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Fractions, Decimals, and Percents Video Support http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=l essons Learn Alberta: percents 4.1 Connect Fractions, Decimals, and Percents 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. Assignment: Let’s go shopping ITEM Original Price Percent Reduced Discount Amount (.0000) 1. 2. 3. 4. 5. 6. 7. Subtotal GST Total Discount Amount (.00) Final Price Marking Rubric 7 items 5 correct discounts (proper rounding) 2 correct regular items (proper rounding) Correct Subtotal Correct GST Correct Total 1 double discount (proper rounding) TOTAL Parent Signature _______________________________ 7 marks 5 marks 2 marks 1 mark 1 mark 1 mark 2 marks /19 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 Percent 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 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% = = 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 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? 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 brother’s share? Solution #1 $84.60 ÷ 2 = 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 $42.30 $42.30 ÷ 2 = $21.15 Check: $21.15 x 4 = $84.60 Each brother’s share is $21.15 Solution #2 $84.60 ÷ 4 = Why divide by 4? $21.15 $84.60 $20 $1 $0.15 $20 $1 $0.15 $20 $1 $0.15 $20 $1 $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 $92.30 ÷ 10 = $9.23 Each co-worker should pay $9.23 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? “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 = 0.28 x 60 = Ex: 52% of 118 Ex: 7% of 242 28% = 28 = 0.28 100 “of” means X Apply What You Know Student 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 70% = 0.70 0.72 = 0.72 Converted to decimals OR ¾ = 75% 70% = 70% 0.72 = 72% Converted 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 Me 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 129-130 11, 14b, 24, 26, 28, 29 15a 5c, 8bd, 14b, 15b 21, 24, 28 2, 3, 5ab, 8bd, 12ab 14b, 16 Show Me What You Know #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? Goalie Shots Saves on Goal M. Kiprusoff 673 606 M. Vernon 586 545 P. Reddock 797 726 T. Bunz 709 658 Save % Decimal Save % 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 Wins Losses Miami 59 23 New Jersey 42 40 Los Angeles 34 48 Winning % (Decimal) Team Percentage = Number of wins Total game played Winning % On Your Own Student 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 New Jersey: 42 + 40 = 82 Team Percentage = 59/82 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 137-138 5cd, 6cd, 7 Practical Quiz #2 Fill in the chart Event 30% off DVD’S Tip is 12% Exam Mark is 86% Fraction Decimal Percent 4.2 Change Fractions to Repeating Decimals 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 6 = 0.833333 = 0.83 Learn Alberta: Repeating Decimals http://www.learnalberta.ca/content/memg/index.html?term=Division03/Repeating_Decimal/index.html Using a Calculator Student 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 = Assignment Page 138-139 8cd, 9cd,10ab, 11ab, 4.2 Estimate Percents Student 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. Solution Student Outcome: I will be able to make estimations using %’s Think: What is 50% of 140? Think: what is 10% of 140? 70 + 14 = 84 TOO LOW 50% + 10% + 10% = 70% of 140 140 ÷ 10 = 14 50% + 10% = 60% of 140 Half of 140 is 70 70 + 14 + 14 = 98 TOO HIGH The answer is between 60% and 70%, but closer to 70% 4.2 Change Terminating Decimals Into Fractions Student 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 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 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) 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 Assignment Page 137-139 5ab, 8b, 15d, 19, 20, 21 17 5ab, 7, 8b, 10c, 14d 19 5ab, 8ab,10cd,14cd,16 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 Tangram Website http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities GAME TIME Fraction-Spiral Game (see handout) Game – Page 150 ITEM Original Price Percent Reduced Discount Amount (.0000) Discount Amount (.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)