CHAPTER 1: BEING A CONSUMER

Math 10-3

RATIO AND PROPORTIONS

many girls to the total number students in the class? boys?

Could we use these numbers to estimate how many boys there are in Mrs. Rawluk’s class right now?

RATIO - A COMPARISON BETWEEN TWO NUMBERS WITH THE SAME UNITS

Fraction form 2/3 Other form 2:3 *you must use this form when dealing with 3 or more

quantities*

Equivalent ratios: If each quantity is multiplied or divided by the same number, the result is an equivalent ratio

Ex. 2/3 is equivalent to 4/6 Ex. 4:5:7 and 12:15:21

*Reducing a ratio is the same as reducing a fraction When will we use this?

Ratios are most useful to use as proportions – a fractional statement of equality between two ratios or rates.

Ex. Solve for the missing terms in each proportion:7 x---- = -----15 45 x = 21  Two ways – cross multiply and divide OR how did

we get from 15 to 45? Multiply by 3 so we must multiply 7 by 3 as well

2:9 = x : 27 x = 6

EXAMPLE PROBLEM:

You are mixing antifreeze and water. The instructions state that the ratio of antifreeze to water should be 1:3

If the bottle of antifreeze is 500 mL, how much water do you need to mix in?

How should we write the ratio? What does it mean? Is there more water or antifreeze in the mixture?

EXAMPLE PROBLEM CONTINUED…

You are mixing antifreeze and water. The instructions state that the ratio of antifreeze to water should be 1:3

If the bottle of antifreeze is 500 mL, how much water do you need to mix in?

3 x--- = ----1 500*hint: Always write what

you are looking for (x) in the numerator (top) of your fraction! Be careful though to make sure your fractions match up.

You need 1500 mL of water.

If your radiator holds 250 mL of liquid, how much water and antifreeze do you need so that you do not damage your radiator?

How many parts are there? How many parts total are there?

If your radiator holds 250 mL of liquid, how much water and antifreeze do you need so that you do not damage your radiator?

Calculate: We have 1 part antifreeze

to 3 parts water. 1+3 = 4 parts total 1/4 parts are to be

antifreeze 3/4 parts are to be water

¼ = x/250 x = 62.5 mL

antifreeze

¾ = x/250 x = 187.5 mL

water

(OR 250 – 62.5 = 187.5 mL)

ASSIGNMENT:

Smarties Activity Ratios and Proportions.docx

DAY 2:

UNIT PRICE AND UNIT RATE

Unit Price - The cost of one unit; a rate expressed as a fraction in which the denominator is 1

Unit Rate – The rate or cost for one item or unit

To calculate a unit price, you can use a proportion where the second rate has a denominator of 1.

where we would see unit prices and unit rates?

EXAMPLE: APPLES COST $0.79/KG . WHAT DOES THIS MEAN? HOW MUCH WILL 5 KG OF APPLES COST?

($3.95)

EXAMPLE: IF YOU BUY 4 ROLLS OF ECO-FRIENDLY TOILET PAPER FOR $2.68, WHAT IS THE COST OF 1 ROLL?

2.68 x ------- = --------- 4 rolls roll x = $0.67

BETTER BUY – WHEN COMPARING TWO PRODUCTS, DETERMINE THE UNIT PRICE. THE LOWER PRICE IS THE BETTER BUY!

Example: Claire picks fresh strawberries at a farm. Each pint basket she picks costs $1.50 or she can fill a 4 L pail for $9.00. Which container is the better buy?

*Always make sure to compare the same units! A pint = 0.5506 L

$1.50 x-------- = ------ x = $2.72/L0.5506L 1L

$9 x----- = ---- x=

$2.25/L4L 1L

The 4 L pail is a better buy.

ASSIGNMENT:

BetterBuy.docx FlyerAssignment.docx

DAY 3:

CONVERTING FRACTIONS, DECIMALS AND PERCENTS & GST SALES

Percent - means “out of 100”. A percentage is a ratio in which the denominator is 0.

Fraction – “Is over Of”; a part of a whole.

