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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**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**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**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% = =**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 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?**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?**$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**$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**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?**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**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?**“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 = 28% = 28 = 0.28 0.28 x 60 = 100 Ex: 52% of 118 “of” means X Ex: 7% of 242**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?**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**Compare Fractions, Decimals, and Percents.**• Solution: Convert all the numbers to decimals, or fractions or percents.**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)**Assignment**• Page 129 • #5ac, 6ac, 8ab, • # 9ab, 10ab, 11 • #12ab, 13ab, 14a, • #20, 21, 24, • Extend #28, 29**Practical Quiz #1**• Question #1 25% of $50.00 • Question #2 Find 10% of $72.40**4.2 Fractions, Decimals, and Percents**Math Links page 132**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.**Example**• Look at the following hockey statistics • Which goalie is having the best save percentage? Why?**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**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?**Convert Fractions to Decimals and Percents**Team Percentage = Number of wins Total game played**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**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**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**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%**Assignment**• Page 137 #5ab, 6ab, 7**Practical Quiz #2**Fill in the chart**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**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 =**On Your Own**Assignment Page 138 #8ab, 9ab, 10ab, 11ab Extend #21**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.**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**On Your Own…**• Assignment Page 138 #12, 13**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.**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**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**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**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)