1. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 1 Chapter 1 Basic

2. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 2 After completing this chapter, you will be able to: Perform arithmetic operations in their proper order Convert fractions to their percent and decimal equivalents Maintain the proper number of digits in calculations Solve for any one of percent rate, portion, or base, given the other two quantities also… Learning Objectives LO 1. LO 2. LO 3. LO 4.

3. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 3 Calculate the… Gross earnings of salaried, hourly wage, or commission employees Simple average or weighted average (as appropriate) of a set of values, and Perform basic calculations of the Goods and Services Tax, Provincial Sales Tax, and Property Tax Learning Objectives LO 5. LO 6. LO 7.

4. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 4 rithmetic perations LO 1. Basic Mathematics Basic Mathematics

5. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 5 B rackets E xponents D ivision M ultiplication A ddition S ubtraction ( ) 2 4(2 - 5) -or 4 x (2 - 5) + – -or 2 x 2 -or / -or 4 * (2 - 5)

6. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 6 How do we evaluate (solve) the following problem? Known as an‘Expression’! 72 (3 x 2 2 ) – 6

7. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 7 72 (3 x 2 2 ) - 6 = 0 72 (3 x 2 x 2) - 6 = 72 12 - 6 = = 6 - 6 = 72 (3 x 2 2 ) - 6 B E D M A S

8. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 8 Decimals to Percents Percents to Decimals Converting LO 2.

9. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 9 Decimal.75 Move decimal point two places to Right for % 75% 5.0500% Move decimal point two places to Left for decimal 35%.35 2.5250% Converting Decimal 1.745174.50%.124 12.4%

10. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 10 Fractions to Percents Percents to Fractions Converting

11. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 11 Converting 10% 1 10 Fraction Top / Bottom * 100 5 13 38.4615% Percents 15% 15 100 Percent / 100 Fraction 384 1000 Percents 38.4%

12. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 12 Decimal Fractions Converting Decimals to

13. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 13 …with appropriate number of zeros Converting Write Digits. 24 Decimal Decimals toDecimal Fractions Step 1 Step 2 Divide by 1 Fractions. 24 100 24 100. 345 1000 345 1000.2.2. 2 10 2 10

14. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 14 Decimals LO 3. Basic Mathematics Basic Mathematics

15. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 15 5 13.384615 DecimalFraction 38.4615% Percent Rounding Decimals 1 2 3.4.4.38.385 5.38462 38.5 38.46 38.462 If next digit is 5 or more, then raise current one to next highest digit. Decimal Places Example

16. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 16 A bag contains 46 M & M’s of various colours. The 46 candies are distributed as follows: 18 Yellow 10 Red 7 Orange 5 Green 6 Brown. Example Show the distribution in (a) fractions, (b) decimals, and (c) as a percent. Calculation

17. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 17 No. Colour Yellow Red Orange Green Brown 18 10 7 5 6 46 18 46 Fraction Decimal (hundredth) Percent (hundredth).3939.13%.2221.74%.1515.22%.11 10.87%.1313.04% 10 46 7 5 5 6 6 46/46 = 11.00 = 1100 % = 1

18. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 18 LO 4. Basic Mathematics Basic Mathematics

19. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 19 This indicates the Portion that has to be found! …using the ‘Triangle’ will help us remember the above formula! P ortion = R ate * B ase Formula The formula to use in percent calculations is: P RB P =P = “…is ” or “…are ” R =R = “%” indicates the Rate B = “…of ” indicates the Base which is 100% or 1 “…of ” indicates the Base which is 100% or 1 Question is asking for…

20. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 20 Where variables are BESIDE EACH OTHER this means to MULTIPLY! Where a variable is ABOVE ANOTHER this means to DIVIDE! P RB Using this tool! P/ R=B P = R*B P ortion = R ate * B ase Formula The formula to use in percent calculations is:

21. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 21 P ortion = R ate * B ase Formula The formula to use in percent calculations is: If you want to find P then R*B If you want to find R then P/R then P/B If you want to find B P RB Using this tool!

22. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 22 P RB Sales of McDonalds drive-thru customers are 60% of total sales. Total McDonald sales are $1,600,000. What are the drive-thru sales ? What do you have to find? P ortion = R ate * B ase Formula P = 60% * $1600000 or P =.60 * $1600000 P = $960,000 Solving for Portion

23. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 23 P RB What do you have to find? R ate = P ortion / B ase Formula R = $640,000 / $1,600,000 Sales of McDonalds drive-thru customers are 60% of total sales. Total McDonald sales are $1,600,000. R = 40% Solving for Rate $1,600,000 - 960,000 $ 640,000 $1,600,000 - 960,000 $ 640,000 What percent of customers eat in the restaurant?

24. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 24 What do you have to find? Sales of McDonalds drive-thru customers are 60% of total sales. Sales of eat-in customers are $640,000. Solving for Base What are McDonald’s total Sales? P RB B = $640,000/ B = $1,600,000 $640,000 = 40% of Base B ase = P ortion / R ate Formula 40% The $640,000 is 40% of what total sales?

25. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 25 You buy a new stereo in Ontario and pay a total of $649. This includes 7% GST and 8% PST. Find (a) the sticker price of the stereo before taxes, and (b) the amount of each tax. Solving for Base What do you have to find? The problem can be restated as: $649 is 115% of the sticker price. 7% GST + 8% PST Calculate

26. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 26 You buy a new stereo in Ontario and pay a total of $649. This includes 7% GST and 8% PST. Find (a) the sticker price of the stereo before taxes, and (b) the amount of each tax. Solving for Base $649 1.15 $649 is 115% (or 1.15) of the sticker price.Statement: = $564.35 (A) (B) $564.35 * 7% GST $564.35 * 8% PST = $45.15 = $39.50 $39.50 GST $45.15 PST $39.50 GST $45.15 PST $564.35 + = $649

27. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 27 If McDonald’s sales increase from $1,600,000 to $2,400,000, what is the percent change? % change = Difference Base This method is referred to as the Base Method This method is referred to as the Base Method $1,600,000 Initial(Base)Value $ 1,600,000 Final Value 2,400,000 Difference$ 800,000 % change = $ 800,000 = 50% or.5 Increase Solving for Rate of Percent Change

28. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 28 8:00a LO 5. Basic Mathematics Basic Mathematics

29. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 29 8:00a Salaried Commissioned Hourly Payroll Cheque $ Pay / 00001 Company Income Earners

30. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 30 Receives an ANNUAL amount. e.g. $50,000 per annum 8:00a Payroll Cheque $ Pay / 00001 Salaried Usually paid Semi-Monthly or Bi-weekly May receive other incentive payments. e.g. Year-end Bonus

31. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 31 Receives a percentage of sales made. e.g. Personal Sales $250,000 @ 10% Commission 8:00a Payroll Cheque $ Pay / 00001 Commissioned Can be paid both a salary and receive commission. May receive other incentive payments. e.g. Exceeding sales quota - $20,000 @ 3% Can be paid Semi-Monthly or Bi-weekly.

32. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 32 8:00a Payroll Cheque $ Pay / 00001 Hourly Where employees are paid on an hourly basis, for an agreed number of hours per day, and for an agreed number of days per week, then the employee is referred to a an hourly employee. In most cases this employee belongs to a recognized labour union, and wages are usually paid weekly. - May also receive ‘production bonuses’.

33. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 33 …Cycle 8:00a Paid Weekly Bi- Weekly Semi- Monthly Monthly Period Once a Week Every Two Weeks Twice a Month Once a Month (b) Payments per Year (a) / (b) Pay (a) Annual Income $40,000 52 26 24 12 = $769.23 = $1,538.46 = $1,666.67 = $3,333.33

34. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 34 8:00a Payroll Cheque $ Pay / 00001 Hourly If an hourly employee has to work more hours than the agreed number, then extra pay is rewarded to recognize this overtime occurrence. The overtime rate is usually 1.5 times the hourly rate Overtime

35. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 35 8:00a You are contracted to work a 40 hour week. Due to the illness of a colleague you have been required to work an extra 8 hour shift. You are paid $15.00 per hour with overtime at time and one-half. What is your Gross pay for the week? Regular Hours worked 40 @ $15.00$600.00 Overtime Hours 8 @ $22.50 180.00 Overtime Rate = $15.00 * 1.5 = Overtime Rate = $15.00 * 1.5 = 48 $780.00 $22.50

36. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 36 8:00a Payroll Cheque $ Pay / 00001 Commission Larry is paid a straight commission of 8%. His computer net sales were $100,000. Larry’s draw was $750. How much commission is still due to Larry? Draw = An advance on future Commission earnings. Calculation

37. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 37 8:00a Larry is paid a straight commission of 8%. His computer net sales were $100,000. Larry’s draw was $750. How much commission is still due to Larry? Net Sales$100,000 * 8% =$8,000 Less: DRAW 750 Commission due to Larry$7,250

38. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 38 8:00a Payroll Cheque $ Pay / 00001 Commission This refers to the payment of different commission rates for various levels of sales. Variable Commission Scale

39. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 39 8:00a Your car net sales were $120,000. Based on the Commission Scale, what are your gross commissions? Up to $25,0005% $25,001 - $40,000 7% Over $40,0018% Commission Scale 120,000 25,000 $ 15,000 80,000 Commission *.05 = $1,250 *.07 = 1,050 *.08 = 6,400 $8,700

40. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 40 8:00a Payroll Cheque $ Pay / 00001 Salary plus Commission You receive a salary of $2,500 per month. In addition, you receive a 5% commission for sales over $15,000. Last month’s sales were $75,000. Calculate your gross pay. Calculation

41. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 41 You receive a salary of $2,500 per month. In addition, you receive a 5% commission for sales over $15,000. Last month’s sales were $75,000. Calculate your gross pay. 8:00a Gross Pay = Salary + Commission = $2,500 + = $5,500. $75,000 -15,000 $60,000 $75,000 -15,000 $60,000 *.05) ($60,000

42. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 42

43. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 43 Ontario Transport has 46 drivers each earning $20.50 per hour, 14 clerical staff members each earning $15.00 per hour, and 10 mechanics each earning $29.00 per hour. What is the Simple Average of the 3 hourly wages? SA Wage = (20.50 + 15.00 + 29.00 ) / 3 = $64.50 / 3 = $21.50 = Wages per hour / # different wages

44. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 44 Ontario Transport has 46 drivers each earning $20.50 per hour, 14 clerical staff members each earning $15.00 per hour, and 10 mechanics each earning $29.00 per hour. (Wage 1* #D + Wage 2*#C + Wage 3*#M) ((20.50(46) +15.00(14) + 29.00(10)) ($943 + 210 + 290) / 70 Calculate the Weighted Average hourly rate earned by the 3 categories of employees. ($1443.00) / 70 WA Wage = Total # of Employees (46+14+10) WA Wage = = $20.61 = 70

45. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 45 LO 7. Basic Mathematics Basic Mathematics

46. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 46 Register sales amounted to $5,000 and included 15% for PST and GST Taxes. What were the actual sales before taxes? = $5,000 1+ 0.15 = $4,347.83 Sales Amount = Amount including tax Actual Sales + tax rate - or- Sales Amount = Amount including tax 1 + tax rate

47. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 47

48. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 48 Property taxes are used by Municipalities to pay for local running costs, e.g. fire and police departments. They are based on the assessed value. The value of property for the purposes of computing property taxes Assessment Rate * Market Value Assessed Value …Also

49. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 49 Mill Rate Property Tax = Mill Rate * Assessed Value 1000 Property Tax = Mill Rate * Assessed Value 1000 Calculating = amount of tax per $1000 of Assessed Value Calculation

50. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 50 = $26.923 * $240 000 1000 If you live in a house with an Assessed Value of $240,000, and the current mill rate is $26.923, find the amount of your property tax for the year. = $6,461.52 Property Tax = Mill Rate * Assessed Value 1000 Property Tax = Mill Rate * Assessed Value 1000 Calculating

51. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 51 $40,000*7.69% $40,000 =400 $100 = 400* $7.69 $40,000 =400 $1000 = 40* $7.69 $76.90*.001 * $40,000 Expressing Tax Rate $3,076 Per $100 of Assessed Value By % 7.69%$7.69 Per $1,000 of Assessed Value $76.90 In Mills $76.90

52. McGraw-Hill Ryerson© Basic Mathematics Basic Mathematics 1 - 52 This completes Chapter 1