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1. Fractions, Decimals, and Percents

2. Video Support http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons 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. PercentStudent 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 \$0.10 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

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 NumbersStudent 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 NumberStudent 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?

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 brother’s share is \$21.15 \$42.30 ÷ 2 = \$21.15

13. \$84.60 ÷ 4 = \$21.15 • 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

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 KnowStudent 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 decimalsConverted to percents 0.70 < 0.72 < 0.75 = ascending 0.75 > 0.72 > 0.70 = descending

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

23. Show What You Know…Student 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?

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 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

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?term=Division03/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: Let’s 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: Let’s 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 FractionsStudent 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. 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)