unit 1 ch 1 3 mathes

©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

Basic

Mathematics

Basic

Mathematics

Chap. 1, 2, 3Chap. 1, 2, 3

Basic

PowerPoint Presentation Prepared by

C Quinn, Seneca College.


Basic

Mathematics

Basic

Mathematics

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 ObjectivesLearning Objectives

LO 1. LO 1.

LO 2. LO 2.

LO 3. LO 3.

LO 4. LO 4.


Basic

Mathematics

Basic

Mathematics

rithmetic

perations

LO 1. LO 1.

Basic

Mathematics

Basic

Mathematics


Basic

Mathematics

Basic

Mathematics Brackets

Exponents

Division

Multiplication

Addition

Subtraction

( )( )

22

4(2 - 5) or 4 x (2 - 5)

+ –

or 2 x 2

or /

or 4*(2 - 5)


Basic

Mathematics

Basic

Mathematics How do we evaluate (solve) the following

problem?Known as an‘Expression’!

72 (3 x 22) – 6


Basic

Mathematics

Basic

Mathematics

72 (3 x 22) - 6

= 0= 0

72 (3 x 2 x 2) - 6=72 12 - 6=72 12 - 6=

6 - 6=

72 (3 x 22) - 6

72 (3 x 22) - 6

BED M

A

S


Basic

Mathematics

Basic

Mathematics

Decimals to Percents

Percents to Decimals

Converting LO 2. LO 2.


Basic

Mathematics

Basic

Mathematics

Decimal

.75

Move decimal point two places to Right

for %75%

5.0 500%

Move decimal point two places

to Left for

decimal

35%.35

2.5 250%

Converting

Decimal

1.745 174.50% .124 12.4%


Basic

Mathematics

Basic

Mathematics

Fractions to Percents

Percents to Fractions

Converting


Basic

Mathematics

Basic

MathematicsConverting

10% 110

Fraction Top / Bottom

* 100

513 38.4615%

Percents

15% 15100

Percent /100Fraction

3841000

Percents

38.4%


Basic

Mathematics

Basic

Mathematics

Decimal Fractions

ConvertingDecimals to


Basic

Mathematics

Basic

Mathematics

…with appropriate number of zeros…and drop the decimal point

…with appropriate number of zeros…and drop the decimal point

Converting

Write Digits .24

Decimal

Decimals to Decimal Fractions

Step 1Step 1

Step 2Step 2 Divide by 1

Fractions

.241 0 0

241 0 0

.345 .34510 0 0

3451 0 0 0

.2 .21 0

21 0


Basic

Mathematics

Basic

Mathematics

Decimals

LO 3. LO 3.

Basic

Mathematics

Basic

Mathematics


Basic

Mathematics

Basic

Mathematics

513 .384615

DecimalFraction

38.4615%

Percent

Rounding

Decimals

1

2

3

.4

.38

.385

5 .38462

38.538.46

38.462

If next digit is 5 or more,

then raise current one to next highest digit.

If next digit is 5 or more,

then raise current one to next highest digit.Decimal

Places

Decimal Places

Example


Basic

Mathematics

Basic

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.

ExampleExample

Show the distribution in (a) fractions, (b) decimals, and (c)

as a percent.

Show the distribution in (a) fractions, (b) decimals, and (c)

as a percent.

Calculation


Basic

Mathematics

Basic

Mathematics

No.No.ColourColour

Yellow

Red

Orange

Green

Brown

18

10

7

5

6

46

18

46

Fraction Decimal (hundredth)

Percent (hundredth)

.39 39.13%

.22 21.74%

.15 15.22%

.11 10.87%

.13 13.04%

1046 746 546

46 6

46/46 = 1 1.00 = 1 100 % = 1


Basic

Mathematics

Basic

Mathematics

LO 4. LO 4.

Basic

Mathematics

Basic

Mathematics


Basic

Mathematics

Basic

Mathematics

This indicates the Portion that has to be found!

This indicates the Portion that has to be found!

…using the ‘Triangle’ will help us

remember the above

formula!

Portion = Rate * BaseFormula Formula

The formula to use in percent calculations is:

PR B

P = “…is ” or “…are ”

R = “%” indicates the Rate“%” 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… Question is asking for…


Basic

Mathematics

Basic

Mathematics

Where variables are BESIDE EACH OTHER this

means to MULTIPLY!

Where a variable is ABOVE ANOTHER this means to

DIVIDE!

PR B

Using this tool!Using this tool!

P/R=BP/R=B

P = R*BP = R*B




Basic

Mathematics

Basic

Mathematics



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

PR B

Using this tool!Using this tool!


Basic

Mathematics

Basic

Mathematics

PR B

Sales of McDonalds drive-thru customers are 60% of total sales. Total McDonald sales are $1,600,000.

What do you have to find?What do you have to find?

Portion = Rate * Base Formula Formula

P = 60% * $1600000 or

P = .60 * $1600000

P = $960,000

Solving for Portion

What are the drive-thru sales?


