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- 1. Basic 1-1 Mathematics Basic Chapter 1 McGraw-Hill Ryerson©
- 2. Basic 1-2 Mathematics Learning Objectives After completing this chapter, you will be able to: LO 1. LO 2. Perform arithmetic operations in their proper order Convert fractions to their percent and decimal equivalents LO 3. Maintain the proper number of digits in calculations LO 4. Solve for any one of percent rate, portion, or base, given the other two quantities McGraw-Hill Ryerson© also…
- 3. Basic Mathematics 1-3 Learning Objectives Calculate the… LO 5. Gross earnings of salaried, hourly wage, or LO 6. Simple average or weighted average (as commission employees appropriate) of a set of values, and LO 7. Perform basic calculations of the Goods and Services Tax, Provincial Sales Tax, and Property Tax McGraw-Hill Ryerson©
- 4. Basic 1-4 Mathematics LO 1. rithmetic perations McGraw-Hill Ryerson©
- 5. Basic Mathematics McGraw-Hill Ryerson© 1-5 ( ) Brackets Exponents 22 -or 2 x 2 Division -or / Multiplication 4(2 - 5) -or 4 x (2 - 5) -or 4*(2 - 5) Addition + Subtraction –
- 6. Basic Mathematics 1-6 How do we evaluate (solve) the following problem? 72 McGraw-Hill Ryerson© ! xpression’ n‘E nown as a K (3 x 22) – 6
- 7. Basic Mathematics 72 B E D M A S McGraw-Hill Ryerson© = = = = 1-7 (3 x 22) - 6 72 72 (3 x 22) - 6 (3 x 2 x 2) - 6 72 72 -6 -6 12 12 6 = 0 = 0 - 6
- 8. Basic 1-8 Mathematics LO 2. Converting Decimals to Percents Percents to Decimals McGraw-Hill Ryerson©
- 9. Basic Mathematics Decimal .75 Converting Move decimal point two places to Right for % 75% Decimal 1-9 Move decimal point two places to Left for decimal .35 35% 5.0 500% 2.5 250% 1.745 174.50% .124 12.4% McGraw-Hill Ryerson©
- 10. Basic 1 - 10 Mathematics Converting Fractions to Percents Percents to Fractions McGraw-Hill Ryerson©
- 11. Basic Mathematics Fraction 1 10 5 13 McGraw-Hill Ryerson© Converting Percents Top / Bottom * 100 10% 38.4615% 1 - 11 Percents Fraction 15 100 384 1000 Percent /100 15% 38.4%
- 12. Basic 1 - 12 Mathematics Converting Decimals to Decimal Fractions McGraw-Hill Ryerson©
- 13. Basic Mathematics Converting 1 - 13 Decimals to Decimal Fractions Fractions Decimal Step Write Digits 1 Step Divide by 1 2 …with …with appropriate appropriate number of zeros number of zeros McGraw-Hill Ryerson© .24 .24 24 100 .345 .2 100 .345 345 10 0 0 .2 10 1000 2 10
- 14. Basic 1 - 14 Mathematics LO 3. Decimals McGraw-Hill Ryerson©
- 15. Basic 1 - 15 Decimals Mathematics Decimal Percent .384615 Fraction 5 13 38.4615% Rounding McGraw-Hill Ryerson© .4 .38 .385 5 Decimal Decimal Places Places 1 2 3 If next digit is If next digit is 5 or more, 5 or more, then raise then raise current one to current one to 38.5 next next highestdigit. 38.46 highest digit. .38462 38.462 Example
- 16. Basic Mathematics Example Example 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. Show the distribution in Show the distribution in (a) fractions, (b) decimals, and (c) (a) fractions, (b) decimals, and (c) as percent. as aapercent. Calculation McGraw-Hill Ryerson©
- 17. Basic 1 - 17 Mathematics Colour No. Yellow 18 Red 10 Orange Green Brown McGraw-Hill Ryerson© 7 5 6 46 Fraction 18 46 10 46 7 46 5 46 6 46 46/46 = 1 Decimal Percent (hundredth) (hundredth) .39 39.13% .22 21.74% .15 15.22% .11 10.87% .13 13.04% 1.00 = 1 100 % = 1
- 18. Basic Mathematics LO 4. McGraw-Hill Ryerson© 1 - 18
- 19. Basic 1 - 19 Mathematics The formula to use in percent calculations is: Formula Formula …using the ‘Triangle’ will help us remember the above formula! P R B McGraw-Hill Ryerson© Portion = Rate * Base Question is asking for… Question is asking for… P= “…is ” or “…are ” This indicates the Portion This indicates the Portion that has to be found! that has to be found! “%” indicates the Rate R = “%” indicates the Rate B = “…of ””indicates the Base “…of indicates the Base which is 100% or 1 which is 100% or 1
- 20. Basic 1 - 20 Mathematics The formula to use in percent calculations is: Formula Formula Portion = Rate * Base Using this tool! Using this tool! P R B McGraw-Hill Ryerson© P = R*B P = R*B P/R=B P/R=B Where variables are BESIDE EACH OTHER this means to MULTIPLY! Where a variable is ABOVE ANOTHER this means to DIVIDE!
