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  • 1. BasicMathematicsBasic Chap. 1, 2, 3 PowerPoint Presentation Prepared by 2008 McGraw-Hill Ryerson Ltd. All Rights ReservedC Quinn, Seneca College.

2. BasicLearning ObjectivesMathematicsAfter 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 equivalentsLO 3.Maintain the proper number of digits in calculationsLO 4.Solve for any one of percent rate, portion, or base, given the other two quantitiesalso 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 3. Basic MathematicsLO 1.rithmeticperations2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 4. BasicMathematics( ) Brackets Exponents 22 or 2 x 2 Division or / Multiplication 4(2 - 5) or 4 x (2 - 5) or 4*(2 - 5) Addition + Subtraction 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 5. BasicMathematicsHow do we evaluate (solve) the followingproblem?722008 McGraw-Hill Ryerson Ltd. All Rights Reserved(3 x 22) 6 6. BasicMathematics72 B E D M A S2008 McGraw-Hill Ryerson Ltd. All Rights Reserved(3 x 22) - 6 72= = = =(3 x 22) - 672(3 x 2 x 2) - 6721272126 =06-6 -6 7. BasicMathematicsLO 2.Converting Decimals to Percents Percents to Decimals2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 8. BasicConvertingMathematicsDecimal .75Move decimal point two places to Right for % 75%DecimalMove decimal point two places to Left for decimal.3535%5.0500%2.5250%1.745174.50%.12412.4%2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 9. BasicMathematicsConverting Fractions to Percents Percents to Fractions2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 10. BasicConvertingMathematicsFractionPercents Top / Bottom * 1001 10 5 132008 McGraw-Hill Ryerson Ltd. All Rights Reserved10% 38.4615%Percents Fraction 15 100 384 1000Percent /100 15% 38.4% 11. BasicMathematicsConverting Decimals to Decimal Fractions2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 12. BasicConvertingMathematicsDecimals to Decimal Fractions FractionsDecimal Step Write Digits 1 Step Divide by 1 2 with appropriate number of zeros and drop the decimal point 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved.24.2424100.345 .2100.34534510 0 01000.221010 13. Basic MathematicsLO 3.Decimals2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 14. BasicDecimalsMathematicsDecimalPercent.384615Fraction 5 1338.4615%Rounding 12008 McGraw-Hill Ryerson Ltd. All Rights Reserved2.383.3855Decimal Places.4If next digit is 5 or more, then raise current one to 38.5 next highest 38.46 digit..3846238.462 Example 15. BasicExampleMathematicsA bag contains 46 M & Ms of various colours. The 46 candies are distributed as follows:18 Yellow 10 Red 7 Orange 5 Green 6 Brown.Show the distribution in (a) fractions, (b) decimals, and (c) as a percent. Calculation 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 16. BasicMathematicsColourNo.Yellow18Red10Orange Green Brown7 5 6 46Fraction18 46 10 46 7 46 5 46 6 46 46/46 = 12008 McGraw-Hill Ryerson Ltd. All Rights ReservedDecimal Percent (hundredth) (hundredth) .3939.13%.2221.74%.1515.22%.1110.87%.1313.04%1.00 = 1100 % = 1 17. Basic MathematicsLO 4.2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 18. BasicMathematicsThe formula to use in percent calculations is:Formula using the Triangle will help us remember the above formula!P R B 2008 McGraw-Hill Ryerson Ltd. All Rights ReservedPortion = Rate * Base Question is asking forP=is or are This indicates the Portion that has to be found!R= B =% indicates the Rateof indicates the Basewhich is 100% or 1 19. BasicMathematicsThe formula to use in percent calculations is:FormulaPortion = Rate * BaseUsing this tool!P R BP = R*BP/R=B2008 McGraw-Hill Ryerson Ltd. All Rights ReservedWhere variables are BESIDE EACH OTHER this means to MULTIPLY! Where a variable is ABOVE ANOTHER this means to DIVIDE! 