Fractions, Decimals, and Percents

Video Support essons Learn Alberta: percents

4.1 Connect Fractions, Decimals, and 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

Student Objective: I will be able to problem solve using percents from 1%-100% 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 “of” means x

Student Objective: I will be able to problem solve using percents from 1%-100% Percent Student Objective: I will be able to problem solve using percents from 1%-100% Ex: 64% = 64 = Ex: 91% = = Ex: 37% = = Bonus Ex: 107% = =

Think Money $0.25 ¼ of a dollar 25% of a dollar $0.50 ½ of a dollar 50% of a dollar $0.10 1/10 of a dollar 10% 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%

Student Objective: I will be able to problem solve using percents from 1%-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?

Student Objective: I will be able to problem solve using percents from 1%-100% 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 $ They each paid 25% of the bill. How much was each brother’s share?

Solution #1 Find 50% of $ % of $84.60 is half of $84.60 Half of $84.60 is $42.30 Now find 25% of $ % 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 $84.60 ÷ 2 = $42.30 $42.30 ÷ 2 = $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 $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 $ How much should each pay?

Answer Find 10% of $ 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 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 = 28% = 28 = x 60 = 100 Ex: 52% of 118 “of” means X Ex: 7% of 242

Student Outcome: I will be able convert %’s, decimals and fractions 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 = 0.75¾ = 75% 70% = 0.70OR70% = 70% 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.

Student Outcome: I will be able convert %’s, decimals and fractions 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? GoalieShots on Goal SavesSave % Decimal Save % M. Kiprusoff M. Vernon P. Reddock T. Bunz709658

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 TeamWinsLossesWinning % (Decimal) Winning % Miami5923 New Jersey4240 Los Angeles3448 Team Percentage = Number of wins Total game played

Student Outcome: I will be able convert %’s, decimals and fractions 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 = =82 Team Percentage = 59/82 New Jersey: = 82 Team Percentage = 42/48 Los Angeles: = 82 Team Percentage = 34/82

Solution B Convert each fraction to a decimal. Miami: 59/82 = New Jersey: 42/82 = 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: x 100% = 51.2% Los Angeles: x 100% = 41.5%

Assignment Page 137 #5ab, 6ab, 7

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

Student Outcome: I will be able convert %’s, decimals and fractions 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= =0.3 3 Ex: 5= = Learn Alberta: Repeating Decimals

Student Outcome: I will be able convert %’s, decimals and fractions 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=

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

Student Outcome: I will be able to make estimations using %’s 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.

Student Outcome: I will be able to make estimations using %’s Solution Student 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 = 84 50% + 10% + 10% = 70% of = 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 $ 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

Student Outcome: I will learn about terminating decimals and how to convert them to fractions. 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

Student Outcome: I will learn about terminating decimals and how to convert them to fractions. 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 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 = 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 # Ex # Ex # Ex# Ex # (Bonus)

Key Ideas To change a fraction to a decimal number, divide the numerator by the denominator. Ex: 3/8 = 3 ÷ 8 = 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

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

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

Game – Page 150