Fractions, Decimals, and Percents

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http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons

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

DiscountPrice

(.0000)

Discount Price (.00)

Final Price

1.          2.          3.          4.          5.          6.          7.

Subtotal

GST

Total

Marking Rubric

7 items 7 marks 5 correct discounts (proper rounding) 5 marks 2 correct regular items (proper rounding) 2 marks Correct Subtotal 1 mark Correct GST 1 mark Correct Total 1 mark 1 double discount (proper rounding) 2 marks

TOTAL /19

Parent Signature

_______________________________

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%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%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

$0.25¼ of a dollar25% of a dollar

$0.50½ of a dollar50% of a dollar

$0.101/10 of a dollar10% 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%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%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 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

$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 $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 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 = 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 fractionsStudent 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 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 Me What You Know…Student Outcome: I will be able convert %’s, decimals and fractionsStudent 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 on Goal

Saves Save %Decimal

Save %

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)

Winning %

Miami 59 23

New Jersey 42 40

Los Angeles 34 48

Team Percentage = Number of wins Total game played

On Your OwnStudent Outcome: I will be able convert %’s, decimals and fractionsStudent 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 137-138

5cd, 6cd, 7

Practical Quiz #2 Fill in the chart

Event Fraction Decimal Percent

30% off DVD’S

Tip is 12%

Exam Mark is 86%

4.2 Change Fractions to Repeating Decimals

Student Outcome: I will be able convert %’s, decimals and fractions 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 = 0.833333 = 0.83

6

Learn Alberta: Repeating Decimalshttp://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 fractionsStudent 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 PercentsStudent Outcome: I will be able to make estimations using %’sStudent 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 %’sStudent 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

4.2 Change Terminating Decimals Into Fractions

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

them to fractions.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 DiscountPrice

(.0000)

Discount Price (.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)