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Chapter 1

Basic. Chapter 1. Review. &. Applications of. PowerPoint Presentation Prepared by C Quinn, Seneca College. Learning Objectives. LO 1. LO 2. LO 3. LO 4. After completing this chapter, you will be able to:. Perform arithmetic operations in their proper order.

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Chapter 1

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  1. Basic Chapter 1 Review & Applications of... PowerPoint Presentation Prepared by C Quinn, Seneca College.

  2. Learning Objectives LO 1. LO 2. LO 3. LO 4. After completing this chapter, you will be able to: Performarithmetic operations in their proper order Convertfractions to their percent and decimal equivalents Maintainthe proper number of digits in calculations Solvefor any one of percent rate, portion, or base, given the other two quantities also…

  3. Learning Objectives LO 5. LO 6. LO 7. 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

  4. Basic Mathematics 1. LO 1. rithmetic perations

  5. Order of Operation Rules ( ) Brackets Exponents 22 or 2 x 2 or / Division or 4 x (2 - 5) Multiplication 4(2 - 5) or 4*(2 - 5) + Addition – Subtraction Review

  6. 72 (3x 22) – 6 How do we evaluate (solve) the following problem? Known as an‘Expression’! Review

  7. 72 (3x 22) - 6 B E 72 (3x 22) - 6 72 (3x2 x 2)- 6 72 12-6 7212- 6 72 (3x 22)- 6 D = M = = A 6 - 6 = S Order of Operation Rules = 0

  8. Using your calculator to solve these expressions: 1. 2. Useacalculator and algebraic sequencing The Sharp EL-733A and Texas Instruments BA-35 Solar calculators perform calculations in the order we enter them. BOTHways will be shown! Use the TI BAII Plus financial calculator with settings for the algebraic operation system!

  9. CPT ENTER ON/OFF 2000(1 + .04 *45/365) Solve… 2nd CF NPV IRR FV I/Y PV N PMT . % . 2 X . . X 1/ x QUIT SET DEL INS x ( ) INV y X X X xP/Y P/Y AMORT BGN CLR TVM 9 7 LN e X 8 K RAND - 6 HYP SIN COS TAN % X! 4 = = = STO 5 + + STAT BOND DATA nPr 3 1 Learn to use RCL ROUND DEPR BRKEVN 2 nCr BA2+ DATE ICONV PROFIT +/- CE/C 0 ANS CLR WORK . . MEM FORMAT RESET Advanced Business Analyst Use a calculator and algebraic sequencing 45 1.00493 2009.86 365 = $2,009.86 .04 1 2000 Skip calculator lesson

  10. CPT ENTER Using your ON/OFF 2nd CF NPV IRR FV I/Y PV N QUIT SET DEL INS PMT % . 2 X xP/Y P/Y AMORT BGN CLR TVM . X 1/ K x RAND x ( ) INV y X HYP SIN COS TAN X! 9 7 LN e X STAT BOND DATA 8 nPr - ROUND DEPR BRKEVN 6 % 4 nCr STO 5 + DATE ICONV PROFIT ANS 3 CLR WORK 1 RCL MEM FORMAT RESET 2 BA2+ Calculator +/- Advanced Business Analyst = CE/C 0 . . Some key Keys!

  11. CPT ENTER ON/OFF 2nd 2nd CF NPV IRR FV I/Y PV N QUIT SET DEL INS PMT % . 2 X xP/Y P/Y AMORT BGN CLR TVM . X 1/ K x RAND x ( ) INV y X HYP SIN COS TAN X! 9 7 LN e X STAT BOND DATA 8 nPr - ROUND DEPR BRKEVN 6 % 4 nCr STO 5 + DATE ICONV PROFIT ANS 3 CLR WORK 1 RCL MEM FORMAT RESET 2 +/- Advanced Business Analyst = CE/C 0 . . Find the following KEYS: Usedto access symbols located “above” another key, i.e. its acts like the SHIFT key on a computer keyboard. Used to format the display and operation of the calculator FORMAT Scroll down key ENTER Used to Enter our settings Used to exit the secondary functions QUIT Used to Set or confirm the display or operation choice SET

  12. CPT ENTER ON/OFF 2nd 2nd 2nd CF NPV IRR FV I/Y PV N PMT % . 2 X . X 1/ x x ( ) INV y X 9 7 LN e X 8 - 6 % 4 STO 5 + 3 1 RCL 2 +/- = CE/C 0 . . SetBA2+calculatorto a floating decimal display Floating-decimal display has now been set DEC= 9 DEC= FORMAT 9 QUIT SET DEL INS ENTER xP/Y P/Y AMORT BGN CLR TVM We must key in this 2 key sequence to close any worksheet you have opened. K RAND QUIT HYP SIN COS TAN X! STAT BOND DATA nPr ROUND DEPR BRKEVN nCr DATE ICONV PROFIT ANS CLR WORK MEM FORMAT RESET Advanced Business Analyst

