Basic

Mathematics

Basic
Chap. 1, 2, 3
PowerPoint Presentation
Prepared by
©2008 McGraw-Hill Ryerson Ltd. All Rights Rese...
Basic

Learning Objectives

Mathematics

After completing this chapter, you will be able to:
LO 1.
LO 2.

Perform arithmet...
Basic
Mathematics

LO 1.

rithmetic

perations

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Basic

Mathematics

( )
Brackets
Exponents
22
or 2 x 2
Division
or /
Multiplication 4(2 - 5) or 4 x (2 - 5)
or 4*(2 - 5)
A...
Basic

Mathematics

How do we evaluate (solve) the following

problem?

72

©2008 McGraw-Hill Ryerson Ltd. All Rights Rese...
Basic

Mathematics

72
B
E
D
M
A
S

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

(3 x 22) - 6
72

=
=
=
=

(3 x 22)...
Basic

Mathematics

LO 2.

Converting
Decimals to Percents
Percents to Decimals

©2008 McGraw-Hill Ryerson Ltd. All Rights...
Basic

Converting

Mathematics

Decimal
.75

Move decimal
point two places
to Right
for %
75%

Decimal

Move decimal
point...
Basic

Mathematics

Converting
Fractions to Percents
Percents to Fractions

©2008 McGraw-Hill Ryerson Ltd. All Rights Rese...
Basic

Converting

Mathematics

Fraction

Percents
Top / Bottom
* 100

1
10
5
13

©2008 McGraw-Hill Ryerson Ltd. All Right...
Basic

Mathematics

Converting
Decimals to
Decimal Fractions

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Basic

Converting

Mathematics

Decimals to Decimal Fractions
Fractions

Decimal
Step
Write Digits
1
Step
Divide by 1
2
…w...
Basic
Mathematics

LO 3.

Decimals

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Basic

Decimals

Mathematics

Decimal

Percent

.384615

Fraction
5
13

38.4615%

Rounding
1

©2008 McGraw-Hill Ryerson Lt...
Basic

Example

Mathematics

A bag contains 46 M & M’s of various colours.
The 46 candies are distributed as follows:

18 ...
Basic

Mathematics

Colour

No.

Yellow

18

Red

10

Orange
Green
Brown

7
5
6
46

Fraction

18
46
10
46
7
46
5
46
6
46
4...
Basic
Mathematics

LO 4.

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Basic

Mathematics

The formula to use in percent calculations is:

Formula
…using the
„Triangle‟
will help us
remember th...
Basic

Mathematics

The formula to use in percent calculations is:

Formula

Portion = Rate * Base

Using this tool!

P
R ...
Basic

Mathematics

The formula to use in percent calculations is:

Formula

Portion = Rate * Base

Using this tool! If yo...
Basic

Mathematics

Solving for Portion
Sales of McDonalds drive-thru customers are 60% of
total sales. Total McDonald sal...
Basic

Mathematics

Solving for Rate
Cash Sales of McDonalds customers amount to
$1,200,000. Total McDonald sales are $1,6...
Basic

Mathematics

Solving for Base
60% of total sales are from drive-thru customers .
Sales of drive-thru customers are ...
Basic

Mathematics

Solving for Base
You buy a new stereo in Ontario and pay a total of
$649. This includes 6% GST and 8% ...
Basic

Mathematics

Solving for Base
You buy a new stereo in Ontario and pay a total of
$649. This includes 6% GST and 8% ...
Basic

Mathematics

Solving for Rate of Percent Change
If McDonald’s sales increase from $1,600,000 to
$2,400,000, what is...
Basic

Mathematics

Consumer Price Index – CPI
Used to compare prices of goods and services
purchased by a typical Canadia...
Basic

Mathematics

Consumer Price Index – CPI

The price of goods and services included in the
Consumer Price Index cost ...
Basic

Mathematics

Consumer Price Index – CPI

The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 200...
Basic

Mathematics

The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base yea...
Basic

Mathematics

The Consumer Price Index was
122.5 in August 2003, and 124.8 in August 2004,
with 1992 as the base yea...
Basic
Algebra

Mathematics

Exponents

Rule of

34
Base

32 *33

3

= 32 + 3
5
=3

Exponent

3

4

i.e. 3*3*3*3
Power = 81...
Basic
Algebra

Mathematics

Exponents

Rule of

3x6y3
x 2 z3

Square each term

Simplify inside
the brackets first

X4

3x...
Basic
Algebra

Mathematics

Exponents

Rule of

…to (a) evaluate (1.62)5
Use
Calculator

1.62

5
11.16

…to (b) evaluate (...
Basic

Mathematics

Ontario Transport has 46 drivers each earning
$20.50 per hour, 14 clerical staff members each
earning ...
Basic

Mathematics

Ontario Transport has 46 drivers each earning
$20.50 per hour, 14 clerical staff members each
earning ...
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Unit 1 ch 1 3 Mathes

