C HAPTER 1: B EING A CONSUMER Math 10-3

R ATIO AND P ROPORTIONS 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?

R ATIO - 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 ---- = 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

E XAMPLE P ROBLEM : 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?

E XAMPLE 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 --- = *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 = mL water (OR 250 – 62.5 = mL)

A SSIGNMENT : Smarties Activity Ratios and Proportions.docx

D AY 2:

U NIT P RICE AND U NIT R ATE 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?

E XAMPLE : A PPLES COST $0.79/ KG. W HAT DOES THIS MEAN ? H OW MUCH WILL 5 KG OF APPLES COST ? ($3.95)

E XAMPLE : I F YOU BUY 4 ROLLS OF E CO - F RIENDLY TOILET PAPER FOR $2.68, WHAT IS THE COST OF 1 ROLL ? 2.68x = rolls roll x = $0.67

B ETTER B UY – W HEN COMPARING TWO PRODUCTS, DETERMINE THE UNIT PRICE. T HE 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 = L $1.50 x = x = $2.72/L L 1L $9x = ---- x= $2.25/L 4L 1L The 4 L pail is a better buy.

A SSIGNMENT : BetterBuy.docx FlyerAssignment.docx

D AY 3:

C ONVERTING F RACTIONS, D ECIMALS AND P ERCENTS & GST S ALES 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

T O CHANGE %  DECIMAL, DIVIDE BY 100 Ex. 15% = 15/100= % = 1.6/100 = % = 124/100 = 1.24

T O CHANGE DECIMAL  %, MULTIPLY BY 100 Ex x 100 = 36% x 100 = 4.7% 1.56 x 100 = 156%

R OUNDING : - W HEN 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 $ 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%

E X. S HELBY, WHO LIVES IN E DMONTON, WANTS TO BUY NEW JEANS WHICH COST $ S HE ONLY HAS $95. A FTER 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% = Multiply retail price by 0.05  $89.95 x 0.05 = $4.50 Add to the retail price  $ $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 = $ Yes she will have enough! Barely..!

Ex 2) Eric is at a furniture store in Saskatoon. The list price for a bedroom suite is $ 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% $ x 1.10 = $

A SSIGNMENT : PercentsDecimalsandGST.docx

D AY 4:

S ALES, % I NCREASES AND D ECREASES 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 $ Which is more appealing, $2.39/100 or $23.90/kg? (both are the same price!)

E X. A RLENE OWNS A FABRIC STORE. S HE PURCHASES FABRIC AT A WHOLESALE PRICE OF $46.00/ M. S HE CHARGES A MARKUP OF 20% ON THE FABRIC. W HAT 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

E X. 2 : R YAN OWNS A RECORD STORE. H E HAS A CRATE OF “A RCADE F IRE ” LP S THAT HE WANTS TO SELL. I F 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. $ $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.

S EASONS AND H OLIDAYS D EMAND 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.

A SSIGNMENT : settingaprice.docx

D AY 5

D ISCOUNTS - % O FF 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 = multiply 0.25 x $800 = $ $200 is 25% of $800

D ISCOUNTS OR SALES ARE USUALLY EXPRESSED AS “ PERCENT OFF ”. T HE AMOUNT THAT YOU SAVE IS SUBTRACTED FROM THE ORIGINAL PRICE. T YPICALLY 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) $ $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?

E X.3 A CAR DEALERSHIP IS OFFERING A SALE OF 1/5 OFF THE RETAIL PRICE OF THEIR NEW T OYOTA M ATRIX, PRICED AT $ W HAT IS THE SALE PRICE ? 1. Change the fraction to a percent. 1/5 = 0.20 = 20% 2. 20% = $ x 0.20 = $ (save) 4. $ $ = $ (sale price) What will the total be including GST? $ x 1.05 = $

E X.4 C LAIRE PAID THE SALE PRICE OF $45 FOR A PAIR OF SHOES THAT WERE ORIGINALLY PRICED AT $ W HAT 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 **

A SSIGNMENT : Discounts.docx

D AY 6:

C URRENCY E XCHANGE 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.

E X 1) T HE EXCHANGE RATE FOR THE EURO IS $ CAD = 1 E URO. Y OU BOOKED A HOSTEL IN R OME, I TALY FOR EUROS. H OW MUCH IS THE HOSTEL IN C ANADIAN DOLLARS ? *SET UP A RATIO!* X CAD/55.00 Euro = $ CAD /1 Euro *notice CAD is in numerator for BOTH ratios!* Cross multiply and divide to find the answer: x / 1 = $90.46 CAD

E X 2) Y OU ARE GOING ON A TRIP TO L ONDON, E NGLAND, AND HAVE SAVED UP $ CAD FOR SPENDING MONEY. H OW MANY B RITISH P OUNDS 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 = British Pounds

C URRENCY 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.

E X 3) Y OU ARE ON VACATION IN H ONG K ONG C HINA. Y OU WANT TO PURCHASE A PAIR OF P UMA RUNNERS FOR 670 ¥. Y OU COULD PURCHASE THE SAME SHOES IN C ANADA FOR $ S HOULD YOU BUY THEM IN C HINA ? 1. Find the exchange rate. You HAVE Chinese Yuan, so start in that column Chinese Yuan = $0.152 CAD. 3. Set up the ratio: x CAD/670¥ = $0.152 CAD/1¥ 4. Cross multiply and divide. 670 x /1 = $ CAD Yes! You should by them in China (it will be cheaper overall)

A SSIGNMENT : CurrencyExchange.docx