Basic

Mathematics

Basic

Mathematics

PR B


Rate = Portion /Base Formula Formula

R = $1,200,000/$1,600,000

Cash Sales of McDonalds customers amount to

$1,200,000. Total McDonald sales are $1,600,000.

R = 12/16 = .75 = 75%12/16 = .75 = 75%

Solving for Rate

What percent of customers pay cash?


Basic

Mathematics

Basic

Mathematics


60% of total sales are from drive-thru customers .

Sales of drive-thru customers are $960,000.

Solving for Base

What are McDonald’s total Sales?

PR B B = $960,000/

B = $1,600,000$1,600,000

Base = Portion /Rate Formula Formula

60%

$960,000 is 60% of what total sales? $960,000 is 60% of what total sales?


Basic

Mathematics

Basic

Mathematics

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

Solving for Base


$649 is 114% of the sticker price.

6% GST + 8% PST

Calculate

Find (a) the sticker price of the stereo before taxes, and (b) the amount of each tax.

The problem can be restated as:


Basic

Mathematics

Basic

Mathematics

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.

Solving for Base

$6491.14

$649 is 114% (or 1.14) of the sticker price.Statement:

= $569.30(A)(A) (B)(B) $569.30 * 6% GST

$569.30 * 8% PST

= $45.54= $45.54

= $34.16= $34.16$34.16 GST$45.54 PST

$34.16 GST$45.54 PST

$569.30 +

= $649


Basic

Mathematics

Basic

Mathematics

If McDonald’s sales increase from $1,600,000 to $2,400,000, what is the percent change?

% change = Difference Base

Base Method Base Method

$1,600,000

Initial(Base)Value $ 1,600,000Final Value 2,400,000

Difference $ 800,000

% change =$ 800,000

= .5 or 50% Increase

Solving for Rate of Percent Change


Basic

Mathematics

Basic

Mathematics

Consumer Price Index – CPIConsumer 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”)

=CPI *100Price of CPI basket on the selected datePrice of CPI basket on the base date


Basic

Mathematics

Basic

Mathematics Consumer Price Index – CPIConsumer 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?

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 Formula

=CPI *100Price of CPI basket on the selected datePrice of CPI basket on the base date

= 25 98023450 *100

= 110.79= 110.79…Also


Basic

Mathematics

Basic

Mathematics Consumer Price Index – CPIConsumer 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?


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.

Amounts with the same purchasing power will be in the same ratio as the CPIs on the respective dates.

2004 $$2003 $$ = 2004 CPI

2003 CPI

2004 $$ $1000 = 124.8

122.5

$10002004 $$ = 124.8*122.5

= $1018.78$1018.78


Basic

Mathematics

Basic

Mathematics The Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004,

with 1992 as the base year.


with 1992 as the base year.What was the overall percent inflation from

Aug.2003 to Aug.2004?

=Percent inflation 2004 CPI - 2003 CPI2003 CPI *100%

124.8 - 122.5122.5 *100%=

= 1.88%= 1.88%

…Also


Basic

Mathematics

Basic

Mathematics The Consumer Price Index was 122.5 in August 2003, and 124.8 in August 2004,

with 1992 as the base year.


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 2003 Salary

2004 CPI 2003 CPI

=

2004 Salary $50 000

124.8 122.5

=

2004 Salary * $50 000124.8 122.5

=

= $50938.77= $50938.77


Basic

Mathematics

Basic

Mathematics

Exponents Rule of

= 32*4

34 34

Base 3Exponent 4 3i.e. 3*3*3*3

Power = 81= 81

32 *33 32 *33

= 32 + 3

= 3 5

= 243= 243

(1 + i)20 (1 + i)20 (1 + i)8 (32)4(32)4

=(1+ i)20-8

= (1+ i)t= 3 8

= 6561= 6561

MoreMore

Algebra


Basic

Mathematics

Basic

Mathematics

Exponents Rule of

X4

3x6y3 2

x2z3

Simplify inside the brackets first

Simplify inside the brackets first

= 3x4y3 2

z3

Square each termSquare each term

= 32x4*2y3* 2 Z3*2

SimplifySimplify

z69x8y6 =

3x6y3 2

x2z3

Algebra


Basic

Mathematics

Basic

Mathematics

Use Calculator

Exponents Rule of

…to (a) evaluate (1.62)5

…to (b) evaluate (1.62)-5

1.6211.1611.16

1.62 5

0.0896 0.0896

5

Algebra


Basic

Mathematics

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.

SA Wage

= (20.50 +15.00 + 29.00) / 3= $64.50 / 3

= $21.50 = $21.50

= Wages per hour / # different wages

What is the Simple Average of the 3 hourly wages?


Basic

Mathematics

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.

[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 =

WA Wage =

WA Wage = = $20.61 = $20.61

= 70= 70

unit 1 ch 1 3 mathes

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