Fractions, Decimals, and Percents

Learn Alberta: percents Video Support http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons Learn Alberta: percents

4.1 Connect Fractions, Decimals, and Percents

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 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

Percent Ex: 91% = = Ex: 37% = = Bonus Ex: 107% = = 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 $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 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

Find a Percent of a Number 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? November 24

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

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

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

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

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?

“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

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?

Solution ¾ = 0.75 ¾ = 75% 70% = 0.70 OR 70% = 70% 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 < 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… 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, 29 Extend #28, 29

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

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 on Goal Saves Save % Decimal M. Kiprusoff 673 606 M. Vernon 586 545 P. Reddock 797 726 T. Bunz 709 658

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 Winning % (Decimal) Miami 59 23 New Jersey 42 40 Los Angeles 34 48 Team Percentage = Number of wins Total game played

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

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

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 = 0.33333 = 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 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 =

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

4.2 Estimate Percents Ex: Paige has answered 94 questions correctly out of 140 questions. Estimate her mark as a percent.

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 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.

Assignment: Let’s go shopping

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

Terminating Decimal Numbers into 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 138-139 #14ab, 15ab, 16, 19

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