- 21. Basic 1 - 21 Mathematics The formula to use in percent calculations is: Formula Formula Portion = Rate * Base Using this tool! Using this tool! If you want to find P P R B McGraw-Hill Ryerson© R If you want to find B If you want to find then R*B then P/B then P/R
- 22. Basic 1 - 22 Mathematics Solving for Portion 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? What do you have to find? P Formula Formula Portion = Rate * Base P = 60% * $1600000 or R B P = P = McGraw-Hill Ryerson© .60 * $1600000 $960,000
- 23. Basic 1 - 23 Mathematics Solving for Rate Sales of McDonalds drive-thru customers are 60% of total sales. Total McDonald sales are $1,600,000. What percent of customers eat in the restaurant? What do you have to find? What do you have to find? P R B McGraw-Hill Ryerson© Formula Formula Rate = Portion /Base $1,600,000 $1,600,000 960,000 -- 960,000 640,000 $$ 640,000 R = $640,000/$1,600,000 40% R = 40%
- 24. Basic 1 - 24 Mathematics Solving for Base Sales of McDonalds drive-thru customers are 60% of total sales. Sales of eat-in customers are $640,000. What are McDonald’s total Sales? The $640,000 is 40% of what total sales? The $640,000 is 40% of what total sales? What do you have to find? What do you have to find? P Formula Formula Base = Portion /Rate R B B = $640,000/ 40% B = McGraw-Hill Ryerson© $1,600,000 $1,600,000 $640,000 = $640,000 = 40% of 40% of Base Base
- 25. Basic 1 - 25 Mathematics Solving for Base 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. What do you have to find? What do you have to find? The problem can be restated as: $649 is 115% of the sticker price. 7% GST + 8% PST McGraw-Hill Ryerson© Calculate
- 26. Basic 1 - 26 Mathematics Solving for Base 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. Statement: (A) (A) $649 1.15 $649 is 115% (or 1.15) of the sticker price. = $564.35 = $649 McGraw-Hill Ryerson© $564.35 + $39.50 GST $39.50 GST $45.15 PST $45.15 PST (B) (B) $564.35 * 7% GST = $39.50 = $39.50 $564.35 * 8% PST = $45.15 = $45.15
- 27. Basic 1 - 27 Mathematics Solving for Rate of Percent Change If McDonald’s sales increase from $1,600,000 to $2,400,000, what is the percent change? This method is referred This method is referred to as to as the Base Method the Base Method Initial(Base)Value $ 1,600,000 Final Value 2,400,000 Difference $ 800,000 % change = Difference % change =$ 800,000 Base $1,600,000 = 50% or .5 Increase McGraw-Hill Ryerson©
- 28. Basic 1 - 28 Mathematics LO 5. 8:00 a McGraw-Hill Ryerson©
- 29. Basic 1 - 29 8:00 a Mathematics Pay Payroll Cheque 00001 / $ Company Income Earners Salaried Commissioned Hourly McGraw-Hill Ryerson©
- 30. Basic 1 - 30 8:00 a Mathematics Pay Payroll Cheque 00001 / $ Salaried Receives an ANNUAL amount. e.g. $50,000 per annum May receive other incentive payments. e.g. Year-end Bonus Usually paid Semi-Monthly or Bi-weekly McGraw-Hill Ryerson©
- 31. Basic 1 - 31 8:00 a Mathematics Pay Payroll Cheque 00001 / $ Commissioned Receives a percentage of sales made. e.g. Personal Sales $250,000 @ 10% May receive other incentive payments. Commission e.g. Exceeding sales quota - $20,000 commission. Can be paid both a salary and receive @ 3% Can be paid Semi-Monthly or Bi-weekly. McGraw-Hill Ryerson©
- 32. Basic 1 - 32 8:00 a Mathematics Pay Payroll Cheque 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’. McGraw-Hill Ryerson©
- 33. Basic 1 - 33 8:00 a Mathematics …Cycle Paid Period (a) Annual Income Weekly Once a Week $40,000 BiWeekly Every Two Weeks $40,000 SemiMonthly Twice a Month $40,000 Monthly Once a Month $40,000 McGraw-Hill Ryerson© (b) Payments per Year (a) / (b) Pay 52 = $769.23 26 = $1,538.46 24 = $1,666.67 12 = $3,333.33
- 34. Basic 1 - 34 8:00 a Mathematics Pay Payroll Cheque im rt Hourly ve O e / 00001 $ 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 The overtime rate is usually 1.5 times the hourly rate 1.5 times the hourly rate McGraw-Hill Ryerson©
