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Fractions, Decimals, and Percents

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Title: Fractions, Decimals, and Percents


1
Fractions, Decimals, and Percents
2
Video Support
  • http//www.learnalberta.ca/content/mesg/html/math6
    web/index.html?pagelessons
  • Learn Alberta percents

3
4.1 Connect Fractions, Decimals, and Percents
4
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

5
PercentStudent 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

6
Percent 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

7
Think Money
0.25 ¼ of a dollar 25 of a dollar
0.50 ½ of a dollar 50 of a dollar
0.10 1/10 of a dollar 10 of a dollar
8
Friendly Percents
  • Discuss with your partner
  • What are FRIENDLY percent numbers percentages
    to work with? and why?

9
Friendly Percents
  • 25 50 75 100

10
Friendly Percent Numbers 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?

11
Find a Percent of a Number 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 brothers share?

12
84.60 2 42.30
  • 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 brothers share is 21.15

42.30 2 21.15
13
  • 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 brothers share is 21.15

84.60 4 21.15
14
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?

15
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
16
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?

17
UnFriendly Percents
  • Discuss with your partner
  • What are UNFRIENDLY percent numbers percentages
    to work with? and why?

18
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

19
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

20
Apply What You KnowStudent 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?

21
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 lt 0.72 lt 0.75 ascending 0.75 gt 0.72 gt
0.70 descending
22
Compare Fractions, Decimals, and Percents.
  • Solution
  • Convert all the numbers to decimals, or fractions
    or percents.

23
Show What You KnowStudent 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)

24
Assignment
  • Page 129
  • 5ac, 6ac, 8ab,
  • 9ab, 10ab, 11
  • 12ab, 13ab, 14a,
  • 20, 21, 24,
  • Extend 28, 29

25
Practical Quiz 1
  • Question 1
  • 25 of 50.00
  • Question 2
  • Find 10 of 72.40

26
4.2 Fractions, Decimals, and Percents
  • Math Links page 132

27
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.

28
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
29
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

30
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?

31
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
32
On Your OwnStudent 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

33
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

34
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

35
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

36
Assignment
  • Page 137 5ab, 6ab, 7

37
Practical Quiz 2
  • Fill in the chart

Event Fraction Decimal Percent
30 off DVDS
Tip is 12
Exam Mark is 86
38
4.2 Change Fractions to Repeating
DecimalsStudent 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 Decimals
  • http//www.learnalberta.ca/content/memg/index.html
    ?termDivision03/Repeating_Decimal/index.html

39
Using a CalculatorStudent 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

40
On Your Own
  • Assignment
  • Page 138 8ab, 9ab, 10ab, 11ab
  • Extend 21

41
4.2 Estimate PercentsStudent 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.

42
SolutionStudent 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
43
On Your Own
  • Assignment
  • Page 138 12, 13

44
Assignment Lets go shopping
  • You have 1000.00 to spend for Christmas.
  • From magazines you will cut out 10 items that are
    on sale
  • and total your cost including Gst 5
  • Items will be glued to a piece of paper with a
    formal bill
  • attached.

45
Assignment Lets go shopping
46
4.2 Change Terminating Decimals Into
FractionsStudent Outcome I will learn about
terminating decimals and how to convert them to
fractions.
  • What is it
  • Terminating Decimal
  • A decimal number in which the digits stop
  • Examples include 0.4, 0.86, 0.125

47
Terminating Decimal Numbers into Fractions
Student Outcome I will learn about terminating
decimals and how to convert them to fractions.
  • Question
  • A) What fraction of a dollar is 0.75?
  • B) Change 0.652 to a fraction

48
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
49



50
How would we say each decimal and write it as a
fraction? Ex 1 0.123 Ex 2 0.056 Ex
3 0.009 Ex4 0.450 Ex 5 14.773 (Bonus)


51
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

52
Assignment
  • Page 138-139 14ab, 15ab, 16, 19

53
Application of Percents
  • Assignment
  • Page 143-144 6, 8, 10, 13, 16, 17
  • Extend 19, 21, 22

54
Game Page 150
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