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Unit 1 ch 1 3 Mathes

  1. 1. Basic Mathematics Basic Chap. 1, 2, 3 PowerPoint Presentation Prepared by ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved C Quinn, Seneca College.
  2. 2. Basic Learning Objectives Mathematics 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 also… ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  3. 3. Basic Mathematics LO 1. rithmetic perations ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  4. 4. Basic Mathematics ( ) 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. 5. Basic Mathematics How do we evaluate (solve) the following problem? 72 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved (3 x 22) – 6
  6. 6. Basic Mathematics 72 B E D M A S ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved (3 x 22) - 6 72 = = = = (3 x 22) - 6 72 (3 x 2 x 2) - 6 72 12 72 12 6 = 0 6 -6 -6
  7. 7. Basic Mathematics LO 2. Converting Decimals to Percents Percents to Decimals ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  8. 8. Basic Converting Mathematics Decimal .75 Move decimal point two places to Right for % 75% Decimal Move decimal point two places to Left for decimal .35 35% 5.0 500% 2.5 250% 1.745 174.50% .124 12.4% ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  9. 9. Basic Mathematics Converting Fractions to Percents Percents to Fractions ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  10. 10. Basic Converting Mathematics Fraction Percents Top / Bottom * 100 1 10 5 13 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 10% 38.4615% Percents Fraction 15 100 384 1000 Percent /100 15% 38.4%
  11. 11. Basic Mathematics Converting Decimals to Decimal Fractions ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  12. 12. Basic Converting Mathematics Decimals to Decimal Fractions Fractions Decimal 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 .24 24 100 .345 .2 100 .345 345 10 0 0 1000 .2 2 10 10
  13. 13. Basic Mathematics LO 3. Decimals ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  14. 14. Basic Decimals Mathematics Decimal Percent .384615 Fraction 5 13 38.4615% Rounding 1 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2 .38 3 .385 5 Decimal Places .4 If next digit is 5 or more, then raise current one to 38.5 next highest 38.46 digit. .38462 38.462 Example
  15. 15. Basic Example Mathematics 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 (a) fractions, (b) decimals, and (c) as a percent. Calculation ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  16. 16. Basic Mathematics Colour No. Yellow 18 Red 10 Orange Green Brown 7 5 6 46 Fraction 18 46 10 46 7 46 5 46 6 46 46/46 = 1 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Decimal Percent (hundredth) (hundredth) .39 39.13% .22 21.74% .15 15.22% .11 10.87% .13 13.04% 1.00 = 1 100 % = 1
  17. 17. Basic Mathematics LO 4. ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  18. 18. Basic Mathematics The 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 Reserved Portion = Rate * Base Question is asking for… P= “…is ” or “…are ” This indicates the Portion that has to be found! R= B = “%” indicates the Rate “…of ” indicates the Base which is 100% or 1
  19. 19. Basic Mathematics The formula to use in percent calculations is: Formula Portion = Rate * Base Using this tool! P R B P = R*B P/R=B ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Where variables are BESIDE EACH OTHER this means to MULTIPLY! Where a variable is ABOVE ANOTHER this means to DIVIDE!
  20. 20. Basic Mathematics The formula to use in percent calculations is: Formula Portion = Rate * Base Using this tool! If you want to find P P R B R If you want to find B If you want to find ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved then R*B then P/B then P/R
  21. 21. Basic 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? P Formula Portion = Rate * Base R B P = 60% * $1600000 or P = P = ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved .60 * $1600000 $960,000
  22. 22. Basic Mathematics Solving 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? P Formula Rate = Portion /Base R B ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved R = $1,200,000/$1,600,000 R = 12/16 = .75 = 75%
  23. 23. Basic Mathematics Solving for Base 60% of total sales are from drive-thru customers . Sales of drive-thru customers are $960,000. What are McDonald‟s total Sales? $960,000 is 60% of what total sales? What do you have to find? P Formula R B B = $960,000/ 60% B = ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Base = Portion /Rate $1,600,000
  24. 24. Basic Mathematics 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 is 114% of the sticker price. 6% GST + 8% PST ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Calculate
  25. 25. Basic Mathematics 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. 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. 26. Basic 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? $ 1,600,000 2,400,000 Difference Base Method Initial(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. 27. Basic Mathematics Consumer 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. 28. Basic Mathematics Consumer Price Index – CPI The 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 = 25 980 23450 *100 = 110.79 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved …Also
  29. 29. Basic Mathematics Consumer Price Index – CPI The 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 Reserved 2004 $$ 2003 $$ = 2004 CPI 2003 CPI 2004 $$ $1000 = 124.8 122.5 2004 $$ 124.8*$1000 = 122.5 = $1018.78
  30. 30. Basic Mathematics The 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 inflation 124.8 - 122.5 100% 122.5 * = 1.88% …Also ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  31. 31. Basic Mathematics The 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. 32. Basic Algebra Mathematics Exponents Rule of 34 Base 32 *33 3 = 32 + 3 5 =3 Exponent 3 4 i.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)4 i)20-8 = 32*4 t = 38 i) = 6561 More
  33. 33. Basic Algebra Mathematics Exponents Rule of 3x6y3 x 2 z3 Square each term Simplify inside the brackets first X4 3x6y3 2 3x4y3 2 z3 = x z3 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2 2 = 2x4*2y3* 2 3 3*2 Z Simplify = 8y6 9x z 6
  34. 34. Basic Algebra Mathematics Exponents Rule of …to (a) evaluate (1.62)5 Use Calculator 1.62 5 11.16 …to (b) evaluate (1.62)-5 1.62 5 0.0896 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  35. 35. Basic 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 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
  36. 36. Basic 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 WA Wage = [$943 + 210 + 290] / 70 WA Wage = $1443.00 / 70 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved = $20.61

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