outcome: I will be able convert %’s, decimals and fractionsStudent 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?
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Solution ¾ = 0.75 ¾ = 75% 70% = 0.70 OR 70% = 70%
0.72 = 0.72 0.72 = 72%Converted to decimals Converted to percents
0.70 < 0.72 < 0.75 = ascending 0.75 > 0.72 > 0.70 = descending
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Compare Fractions, Decimals, and Percents.
Solution:
Convert all the numbers to decimals, or fractions or percents.
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Show Me What You Know…Student Outcome: I will be able convert %’s, decimals and fractionsStudent Outcome: I will be able convert %’s, decimals and fractions
A) 56%, 0.48, ½ (place in ascending order)
B) 35%, 39/100, 0.36 (place in descending order)
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Assignment Page 129-130
11, 14b, 24, 26, 28, 29
15a 5c, 8bd, 14b, 15b
21, 24, 28
2, 3, 5ab, 8bd, 12ab
14b, 16
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Show Me What You Know #1 Question #1
25% of $50.00
Question #2
Find 10% of $72.40
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4.2 Fractions, Decimals, and Percents
Math Links page 132
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Objective After this lesson I will be able to…
Convert between fractions, decimals, and percents
Estimate percent values Distinguish between terminating and repeating
decimals Relate fractions to terminating and repeating
decimals.
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Example Look at the following hockey statistics Which goalie is having the best save percentage? Why?
Goalie Shots on Goal
Saves Save %Decimal
Save %
M. Kiprusoff 673 606
M. Vernon 586 545
P. Reddock 797 726
T. Bunz 709 658
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Using Your Table Goalies can be rated on “save percentages.”
This statistic is the ratio of saves to shots on goal.
Save Percentage = Number of Saves
Shots on Goal
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Extending Your Thinking!! 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?
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Convert Fractions to Decimals and Percents
Team Wins Losses Winning %(Decimal)
Winning %
Miami 59 23
New Jersey 42 40
Los Angeles 34 48
Team Percentage = Number of wins Total game played
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On Your OwnStudent Outcome: I will be able convert %’s, decimals and fractionsStudent Outcome: I will be able convert %’s, decimals and fractions
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
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Solution A Total Games = wins + losses
Miami: Total Games = 59 + 23 =82 Team Percentage = 59/82
New Jersey: 42 + 40 = 82 Team Percentage = 42/48
Los Angeles: 34 + 48 = 82 Team Percentage = 34/82
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Solution B Convert each fraction to a decimal.
Miami: 59/82 = 0.720 New Jersey: 42/82 = 0.512 Los Angeles: 34/82 = 0.415
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Solution C To convert to a percent, multiply the
decimal by 100 Miami: 0.72 x 100% = 72% New Jersey: 0.512 x 100% = 51.2% Los Angeles: 0.415 x 100% = 41.5%
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Assignment Page 137-138
5cd, 6cd, 7
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Practical Quiz #2 Fill in the chart
Event Fraction Decimal Percent
30% off DVD’S
Tip is 12%
Exam Mark is 86%
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4.2 Change Fractions to Repeating Decimals
Student Outcome: I will be able convert %’s, decimals and fractions Student Outcome: I will be able convert %’s, decimals and fractions
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
Ex: 1 = 0.33333 = 0.3 3
Ex: 5 = 0.833333 = 0.83
6
Learn Alberta: Repeating Decimalshttp://www.learnalberta.ca/content/memg/index.html?term=Division03/Repeating_Decimal/index.html
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Using a CalculatorStudent Outcome: I will be able convert %’s, decimals and fractionsStudent Outcome: I will be able convert %’s, decimals and fractions
Change the following fractions into a repeating decimal.
A) 1/3 =
B) 5/9 =
C) 5/6 =
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Assignment Page 138-139
8cd, 9cd,10ab, 11ab,
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4.2 Estimate PercentsStudent Outcome: I will be able to make estimations using %’sStudent Outcome: I will be able to make estimations using %’s
Ex: Paige has answered 94 questions correctly out of 140 questions.
Estimate her mark as a percent.
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SolutionStudent Outcome: I will be able to make estimations using %’sStudent Outcome: I will be able to make estimations using %’s
Think: What is 50% of 140? Half of 140 is 70
Think: what is 10% of 140? 140 ÷ 10 = 14
50% + 10% = 60% of 140 70 + 14 = 84
50% + 10% + 10% = 70% of 140 70 + 14 + 14 = 98
The answer is between 60% and 70%, but closer to 70%
TOO LOW
TOO HIGH
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4.2 Change Terminating Decimals Into Fractions
Student Outcome: I will learn about terminating decimals and how to convert Student Outcome: I will learn about terminating decimals and how to convert them to fractions.them to fractions.
What is it… Terminating Decimal
A decimal number in which the digits stop Examples include 0.4, 0.86, 0.125
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Terminating Decimal Numbers into Fractions
Student Outcome: I will learn about terminating decimals and how to convert Student Outcome: I will learn about terminating decimals and how to convert
them to fractions.them to fractions.
Question: A) What fraction of a dollar is $0.75? B) Change 0.652 to a fraction
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Solution 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
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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)
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Key Ideas 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 Ex: 1/3 = 0.333… = 0.3
To express a terminating decimal number as a fraction, use place value to determine the denominator 0.9 = 9/10 0.59 = 59/100 1.463 = 1463/1000
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Assignment Page 137-139
5ab, 8b, 15d, 19, 20, 21
17 5ab, 7, 8b, 10c, 14d
19
5ab, 8ab,10cd,14cd,16
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Assignment 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
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Tangram Website http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities
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GAME TIME
Fraction-Spiral Game(see handout)
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Game – Page 150
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ITEM Original Price Percent Reduced DiscountPrice
(.0000)
Discount Price (.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)