  13. CPT ENTER ON/OFF 2nd 2nd CF NPV IRR FV I/Y PV N PMT % . 2 X . X 1/ x QUIT SET DEL INS x ( ) INV y X xP/Y P/Y AMORT BGN CLR TVM 9 7 LN e X 8 K RAND - 6 HYP SIN COS TAN % X! 4 = STO 5 + STAT BOND DATA nPr 3 1 RCL ROUND DEPR BRKEVN 2 nCr DATE ICONV PROFIT +/- CE/C 0 ANS CLR WORK . . MEM FORMAT RESET Advanced Business Analyst SetBA2+calculator format settings Re-enter the format worksheet… Scroll to see other items, stopping at the final item, CHN or AOS FORMAT 0.000000 DEG US 12-31-1990 US 1,000 Chn DEC 9 The chain method performs operations in the sequence you enter them

  14. CPT ENTER ON/OFF 2nd CF NPV IRR FV I/Y PV N PMT % . 2 X . X 1/ x QUIT SET DEL INS x ( ) INV y X xP/Y P/Y AMORT BGN CLR TVM 9 7 LN e X 8 K RAND - 6 HYP SIN COS TAN % X! 4 = STO 5 + STAT BOND DATA nPr 3 1 RCL ROUND DEPR BRKEVN 2 nCr DATE ICONV PROFIT +/- CE/C 0 ANS CLR WORK . . MEM FORMAT RESET Advanced Business Analyst SetBA2+calculator format settings Chn The chain method performs operations in the sequence you enter them 5 + 4 * 2 = = 18

  15. CPT ENTER ON/OFF 2nd 2nd 2nd CF NPV IRR FV I/Y PV N PMT % . 2 X . X 1/ x QUIT SET DEL INS x ( ) INV y X xP/Y P/Y AMORT BGN CLR TVM 9 7 LN e X 8 K RAND - 6 HYP SIN COS TAN % X! 4 = STO 5 + STAT BOND DATA nPr 3 1 RCL ROUND DEPR BRKEVN 2 nCr DATE ICONV PROFIT +/- CE/C 0 ANS CLR WORK . . MEM FORMAT RESET Advanced Business Analyst SetBA2+calculatortoAlgebraic Operating System To change to AOS, press Chn 0. AOS 13 SET We must key in this sequence to close any worksheet you have opened. The calculator now uses the order of operations discussed in BEDMAS QUIT Now 5 + 4 * 2 = = 13

  16. CPT ENTER ON/OFF 2nd CF NPV IRR FV I/Y PV N PMT . % . 2 X . . X 1/ x QUIT SET DEL INS x ( ( ) ) INV y X X xP/Y P/Y AMORT BGN CLR TVM 9 7 LN e X 8 K RAND - 6 HYP SIN COS TAN % X! 4 = = STO 5 + + STAT BOND DATA nPr 3 1 RCL ROUND DEPR BRKEVN 2 nCr DATE ICONV PROFIT +/- CE/C 0 ANS CLR WORK . . MEM FORMAT RESET Advanced Business Analyst UseBA2+calculatorandalgebraic operation system 2000(1 + .04 *45/365) Solve… 2000 1.00493 2009.86 1 .04 = $2,009.86 45 365

  17. Decimalsto Percents PercentstoDecimals LO 2. Converting

  18. Decimal Converting Move decimalpointtwo places to Right for % Move decimal pointtwo places to Left fordecimal Decimal .75 75% .35 35% 5.0 500% 2.5 250% .124 1.745 174.50% 12.4%

  19. Fractionsto Percents PercentstoFractions Converting

  20. Fraction 1 10 5 13 15 100 384 1000 Converting Percents Percents Top / Bottom* 100 Fraction Percent/100 10% 15% 38.4615% 38.4%

  21. Decimals to Decimal Fractions Converting

  22. Decimals to Decimal Fractions Fractions Step 1 Step 2 2 .24 24 1 0 0 .345 345 1 0 0 0 .2 1 0 Converting Decimal .24 Write Digits Divide by1 1 0 0 …with appropriate number of zeros …and drop the decimal point .345 1 0 0 0 .2 1 0

  23. Basic Mathematics 1 Rounding Rounding LO 3. Decimals

  24. Decimals Percent Decimal .384615 38.4615% 5 13 Rounding Rounding 38.5 38.46 38.462 Example Fraction If next digit is 5 or more, then raise current one to next highest digit. Rounding 1 .4 Decimal Places 2 .38 3 .385 5 .38462

  25. Example Q A bag contains 46 M & M’s of various colours. The 46 candies are distributed as follows: 18 Yellow10 Red7 Orange5 Green6 Brown. Show the distribution in(a)fractions, (b)decimals, and (c) asa percent. Calculation

  26. Decimal (hundredth) Percent (hundredth) Fraction Colour No. 18 Yellow 10 46 7 Red 46 Orange Green 5 46 Brown 6 46 Bag of M&M’s 18 .39 39.13% 46 10 .22 21.74% 7 .15 15.22% 5 .11 10.87% 6 .13 13.04% 46 46/46 = 1 1.00 = 1 100 % = 1

  27. Basic Mathematics 1 LO 4. % Formula

  28. Percentage Formula The formula to use in percent calculations is: Portion = Rate *Base Formula …using the‘Triangle’ will help us remember the above formula! Question is asking for… P= “…is ” or “…are ” This indicates the Portionthat has to be found! R= “%” indicates the Rate P B = “…of ” indicates the Base which is 100% or 1 R B

  29. Using this tool! P P = R*B P/R=B R B Percentage Formula The formula to use in percent calculations is: Portion = Rate *Base Formula Where variables are BESIDE EACH OTHER this means to MULTIPLY! Where a variable is ABOVE ANOTHER this means to DIVIDE!

