Chapter.1.Basic Mathematics

8/13/2019 Chapter.1.Basic Mathematics

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Slide 1

2002 McGraw-Hill Australia, PPTs t/a Introductory

Mathematics & Statistics for Business4e by John S. Croucher 1

Introductory Mathematics & Statistics

for Business

4th Edition

John S. Croucher


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Slide 2



Basic mathematics

Learning Objectives Carry out calculations involving whole numbers

Carry out calculations involving fractions Carry out calculations involving decimals

Carry out calculations involving exponents

Use and understand scientific notation

Use and understand logarithms

Chapter M1


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Slide 3



Whole numbers

The decimal system Numerals

symbols i.e. 0, 1, 2, 3

are numerals represent natural numbersor whole numbers

used to count whole objects or fractions of them

Integer is another name for a whole number

Digits

numerals consist of one or more digits


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Slide 4



Mathematical operations

Four basic mathematical operations

performed on numbers

multiplication represented by: x division represented by:

addition represented by: +

subtraction represented by: -


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Slide 5



Rules for mathematical operations

Order of operations:

Multiplication and division

BEFORE

Addition and subtraction


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Multiplication and division

same signs givepositive result

different signs give negative result

perform calculations in brackets first

5

4

201165

&

2

1

6

3&2045

39763


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Slide 7




Addition like signsuse the sign and add

unlike signsuse sign of greater and subtract

SubtractionTwo signs next to each other

minusa minusis aplus

-(-3)=3 minus aplus isaminus-(+3)=-3


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Slide 8



Fractions

A fraction appears as:

Proper fraction

numerator less than denominator

Improper fractionnumerator greater than denominator

atormindeno

numerator

b

a

8

3

7

15


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Slide 9



Addition & subtraction of fractions

Different denominators

change denominatorsto lowest common multiple

LCM (Lowest Common multiple) is the smallestnumber into which all denominators will divide

18

71

18

25

18

1546

6

5

9

2

3

1


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Slide 10



Multiplication & division of fractions

Multiply numeratorsto get new numerator

Multiply denominatorsto get new denominator

Cancel common factors of nominators and

numerators by multiplying


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Slide 11



Decimals

Any fractions can be expressed as a

decimal by dividing the numerator by

the denominator.

A decimal consists of three

components: an integer

a decimal point

another integer.


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Slide 12



Rules for decimals

Addition and subtraction Align the numbers so that the decimal points are

directly underneath each other.

312.4

1.672

34.0

3.2

672.134.03.2 Add


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Slide 13



Rules for decimals

Multiplication and division1. Count the number of digits to the right of each decimal

point for each number.

2. Add the number of digits in Step 1 to obtain a number,say x.

3. Multiply the two original decimals, ignoring decimal

points.

4. Mark the decimal point in the answer to Step 3 so that

there are xdigits to the right of the decimal point.


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Slide 14



Exponents

An exponentorpowerof a number is

written as a superscriptto a number

called the base. Thebase number is said to be in

exponential form.

Exponential form

an where ais the base

where nis the exponent or power


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Slide 15



Rules for exponents

Positive exponents Two numbers with same basean & am

The product will have the same base; the exponent willbe the sum of the two original exponentsanx am= an+m

The quotient of the two numbers will have the same

base; the exponent will be the difference between the

original exponentsan am

=an-m


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Slide 16



Rules for exponents

Positive exponents A number in exponential form is raised to another exponent.

The result is the original base raised to the product of the

exponents. (an)m= anm

Negative exponents A number expressed with a negative exponent is equal to

the reciprocal of the same number with the negative sign

removed.

n

n

a

a

1


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Slide 17



Rules for exponents

Fractional exponents Exponents can be expressed as a fraction

where kis an integer and is said to be the kth root of a

when k=2 it is the square root; k=3 is the cube root

ka

1


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Slide 18



Rules for exponents

Scientific notation Scientific notation is a shorthand way of writing very large

and very small numbers.

Scientific notation expresses the number as a numeral (less

than 10) multiplied by the base number 10 raised to an

exponent.

The reference position for the decimal point in a number is

immediately to the right of the first non-zero digit.


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Slide 19



Logarithms

Logarithms are closely connected to the theory of

exponents.

Calculations using logarithms have been replaced by

calculators since the 1970s. An understanding of logarithms can be useful in

statistics, physics, engineering etc.

The logarithm of a number Nto a base bis the power

to whichb

must be raised to obtainN

.log

bN

That is, if x= logbN, then N= bx

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Chapter.1.Basic Mathematics