Decimal - a fraction that has been divided. Ex. ¼ = 0.25

TO CHANGE % DECIMAL, DIVIDE BY 100

Ex. 15% = 15/100= 0.15

1.6% = 1.6/100 = 0.016

124% = 124/100 = 1.24

TO CHANGE DECIMAL %, MULTIPLY BY 100

Ex. 0.36 x 100 = 36%

0.0047 x 100 = 4.7%

1.56 x 100 = 156%

ROUNDING: - WHEN ROUNDING “MONEY” ALWAYS ROUND TO THE NEAREST CENT (2 DECIMAL PLACES).

Look at the number to the right: If it is less than 4, keep the number the same. If it is 5 or greater, round the number up 1.

Ex. $5.678 rounds up to $5.68

$24.543 rounds to $24.54

GST

Taxes are calculated as a percentage of the price paid. All Canadians pay the federal Goods and Services Tax (GST), which is currently 5%. Most provinces also charge a Provincial Sales Tax (PST).

Alberta – 0% BC – 7% Manitoba – 7%

Saskatchewan – 5%

EX. SHELBY, WHO LIVES IN EDMONTON, WANTS TO BUY NEW JEANS WHICH COST $89.95. SHE ONLY HAS $95. AFTER GST IS ADDED, WILL SHE HAVE ENOUGH? There are two ways to

calculate the tax on an item:

*First though, always change your percent to a decimal!*

5% = 0.051. Multiply retail price by

0.05 $89.95 x 0.05 = $4.50

Add to the retail price $89.95 + $4.50 = $94.45

OR…2. Multiply retail price

by decimal + 1 (1.05). This calculates the retail price in so you don’t have to add after!

$89.95 x 1.05 = $94.45 - Yes she will have enough! Barely..!

Ex 2) Eric is at a furniture store in Saskatoon. The list price for a bedroom suite is $1599.00. What will the total cost be, including GST and PST?

To make this easier, add the two tax rates together!

GST = 5% PST (Sask)= 5% Total tax = 10%

$1599.00 x 1.10 = $1758.90

ASSIGNMENT:

PercentsDecimalsandGST.docx

DAY 4:

SALES , % INCREASES AND DECREASES

Markup – the difference between the amount a dealer sells a product for and the amount he or she paid for it. Usually the markup is a percent of the wholesale price.

Wholesale – what the dealer paid Retail – what you (the consumer) pays.

why a retailer might sell something for $39.95 instead of $40.00. Which is more appealing, $2.39/100 or $23.90/kg? (both are the same price!)

EX. ARLENE OWNS A FABRIC STORE. SHE PURCHASES FABRIC AT A WHOLESALE PRICE OF $46.00/M. SHE CHARGES A MARKUP OF 20% ON THE FABRIC. WHAT DOES SHE CHARGE HER CLIENTS?

$46.00/m x 0.20 = $9.20

$46.00/m+$9.20 = $55.20/m

OR…. $46.00/m x 1.20 = $55.20/m

EX. 2 : RYAN OWNS A RECORD STORE. HE HAS A CRATE OF “ARCADE FIRE” LPS THAT HE WANTS TO SELL. IF HE BOUGHT THE RECORDS FOR WHOLESALE $15.00 /RECORD AND SELLS THEM FOR $21.00 EACH, WHAT IS HIS PERCENT MARK UP? First, we need to

determine how much he increased the price.

$21.00 - $15.00 = $6.00 increase.

We now take this number and divide it by the wholesale price.

$6/$15 = 0.40

Last, we multiply by 100 to change to a percent

0.40 x 100 = 40% markup.

SEASONS AND HOLIDAYS DEMAND FOR GOODS AND SERVICES VARIES WITH THE SEASONS, AND AS A RESULT SO DOES THE PRICE OF THESE GOODS AND SERVICES. Consider the price of roses. What time of

year are the roses most expensive? Why? Mother’s day, valentine’s day, because

people like to give roses for these occasions Consider the price of gasoline. What time of

the year is gasoline most expensive? Why? Summer, long weekends, holidays, because

this is the time when people like to travel long distances.

ASSIGNMENT:

settingaprice.docx

DAY 5

DISCOUNTS- % OFF

Percent means out of 100! Percents are easier to work with if we change them to a decimal first.