  30. The formula to use in percent calculations is: Portion = Rate *Base Formula Using this tool! P R B Percentage Formula thenR*B If you want to find P thenP/B If you want to find R If you want to find B thenP/R

  31. Q Portion = Rate *Base Formula P R B Percentage Formula Solving for Portion Salesof McDonalds drive-thru customers are60%of total sales. TotalMcDonaldsalesare$1,600,000. Whatarethe drive-thru sales? What do you have to find? 60% * P = $1600000 or .60 * P = $1600000 $960,000 P =

  32. Q Cash Salesof McDonalds customers amount to $1,200,000. TotalMcDonaldsalesare$1,600,000. Rate = Portion /Base Formula P R B Percentage Formula Solving forRate Whatpercentof customers pay cash? What do you have to find? $1,200,000/$1,600,000 R = 12/16 = .75 = 75% R=

  33. Q 60%of total sales are from drive-thru customers . Sales of drive-thrucustomers are $960,000. Base = Portion /Rate Formula P R B Percentage Formula Solving for Base Whatare McDonald’s total Sales? $960,000 is 60% ofwhat total sales? What do you have to find? B= $960,000/ 60% $1,600,000 B=

  34. Q 6% GST + 8% PST Calculate Percentage Formula Solving for Base You buy a new stereo in Ontario and pay a total of $649. This includes 6% 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? The problem can be restated as: $649 is114%of the sticker price.

  35. Q Statement: $649 is114% (or 1.14)of the sticker price. 1.14 = $569.30 Proof $34.16 GST $45.54 PST + $569.30 = $649 Percentage Formula Solving for Base You buy a new stereo in Ontario and pay a total of $649. This includes 6% GST and 8% PST. Find (a) the sticker price of the stereo before taxes, and (b) the amount of each tax. $649 (A) (B) $569.30 * 6% GST =$34.16 $569.30 * 8% PST =$45.54

  36. Q 2,400,000 $ 800,000 $ 800,000 Percentage Formula Solving forRate of Percent Change If McDonald’s sales increase from $1,600,000 to$2,400,000, what is thepercent change? Initial(Base)Value $1,600,000 Final Value Base Method Difference % change = Difference Base % change = $1,600,000 = .5 or 50% Increase

  37. Basic Mathematics 1 8:00a Pay Roll LO 5.

  38. Company Income Earners 8:00a Payroll Cheque 00001 Pay Pay Roll / $ Salaried Commissioned Hourly

  39. 8:00a Payroll Cheque 00001 Pay Pay Salaried Roll / $ • 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

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

  41. Hourly 8:00a Payroll Cheque 00001 Pay Pay Roll / $ 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’.

  42. 52 26 24 12 8:00a Pay Roll = $769.23 = $1,538.46 = $1,666.67 = $3,333.33

  43. Hourly 8:00a Payroll Cheque 00001 Pay Pay Roll / $ Overtime If an hourly employee has to work more hours than the agreed number, then extra pay is rewarded to recognize this overtimeoccurrence. Theovertime rate is usually1.5 times the hourly rate

  44. Q 8:00a Pay Roll $780.00 You are contracted to work a 40 hour week. Due to the illness of a colleague you have been required towork 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? 40 @ $15.00 $600.00 Regular Hours worked 8 @ $22.50 180.00 Overtime Hours Overtime Rate = $15.00 * 1.5 = 48 $22.50

  45. Q Calculation Commission 8:00a Payroll Cheque 00001 Pay Pay Roll / $ 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.

  46. Q 8:00a Pay Roll $7,250 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

  47. Commission 8:00a Payroll Cheque 00001 Pay Pay Roll / $ Variable Commission Scale This refers to the payment of different commission rates for various levels of sales.

  48. Q 8:00a Commission Scale Pay Roll Up to$25,0005% $25,001 - $40,0007% Over$40,0018% Your car net sales were $120,000. Based on the Commission Scale, what are your gross commissions? $ Commission * .05 = $1,250 25,000 * .07 = 1,050 15,000 * .08 = 6,400 80,000 $8,700 120,000

  49. Calculation Salary plus Commission 8:00a Q Payroll Cheque 00001 Pay Pay Roll / $ You receive a salary of $2,500 per month. In addition, you receive a 5% commissionfor sales over $15,000. Last month’s sales were $75,000. Calculate your gross pay.

  50. You receive a salary of $2,500 per month. In addition, you receive a 5% commissionfor sales over $15,000. Last month’s sales were $75,000. Calculate your gross pay. 8:00a Q Pay Roll • $75,000 • 15,000 • $60,000 Gross Pay = Salary +Commission = $2,500+ ($60,000 * .05) = $5,500.

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