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4.1 Percents Greater than 100% I Represi Represent and interpret percents greater than 100%.

Represent each percent on the 10-by-10 grids.

Use one ful l gr id to represent 100%.

a) 175%

b) 280%

2. Solve.

a) 140% of 80 =

b) 210% of 11 =

c) 160% of 30

d) 350% of 50

Percent means "per one hundred." To represent a percent greater than 100%, first represent 100%. Use this representation to show percents greater than 100%.

For example, represent 150% using 10-by-10 grids:

one grid is 100%

100% + 50% = 150%

For example, 150% of 30 = ? 100% of 30 = 30 50% of 30 = 1 5 150% of 30 = 30 + 15 = 45

3. Calculate each amount.

a) 250% of $30 =

b) 175% of $30 =

c) 350% of $30 =

4. There are 500 students enrolled in David's school.

This is 175% of the enrol lment in the school when it opened 10 years ago.

How many students were in David's school when it opened?

Copyright 2009 by Nelson Education Ltd. Chapter 4: Percents 31

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Fractional Percents

Represi Represent and interpret percents between 0% and 1%.

1. Represent each percent on a thousandths gr id,

a) 25.5%

b) 4.3%

To represent percents that involve parts of 1%, divide 1% into parts.

For example, you can express 2.5% as 2% + 0.5%. 0.5% is half of 1%.

Represent 2.5% on a thousandths grid.

)

OK

25 thousandths, or T^. 1000

2. Suppose 4% of a container of ice cream is 16 mL. Calculate each amount of ice cream,

a) 1 % = b) 0 .1% = c) 1.6% =

3. There are 28 students in Darren's class.They make up 18.3% of students in his school.

How many students are in his school?

4. Is 3.9% of a number always very close to 4% of the same number? Explain.

32 Chapter 4: Percents Copyright 2009 by Nelson Education Ltd.

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4.3 Relating Percents to Decimals and Fractions Express a percent as an equivalent decimal or fraction,

or a decimal or fraction as an equivalent percent.

o

Describe the shaded area as a fract ion, a decimal, and a

percent. Use one ful l grid to represent 100%.

y>*

( K ( ( K ( I s

fract ion

decimal

percent .%

Katie's DVD collection is 350% larger than Mike's.

Write the ratio as a fraction and a decimal.

fract ion = decimal =

3. Complete the table.

Percent Equivalent fraction Equivalent decimal

4.8%

0.052

133 100

2.5%

To express a percent as a decimal, first write it as a fraction with a denominator of 100. Then write the decimal.

For example, 27

27% = 27 100

= 0.27

104% = 104 100 = 1.04

To express a decimal as a percent, first express it as a number of hundredths.

For example, 0.375 = 37 hundredths + 5 thousandths, or 37.5%

To express a fraction as a percent, divide the numerator by the denominator.

For example,

1 = 3 + 8 = 0.375 or 37.5%

Copyright 2009 by Nelson Education Ltd. Chapter 4: Percents 33

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4.4 Date:

Solving Problems Using a Proportion

Solve.

a) 410% of 89

b) 83.5% of 67 =

c) 640% of = 22

Sylvia answered 62% of the questions on a math test

correctly.

There were 30 questions on the test.

How many questions did Sylvia answer correctly?

3. In 2004, there were 576 students in Daniel's school.

In 2008, the number of students in Daniel's school was

135.4% of that number.

How many students were in Daniel's school in 2008?

To solve a percent problem, you can set up a proportion using an equivalent ratio.

For example, suppose 40 is 160% of a number and you want to solve for the number. Set up a proportion:

4X

40 160 40 160

100

Since 40 X 4 = 160, then X 4 = 100.

Since 25 X 4 = 100, then = 25.

100

4X

4. What number is 75% of 4?

5. 8 is 40% of what number?

34 Chapter 4: Percents Copyright 2009 by Nelson Education Ltd.

Name: Date:

4.5 Solving Percent Problems Using Decimals Use the decimal representation of a percent to solve a problem.

I. Write equations involving decimals you can use to solve

each, then solve the equations.

a) 13.2% of 87

b) 85.5% of 298

c) 146% of 50

d) 0.5% of 9

!. Calculate.

a) 12% of 90 =

b) 175% of 30 = .

c) 3.2% of 300 =

3. Mike's parents bought h im a new computer for $999.

It was on sale for 75% of the original cost.

What was the original price?

$

To express a percent as a decimal, express it as a number of hundredths.