20. BasicMathematicsThe formula to use in percent calculations is:FormulaPortion = Rate * BaseUsing this tool! If you want to find PP R BR If you want to find B If you want to find2008 McGraw-Hill Ryerson Ltd. All Rights ReservedthenR*BthenP/BthenP/R 21. BasicMathematicsSolving 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?PFormula Portion = Rate * BaseR BP = 60% * $1600000 or P = P =2008 McGraw-Hill Ryerson Ltd. All Rights Reserved.60 * $1600000$960,000 22. BasicMathematicsSolving for Rate Cash Sales of McDonalds customers amount to $1,200,000. Total McDonald sales are $1,600,000. What percent of customers pay cash? What do you have to find?PFormula Rate = Portion /BaseR B 2008 McGraw-Hill Ryerson Ltd. All Rights ReservedR = $1,200,000/$1,600,000 R = 12/16 = .75 = 75% 23. BasicMathematicsSolving for Base 60% of total sales are from drive-thru customers . Sales of drive-thru customers are $960,000. What are McDonalds total Sales? $960,000 is 60% of what total sales? What do you have to find?PFormulaR BB = $960,000/ 60% B =2008 McGraw-Hill Ryerson Ltd. All Rights ReservedBase = Portion /Rate$1,600,000 24. BasicMathematicsSolving 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 is 114% of the sticker price. 6% GST + 8% PST2008 McGraw-Hill Ryerson Ltd. All Rights ReservedCalculate 25. BasicMathematicsSolving 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.Statement: (A)$649 1.14$649 is 114% (or 1.14) of the sticker price.=$569.30(B) $569.30 * 6% GST = $34.16$569.30= $649 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved+$34.16 GST $45.54 PST$569.30 * 8% PST = $45.54 26. BasicMathematicsSolving for Rate of Percent Change If McDonalds sales increase from $1,600,000 to $2,400,000, what is the percent change? $ 1,600,000 2,400,000DifferenceBase MethodInitial(Base)Value Final Value$ 800,000% change = Difference % change =$ 800,000 $1,600,000 Base = .5 or 50% Increase 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 27. BasicMathematicsConsumer Price Index CPI Used to compare prices of goods and services purchased by a typical Canadian family. Statistics Canada tracks the prices of about 600 consumer goods and services (the CPI basket) Price of CPI basket on the selected date *100 CPI = Price of CPI basket on the base date 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 28. BasicMathematicsConsumer Price Index CPIThe price of goods and services included in the Consumer Price Index cost $23 450 on the base date. Six years later, the same basket cost $25 980. What was the CPI on the latter date?Formula Price of CPI basket on the selected date *100 CPI = Price of CPI basket on the base date= 25 98023450 *100= 110.79 2008 McGraw-Hill Ryerson Ltd. All Rights ReservedAlso 29. BasicMathematicsConsumer Price Index CPIThe Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004, with 1992 as the base year. What amount in Aug. 2004 had the same purchasing power as $1000 in Aug. 2003?Amounts with the same purchasing power will be in the same ratio as the CPIs on the respective dates. 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved2004 $$ 2003 $$=2004 CPI 2003 CPI2004 $$ $1000=124.8 122.52004 $$124.8*$1000 = 122.5 = $1018.78 30. BasicMathematicsThe Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004, with 1992 as the base year. What was the overall percent inflation from Aug.2003 to Aug.2004?=2004 CPI - 2003 CPI 100% * 2003 CPI=Percent inflation124.8 - 122.5 100% 122.5 *= 1.88%Also 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 31. BasicMathematicsThe Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004, with 1992 as the base year. If you earned $50 000 in 2003, how much would you have to earn in 2004 to keep up with inflation?2004 Salary = 2004 CPI 2003 Salary 2003 CPI 2004 Salary = 124.8 $50 000 122.5 2004 Salary = 124.8 * $50 000 122.5 = $50938.77 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 32. Basic AlgebraMathematicsExponentsRule of34 Base32 *333= 32 + 3 5 =3Exponent34i.e. 3*3*3*3 Power = 81 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved= 243(1 + i)20 (1 + i)8=(1+ = (1+(32)4i)20-8= 32*4t= 38i)= 6561More 33. Basic AlgebraMathematicsExponentsRule of3x6y3 x 2 z3Square each termSimplify inside the brackets firstX43x6y3 2 3x4y3 2 z3 = x z3 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved22=2x4*2y3* 2 33*2 ZSimplify=8y6 9xz6 34. Basic AlgebraMathematicsExponentsRule ofto (a) evaluate (1.62)5 Use Calculator1.625 11.16to (b) evaluate (1.62)-51.625 0.08962008 McGraw-Hill Ryerson Ltd. All Rights Reserved 35. BasicMathematicsOntario 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 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 36. BasicMathematicsOntario 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 WA Wage = [$943 + 210 + 290] / 70 WA Wage = $1443.00 / 70 2008 McGraw-Hill Ryerson Ltd. All Rights Reserved= $20.61