1. Fractions, Decimals, and Percents

2. Learn Alberta: percents
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Learn Alberta: percents

3. 4.1 Connect Fractions, Decimals, and Percents

4. 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. Percent What does it mean?? 100 “of” means x “out of 100”
Ex: 20 out of 100 or 20% or 20 or 0.20
100
“of” means x

6. Percent Ex: 91% = = Ex: 37% = = Bonus Ex: 107% = = Ex: 64% = 64 = 0.64
100
Ex: 91% = =
Ex: 37% = =
Bonus
Ex: 107% = =

7. Think Money $0.10 1/10 of a dollar 10% of a dollar $0.25 ¼ of a dollar
$0.50
½ of a dollar
50% 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% % 75% %

10. Friendly Percent Numbers
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?
November 24

11. Find a Percent of a Number
Question:
Before you start make a good estimation
4 brothers bought their mother a birthday present for $ They each paid 25% of the bill. How much was each brother’s share?
November 24

12. Solution #1 Find 50% of $84.60. 50% of $84.60 is half of $84.60
$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 brother’s share is $21.15
$42.30 ÷ 2 = $21.15

13. Solution #2 Why divide by 4? $84.60 Check: $21.15 x 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

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 $ 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. Practical Quiz #1 Question #1 25% of $50.00 Question #2
Find 10% of $72.40

17. Apply What You Know Use mental math to find each percent. A) 90% of 16
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?

18. “UnFriendly” Percents
Discuss with your partner What are UNFRIENDLY percent numbers “percentages” to work with? and why?

19. “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

20. “UnFriendly” Percents
Ex: 28% x 60 = 28% = 28 = 0.28
0.28 x 60 =
Ex: 52% of “of” means X
Ex: 7% of 242

21. What strategies did you use?
Apply What You Know
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?

22. Solution ¾ = 0.75 ¾ = 75% 70% = 0.70 OR 70% = 70%
¾ = ¾ = 75%
70% = OR 70% = 70%
0.72 = = 72%
Converted to decimals Converted to percents
0.70 < 0.72 < 0.75 = ascending
0.75 > 0.72 > 0.70 = descending

23. Compare Fractions, Decimals, and Percents.
Solution:
Convert all the numbers to decimals, or fractions or percents.

24. Show What You Know… A) 56%, 0.48, ½ (place in ascending order)
B) 35%, 39/100, 0.36 (place in descending order)

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

26. Practical Quiz #2 Fill in the chart Event Fraction Decimal Percent
30% off DVD’S
Tip is 12%
Exam Mark is 86%

27. 4.2 Fractions, Decimals, and Percents
Math Links page 132

28. 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.

29. Example Look at the following hockey statistics
Which goalie is having the best save percentage? Why?
Goalie
Shots on Goal
Saves
Save %
Decimal
M. Kiprusoff
673
606
M. Vernon
586
545
P. Reddock
797
726
T. Bunz
709
658

30. 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

31. 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?

32. Convert Fractions to Decimals and Percents
Team
Wins
Losses
Winning %
(Decimal)
Miami 59 23
New Jersey 42 40
Los Angeles 34 48
Team Percentage = Number of wins
Total game played

33. On Your Own
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

34. Solution A Total Games = wins + losses
Miami: Total Games = =82
Team Percentage = 59/82
New Jersey: = 82
Team Percentage = 42/48
Los Angeles: = 82
Team Percentage = 34/82

35. 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

36. Solution C To convert to a percent, multiply the decimal by 100
Miami: 0.72 x 100% = 72%
New Jersey: x 100% = 51.2%
Los Angeles: x 100% = 41.5%

37. Assignment
Page 137 #5ab, 6ab, 7

38. 4.2 Change Fractions to Repeating Decimals
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 = = 0.3 3
Ex: 5 = = 0.83 6
Learn Alberta: Repeating Decimals

39. Using a Calculator A) 1/3 = B) 5/9 = C) 5/6 =
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 Percents
Ex: Paige has answered 94 questions correctly out of 140 questions.
Estimate her mark as a percent.

42. The answer is between 60% and 70%, but closer to 70%
Solution
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
= 84
50% + 10% + 10% = 70% of 140
= 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: Let’s go shopping
You have $ 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: Let’s go shopping

46. 4.2 Change Terminating Decimals Into 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
Question:
A) What fraction of a dollar is $0.75?
B) Change 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

50. How would we say each decimal and write it as a fraction?
Ex #
Ex #
Ex #
Ex#
Ex # (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/ = 59/ = 1463/1000

52. Assignment
Page #14ab, 15ab, 16, 19

53. Application of Percents
Assignment
Page # 6, 8, 10, 13, 16, 17
Extend #19, 21, 22