For example, what is 124% of 18?

124% is 124 hundredths, or 1.24. 124% of 18 = 1.24 X 18

= 22.32

For example, if 200 is 40% of a number, what is the number?

40% of number = 200 0.40 X number = 200

number = 200 + 0.40 = 500

Rachel is planning to buy an MP3 player.

It costs $299, which is 137% of the amount in her bank account.

How much money has Rachel saved?

$

5. There are 13 students in Maria's class who play in the local vol leybal l league.

These students make up 9% of the league. How many students are in the league?

$

Copyright 2009 by Nelson Education Ltd. Chapter 4: Percents 35

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4.6 Date:

Solve Problems by Changing Your Point of View

You may need a calculator for this lesson.

1. The local football team wants to sell their team photo as

a poster for next season.The current photo is 30 cm x

24 cm and must be enlarged to 420% of its original size.

a) What is the area of the rectangular photo?

c m 2

b) Explain how you can determine the area of the poster

at 420% of the original size.

To determine the amount by which to enlarge or reduce an area, express the percent as a decimal.

For example, to enlarge an area of 10.0 m 2 by 110%:

110% of 10.0 m 2 = 1.10 x 10.0 = 11.0 m 2

c) Complete the table to show another way to solve the problem.

Original size

Enlargement or reduction

Parti

Enlargement or reduction

Part 2 Total

enlargement

Area

% 100% 20% 400% 420%

d) How else can you solve this problem using the photo's measurements?

36 Chapter 4: Percents Copyright 2009 by Nelson Education Ltd.

Name: Date:

4 - j Solving Percent Problems Using . / Fractions and solve a percent problem using fractions.

1. Write each percent as a fract ion.

a) 75% =

b) 25% =

c) 60% =

d) 15% =

2. Girls make up 50% of a Grade 8 math class. There are 32 students in the class.

How many students are girls?

3. There are 20 students on the school hockey team.

The hockey players make up 5% of the school's populat ion.

How many students attend this school?

4. Angel ie saw 15 movies in the past three months.

They made up 75% of the movies she has seen this year.

How many movies has she seen this year?

5. Nathan read 16 graphic novels in the past few weeks.

They made up 25% of the novels he has read this year.

How many novels has he read this year?

When you multiply a whole number by a proper fraction, the answer will always be less than the original number.

For example, 5 X J = 1 J

When you divide a whole number by a proper fraction, the answer will always be greater than the original number.

For example, 5 + \ = 20

V J

Copyright 2009 by Nelson Education Ltd. Chapter 4: Percents 37

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4.8 Combining Percents ] Use pei Use percents to solve problems involving two percentages.

1. Determine each amount,

a) 10% of 100 + 4% of 100

= % of 100

b) 7% of 100 + 10% of 100

= % of 100

You can add percents when they are both a percent of the same amount.

For example, 5% of $50 is $2.50 and 7% of $50 is $3.50, so 12% of $50 is $2.50 + $3.50 = $6.00

c) 17% of 100 + 14% of 100

= % of 100

2. Joan lives in Alberta, where the GST is 5% and there is no PST.

She plans to buy an MP3 player that is on sale for 15% off the regular price of $99.95.

Calculate the discounted price and the final cost.

3. Krista wants to buy a DVD. Store A sells the DVD at 10% off the regular price of $19.99.

Store B sells the same DVD for $22.99, w i th 15% off. Which store has the better price?

38 Chapter 4: Percents Copyright O 2009 by Nelson Education Ltd.

Name: Date:

4.9 Percent Change

1. Calculate each increase or decrease,

a) 35% increase f rom 15 =

b) 10% decrease f rom 27 =

2. Calculate each percent increase or decrease,

a) f rom 150 to 200 =

b) f rom 400 to 125 = . %

To calculate a percent increase or decrease, add or subtract that percent to 100% of the original amount.

For example, a 20% increase from 40 is 100% of 40 + 20% of 40 = 120% of 40 = 1.2 x 40 = 48

For example, a 20% decrease from 40 is 100% of 40 - 20% of 40 = 80% of 40 = 0.8 X 40 = 32

3. A footbal l player increased in mass f rom 100 kg to 115 kg in the off-season. Muscle makes up of human body weight.

What was the percent increase in amount of muscle?

4. Calculate the percent increase.

a) A retailer buys a pair of jeans for $25 and sells the jeans for $95.

b) An entertainment store buys CDs for $7 and sells them for $22.95.