Ex. Find 25% of $800 1) Change % to a decimal: 25/100 = 0.25 -multiply 0.25 x $800 = $200.00

$200 is 25% of $800

DISCOUNTS OR SALES ARE USUALLY EXPRESSED AS “PERCENT OFF”. THE AMOUNT THAT YOU SAVE IS SUBTRACTED FROM THE ORIGINAL PRICE. TYPICALLY ANY SALES ARE CALCULATED BEFORE GST IS ADDED. Ex.2 A pair of jeans

that cost $80.00 are on sale for 25% off. What is the sale price?

25% = 0.25 $80.00 x 0.25 = $20

(save) $80.00 - $20.00 =

$60.00 (sale price)

What will the total be including GST (5%)?

5% = 0.05 Remember, the “trick” add 1!

$60.00 x 1.05 = $63.00

What if the sale is given as a fraction?

EX.3 A CAR DEALERSHIP IS OFFERING A SALE OF 1/5 OFF THE RETAIL PRICE OF THEIR NEW TOYOTA MATRIX, PRICED AT $16 665.00. WHAT IS THE SALE PRICE?

1. Change the fraction to a percent. 1/5 = 0.20 = 20%

2. 20% = 0.20 3. $16 665 x 0.20 =

$3 333.00 (save) 4. $16 665 - $3

333.00 = $13 332.00 (sale price)

What will the total be including GST?

$13 332.00 x 1.05 = $13 998. 00

EX.4 CLAIRE PAID THE SALE PRICE OF $45 FOR A PAIR OF SHOES THAT WERE ORIGINALLY PRICED AT $60.00. WHAT DISCOUNT WAS SHE GIVEN?

Sale price = percent of original price Original price $45/$60 = 0.75 or 75% -- this means she

PAID 75% of the original price. To determine the sale percent, subtract from 100%

100% - 75% = 25% the sale was 25% off.

*check* $60 x 0.25 = $15 $60 - $15 = $45 **

ASSIGNMENT:

Discounts.docx

DAY 6:

CURRENCY EXCHANGE Discuss international travel with students. Discuss

that sometimes, your bank may have to order foreign currency in for you, if they do not normally carry it. Always plan ahead!

Currency - the system of money a country uses. Exchange rate - the price of one country’s currency

in terms of another nation’s currency. *Currency Exchange rates change every day!*

Currency exchange can get confusing. The best thing to do is to always set up a ratio with what you WANT in the numerator and what you HAVE in the denominator.

EX1) THE EXCHANGE RATE FOR THE EURO IS $1.644814 CAD = 1 EURO. YOU BOOKED A HOSTEL IN ROME, ITALY FOR 55.00 EUROS. HOW MUCH IS THE HOSTEL IN CANADIAN DOLLARS?

*SET UP A RATIO!* X CAD/55.00 Euro = $1.644814 CAD /1 Euro *notice CAD is in numerator for BOTH ratios!*

Cross multiply and divide to find the answer: 55.00 x 1.644814 / 1 = $90.46 CAD

EX 2) YOU ARE GOING ON A TRIP TO LONDON, ENGLAND, AND HAVE SAVED UP $800.00 CAD FOR SPENDING MONEY. HOW MANY BRITISH POUNDS CAN YOU PURCHASE IF THE EXCHANGE RATE IS $1.650 CAD = 1 BP?

X BP/$800 CAD = 1 BP/$1.650 CAD $800 x 1 / $1.650 = 484.85 British Pounds

CURRENCY TABLE

To use the currency chart, find the COLUMN (up/down) for the currency you are starting with. Go down the column to find the exchange rate for the currency you want to convert to.

EX3) YOU ARE ON VACATION IN HONG KONG CHINA. YOU WANT TO PURCHASE A PAIR OF PUMA RUNNERS FOR 670 ¥ . YOU COULD PURCHASE THE SAME SHOES IN CANADA FOR $120.00. SHOULD YOU BUY THEM IN CHINA?

1. Find the exchange rate. You HAVE Chinese Yuan, so start in that column.

2. 1.00 Chinese Yuan = $0.152 CAD. 3. Set up the ratio: x CAD/670¥ = $0.152

CAD/1¥ 4. Cross multiply and divide. 670 x 0.152 /1

= $101.84 CAD Yes! You should by them in China (it will be

cheaper overall)

ASSIGNMENT:

CurrencyExchange.docx