Percent

N.3: bemonstrate an understanding of percents greaterthan or equal to 0%, including greater than 100%.

Percents Greater than 100%Sometimes percents can be more than 100%. If 100% representsone whole then amounts greater than 100% are more than onwhole.

How could you represent 125%?

Here is an example:

Bill has this much money: Gabe has this much money:

Gabe has 125% of the amount Bill does.

How else can we represent percents greater than 100%

130%I

[EE

150%

To calculate percents greater than 100% you canpercent to a decimal and multiply.

convert the

Ex. Jimmy is 145% of his height three yearsIf he was 110 cm three years ago, howtall is he now?

145% of 110cm

1.45 x 110cm 159.5cm

Jimmy is now 159.5 cm tall.

ago.

wkst. 4.1p. 147-149 # 1, 2, 3, 5, 6, or 5, 8-10, 13

Date:

Represent and interpret percents greater than 100%.

100%

1. Represent each percent on the 10-by-iC grids.Use one full grid to represent 100%.

a) 175%

b) 280%

AtHome Heft,Percent means “per one hundred:’To represent a percent greaterthan 100%, first represent 100%.Use this representation to showpercents greater than 100%.For example, represent 150%using lO-by-lO grids:one grid is 100%

For example, 150% of 30 =?100%of3O =3050%of3O =15150% of 30 = 30 ÷ 15 = 45

2. Solve.

a) 140%of8O=

___

b) 210% of 11 =

____

3. Calculate each amount.

a) 250% of $30=

___

b) 175%of$30=

___

c) 350% of $30 =

____

c) 160%of3O=

___

d) 350% of 50 =

____

4. There are 500 students enrolled in David’s school.This is 175% of the enrollment in the school when it opened 10 years ago.How many students were in David’s school when it opened?

GOAL

I

100% + 50% = 150%

Copyright 02009 by Nelson Education Ltd.Chapter 4: Percents 31

Fractional PercentsA fractional percent is a percent between 0% and 1%.

When we write a fractional percent as a decimal wefollow the same rule of moving the decimal two placesto the left.

Ex. In a survey of Albertans, 0.6% of people said they do notlike chocolate. If there are 620 students in our school, howmany do not like chocolate?

0.6% Qf 620 is

0.006 x 620 3.72

3.72 kids do not like chocolate

wkst. 4.2p. 152-153 # 1, 2, 3,4, 6 or 4, 6, 8, 9

When we look at a hundred grideach box represents 1%

What if one of those boxes isonly partly used.

This is a fractional percent.

-F

04.2 Fractional Percents

GOAL

Represent and interpret percents between 0% and 1%.

At-Home ,jIj)

To represent percents that involve

parts of 1%, divide 1% into parts.

For example, you can express2.5% as 2% + 0.5%. 0.5% is halfof 1%.

Represent 2.5% on athousandths grid.

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.

.:-.

iW Date

(3

1. Represent each percent on a thousandths grid.

a) 25.5% II111111111

HJ__

Il1

Dffi+H1iIlIIlI(III I’llmmiriiir 1111

1111111 111111iiiiiiiiiii.FfI1r.E11 1—141I

III

b) 4.3%

I I I(LI,,

m

UJlffF[ml

11+fffHFfffl-iII

ii

lIIlIIIIIllIIliii’Ffli

25 thousandths, or

IFq:

32 Chapter 4: Percents Copyright 0 2009 by Nelson Education Ltd.

Solving Problems with PercentRemember, when solving problems with percent, there arethree components to the question.

Total - this is the amount representing 100%Amount - this is the amount equal to the percentPercent - this is the percent equal to the amount

Jeff paid $32 for avideo game which wason sale for 10% off.How much was theregular price?

Cindy bought a shirtwhich cost $25.When she got to thetill she found out iswas on sale for 25%off. How much didshe pay?

%xTA

Percent of Total is Amount

When solving percent problems, you will usually have two ofthese pieces of information and need to solve for thethird.

Remember -

always convert or/todecimalbefore doing /o X T Acalculations.

If you put in the variables, treat it like an algebraic equationand solve for the unknown variable you will have your answer.

Greg bought acollector comic bookfor $15 three yearsago. He sold it for$23 at a collectorshow. What percentof the original pricedid he sell it for?

%xT A %xTA

biscounts and Taxesbiscount: when the regular price of an item is reduced, or theprice is dropped. This can happen as a sale (25% off) or acoupon ($10 off).

This leaves us with two prices:

1. The regular price: represented by 100% of thecost of the item

2. The sale or discounted price: represented bya portion of the regular price

For example:A pair of jeans costs $75.00. They are on sale for 30%off. What is the sale price of the jeans?

If the cost of the jeans is 100% and the sale is 30%, thenthe sale price of the jeans will be:

100% - 30% 70%

70% Of the original cost

0.70 X $75.00 $52.50

The sale price of the jeans is $52.50!

0

Sometimes, we want to know how much we saved.

We can figure this out in two ways:

1. We could find the difference between the regular price

and the sale price:

$75.00 - $52.50 $22.50

We saved $22.50 on the jeans

OR

2. We could find the percent of the original price we saved:

30°/a of $75.00 was saved

0.30 X $75.00 $22.50

We saved $22.50 on the jeans

Taxes: Often there is an additional charge added on to our

purchases. These are taxes we pay to the government. Taxes

are always applied to the amount you pay, so make sure you take

discounts off before calculating taxes!

