A. Proportional Money

1. A. Proportional Money Math 10: A and W WA10.10 Apply proportional reasoning to solve problems involving unit pricing and currency exchange.

2. Key Terms: • Find the definition of each of the following terms: • Buying Rate • Exchange Rate • Mark up • Promotion • Proportion • Rate • Ratio • Selling Rate • Unit Rate • Unit Price • Percent • Currency • Discount

3. 1. Proportional Reasoning • WA10.10 • Apply proportional reasoning to solve problems involving unit pricing and currency exchange.

4. 1. Proportional Reasoning • Math on the Job p.12 • Read through together and solve

6. a) Ratio – remember that a ratio compares 2 numbers that are measured in the same units • It can be written in several ways: • Examples 20 to 50, 20:50,

7. The notation will be most useful to us because our knowledge of fractions can help us to solve equations

8. When working with ratios its always best to simplify first. • Example Simplify

9. The two ratios 20:50 and 2:5 are equivalent statements and the fractional equation is referred to as a Proportion • Ratios are expressed in real-life situations as proportions. • For example, you may need to mix a certain shade of paint. The proportion needed is 3 parts blue and 1 part blue, or 3:1. You can use the ratio to mix the amount of paint you need in the correct proportion.

10. In a ratio, since the units are the same, they essentially cancel each other out. • So when doing calculations you can omit the units but must remember to included them in your answer.

11. Discuss the Ideas – Adapt a Recipe p. 13

12. Example 1

13. Example 2

14. Activity 1.1 – Visualize a Proportion p.15 • Work through individually using graph paper

16. Activity 1.2 – Fruit Drink Taste Tester p.16 • Work through individually making a copy of the chart in your notes

19. b) Rate – is a similar ratio, but it compares 2 numbers with different units • Examples • Number of words per minute • Price of lumber per foot • Price of apples per pound • Speed in kilometers per hour

20. A rate can be expressed in the same way as a ratio. • Because the units are different they must be included. • For example if you see salmon on sale for $1.89 for 100 grams you can write it as: • $1.89:100 grams, $1.89/100 grams, or

21. You can also think of a proportion as an equivalent statement between 2 rates. • For example, lets write a proportion for the salmon sale rate we just looked at.

22. Discuss the Ideas – Speed Skater p. 18 • Read through together and solve

23. Example • If salmon costs $1.89 for 100 grams, how much will it cost to but 250g of salmon? • A local plumber store sells 100 copper-plated pipe straps for $4.97. You have estimated that you require 75 straps. How much will you pay for 75 straps?

24. Mental Example • No calculators allowed, try to just use your brain. 1. The pipe straps in the previous example each cost $0.0497. About how much will 50 straps cost?

25. Building your Skills • Ex. 1.1 (p.21) #1-9

26. 2. Unit Price • WA10.10 • Apply proportional reasoning to solve problems involving unit pricing and currency exchange.

27. 2. Unit Price • Math on the Job p. 23 • Read through together and solve

29. a) Unit Price • Different brands may package their products in different sizes of packages • Finding a unit price will allow you to compare prices, and help you determine the best buy

30. Consumer goods, such as pens and toilet paper are sold in bundles. To compare the price when the quantity in the package is not the same, it is often useful to look at the unit cost of one item. • Businesses who purchase in bulk and then want to charge customers for one item at a time also need to calculate the cost of 1 item

31. A Unit Price is the cost of one unit. It is sometimes referred to as a unit rate. • To calculate a unit price, you can set up a proportion when the second rate has a denominator of 1

32. Example • If you buy a package of 4 rolls of paper towel for $2.68, calculate the cost of one roll.

33. Therefore, cost per unit or unit price can be determined by dividing the price of a product by the number of units contained in a product

34. Comparing unit prices can save you money at home and in the workplace • What other factors should you consider when purchasing items in packages: • More than you need • Previous experience with brand • Quality of product

35. Example • Steph buys supplies for the hamlet office where she works as a clerk. She wants to buy pens. The supplier sells a box of 12 pens for $6.25. Calculate the unit price of 1 pen.

36. Example • Bryce picks fresh strawberries at a U-pick farm in Portage la Prairie, Manitoba. If he fills a pint basket (0.5506 liters), it will cost him $1.50. If he fills a 4-liter ice cream pail, it will cost $9.00. Which size of container will give her a better buy?

37. Activity 1.3 – Which Price is Right? P. 25 • Work through with a partner.

38. Building your Skills • Ex. 1.2 (p.26) #1-7

39. 3. How Prices are Set • WA10.10 • Apply proportional reasoning to solve problems involving unit pricing and currency exchange.

40. 3. How Prices are Set • Math on the Job p. 28 • Why would businesses have sales? • Read through together and solve

42. What must be taken into consideration when estimating a job and what are consequences that happen when it is done poorly? Estimating to little time can lead to labour shortages, costs over running, disappointed clients and so on. The cost estimator must ensure that the final price covers all cost plus make a profit.

43. Prices rise and fall due to consumer demand and supply. • If demand rises, suppliers are able to charge more. • If demand falls, or if there is a large supply of a product, prices may fall.

44. Prices also rise and fall according to the cost of the materials and labour that go into the creation of a product or services • An additional amount, called Markup, is added to these costs so that a profit can be made.

45. For example, when an owner of a market buys items to re-sell them, he or she buys them at a wholesale price. They then markup that price so the item is sold at a higher price to make a profit. • The markup, is usually a percent of the wholesale price

46. When setting a price for goods and services, companies consider psychological factors that have an impact on buyers as well. • Have you ever wondered why something costs $39.95 instead of $40.00? The final price is not that different but it seems less expensive to the buyer before taxes.

47. A butcher may advertise a price of $2.39/100g for meat instead of $23.90/kg because it seems less expensive, even though they are equivalent.

48. Remember that in many cases taxes are added to arrive at the total price. Taxes are calculated as a % of the price paid. • All Canadians pay the Federal Goods and Services Tax (GST), which is 5%. Most Provinces also charge a Provincial sales tax (PST) • Alberta 0% • BC 7% • Manitoba 7% • Saskatchewan 5%

49. Discuss the Ideas – Concert Promoter p.29 • Read through together and solve