- 35. Basic Mathematics 8:00 a 1 - 35 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 Overtime Rate 48 $780.00 48 = $15.00 * 1.5 = = $15.00 * 1.5 = $22.50 McGraw-Hill Ryerson©
- 36. Basic 1 - 36 8:00 a Mathematics Pay Payroll Cheque 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 McGraw-Hill Ryerson©
- 37. Basic Mathematics 8:00 a 1 - 37 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 Commission due to Larry McGraw-Hill Ryerson© 750 $7,250
- 38. Basic 1 - 38 8:00 a Mathematics Pay Payroll Cheque 00001 / $ Commission Variable Commission Scale This refers to the payment of different This refers to the payment of different commission rates for various levels of sales. commission rates for various levels of sales. McGraw-Hill Ryerson©
- 39. Basic 1 - 39 8:00 a Mathematics Your car net sales were $120,000. Based on the Commission Scale, what are your gross commissions? $ Commission Commission Scale Up to $25,000 5% 25,000 * .05 = $1,250 $25,001 - $40,000 7% 15,000 * .07 = 1,050 80,000 120,000 120,000 * .08 = 6,400 $8,700 $8,700 Over $40,001 McGraw-Hill Ryerson© 8%
- 40. Basic 1 - 40 8:00 a Mathematics Pay Payroll Cheque 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 McGraw-Hill Ryerson©
- 41. Basic 8:00 a 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. Gross Pay = Salary + Commission $75,000 $75,000 --15,000 15,000 $60,000 $60,000 McGraw-Hill Ryerson© = $2,500 + ($60,000 * . 05) = $5,500.
- 42. Basic Mathematics McGraw-Hill Ryerson© 1 - 42
- 43. Basic 1 - 43 Mathematics 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 = Wages per hour / # different wages = (20.50 +15.00 + 29.00) / 3 = $64.50 / 3 = $21.50 = $21.50 McGraw-Hill Ryerson©
- 44. Basic 1 - 44 Mathematics 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. Calculate the Weighted Average hourly rate earned by the 3 categories of employees. WA Wage = (Wage 1* #D + Wage 2*#C + Wage 3*#M) Total # of Employees ((20.50(46) +15.00(14) + 29.00(10)) WA Wage = (46+14+10) = 70 = 70 WA Wage = ($943 + 210 + 290) / 70 WA Wage = ($1443.00) / 70 McGraw-Hill Ryerson© = $20.61 = $20.61
- 45. Basic Mathematics LO 7. McGraw-Hill Ryerson© 1 - 45
- 46. Basic 1 - 46 Mathematics Register sales amounted to $5,000 and included 15% for PST and GST Taxes. What were the actual sales before taxes? Sales Amount = Sales Amount = = Amount including tax Actual Sales + tax rate Amount including tax 1 + tax rate $5,000 1+ 0.15 McGraw-Hill Ryerson© - or- = $4,347.83 = $4,347.83
- 47. Basic Mathematics McGraw-Hill Ryerson© 1 - 47
- 48. Basic 1 - 48 Mathematics 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 value of property for Assessed Value the purposes of the purposes of computing property taxes computing property taxes Assessment Rate * Market Value McGraw-Hill Ryerson© …Also
- 49. Basic 1 - 49 Mathematics Calculating Property Tax = Mill Rate * Assessed Value Property Tax = Mill Rate * Assessed Value 1000 1000 Mill Rate Mill Rate = amount of tax per $1000 of Assessed Value McGraw-Hill Ryerson© Calculation
- 50. Basic 1 - 50 Mathematics Calculating 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. Property Tax = Mill Rate **Assessed Value Property Tax = Mill Rate Assessed Value 1000 1000 = $26.923 * $240 000 1000 = $6,461.52 McGraw-Hill Ryerson©
- 51. Basic 1 - 51 Mathematics Expressing Tax Rate By % Per $100 of Assessed Value 7.69% $7.69 $40,000*7.69% $40,000 =400 $100 $3,076 McGraw-Hill Ryerson© = 400* $7.69 $3,076 Per $1,000 of Assessed Value In Mills $76.90 $76.90 $40,000 =400 $76.90*.001 * $40,000 $1000 = 40* $7.69 $3,076 $3,076
- 52. Basic 1 - 52 Mathematics This completes Chapter 1 McGraw-Hill Ryerson©

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