• This leaves us with two prices:

1. The regular price: represented by 100% of the cost

of the item

2. Price plus tax: the regular price plus taxes

For example:

A pair of jeans costs $80. In Alberta we pay 5% GST.

What is the cost of the jeans?

If the cost of the jeans is 100% and the taxes are 5%, then

the cost of the jeans will be:

100%+5%: 105%

105% of the original price

1.05 X $80.00 $84.00

The jeans cost $84.00!

Sometimes we want to know how much taxes we paid. Wecould find this in two different ways:

1. We could find the difference between the regular price andthe price with taxes:

$84.00 - $80.00 $4.00

We paid $4.00 in taxes

or

2. We could find the percent of the original price we paid:

5% of $80.00 was taxes

0.05 X $80.00: $4.00

We paid $4.00 in taxes

In some provinces, there is also a provincial sales tax along withthe GST. To calculate the total taxes, you Just need to add thetaxes together and find the percent of the original price.

For example:

When shopping in BC you buy a really cool T-shirt. Theprice on the tag says $15, but you know that there is 7%PST as well as 5°le GST added on.

If the cost of the shirt is 100%, then we just need toadd the cost of the taxes:

100%+7%+5%= 112%

112% of the original price

1.12 X $15 t $16.80

wkst. 4.5,4.7p. 166-157 # 3-6 or 7-12

Date:

ig Percent Problems Usingimals

1. Write equations involving decimals you can use to solveeach, then solve the equations.

a) 13.2% of 87

b) 85.5% of 298

c) 146%of5O

d) 0.5%of9

2. Calculate.

At-Home i-k4pTo express a percent as a decimal,express it as a number ofhundredths.For example, what is 124% of 18?124% is 124 hundredths, or 1.24.124% of 18 = 1.24 X 18

= 22.32For example, if 200 is 40% of anumber, what is the number?

40% of number = 2000.40 X number = 200

number 200 ÷ 0.40= 500

Ia) 12% of 90=_

b) 175%of3O=.

c) 3.2% of 300 =

3. Mike’s parents bought him a new computer for $999.It was on sale for 75% of the original cost.What was the original price?

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

GOAL

Copyright 02009 by Ne’son Education Ltd.Chapter 4: Percents 35

__________________

Date:

________________________

Percent Problems Using

I

Create and solve a percent problem using fractions.

1. Write each percent as a fraction.

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 population.How many students attend this school?

4. Angelie 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?

Copyright © 2009 by Nelson Education Ltd.

[At-Home!When you multiply a wholenumber by a proper fraction, theanswer will always be less thanthe original number.Forexample,5 x = 1When you divide a whole numberby a proper fraction, the answerwill always be greater than theoriginal number.For example, 5 ÷ = 20

-J

Chapter 4: Percents 37

GOAL

Combining Percents

When calculating two percentages of the same number you can combinethe percents together.

Ex. In all other provinces, except Alberta, there is both a provincialsales tax (PST) and GST. In British Columbia the provincial soles tax is7% and they also pay the 5% GST. The cost of the item can be figuredout by:

Finding out the PST and GST Combining the percentagesseparately and adding the together and then finding outamounts together. the combined percentage of the

total.

5 % of $25: $1.25 5% + 7%: 12%

7% of $25: $1.75 12% of $25: $3.00

$1.25 + $1. 75: $3.00 5 the total tax is $3.00

So the total tax is $3.00

wkst. 4.8p. 176-177 #1-4 or 5-9

Date:

________________________

bining Percents

1Use 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

c) 17% of 100 + 14% of 100

_____________%

of 100

38 Chapter 4: Percents

At-HomeYou can add percents when theyare both a percent of the same

_______________

amount.

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

:3

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, with 15% off. Which store has the better price?

Copyright 0 2009 by Nelson EducatIon Ltd.

GOAL

Percent ChangePercent chan9e is a way of expressing a change (of amount,money, population, mass...) as a percent.

1. To calculate a percent increase:

Add that percent to 100% of the originalamount

For example: A 40% increase from $75 is:

100%÷40%

140% of $75

1.4 X $75 $105.00

$105 is a 40% increase from $75

2. To calculate a percent decrease:

• Subtract that percent from 100% of the original amount

For example: A 20% decrease from $110

100%- 20% 80%

0.8 X $110 $88.00

$88 is a 20% decrease from $110

BLM 4.9

p. 181-183 # 1, 2, 3, 4, 6 or 6, 7, 10, 13

Date:

21

Solve problems involving changes described as percents.

1. Calculate each increase or decrease.

a) 35% increase from 15 =

_____________

b) 10% decrease from 27 =

______________

2. Calculate each percent increase or decrease.

a) from 150 to 200 =

_____________%

b) from 400 to 125 =

_____________%

3. A football player increased in mass from 100Muscle makes up of human body weight.What was the percent increase in amount of muscle?

4. Calculate the percent increase.

Copyright 02009 by Nelson Education Ltd.

At-Home H4pTo calculate a percent increase ordecrease, add or subtract thatpercent to 100% of the originalamount.

_______________

For example, a 20% increasefrom 40 is100% of 40 + 20% of 40= 120% of4O= 1.2 x 40= 48For example, a 20% decreasefrom 40 is100% of 40 — 20% of 40= 80% of 40

______________

= 0.8 x 40= 32

kg to 115 kg in the off-season.

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.

Chapter 4: Percents 39

GOAL